Par Maksym LOGINOV - tai teamtai-team.fr/upload/files/These_Maksym_Loginov.pdf · Par Maksym LOGINOV Thèse présentée pour l’obtention du grade de Docteur de l’UTC Soutenue

Par Maksym LOGINOV

Thèse présentée pour l’obtention du grade de Docteur de l’UTC

Preparation of concentrated mineral and bio-suspensions by filtration with alternative pretreatments, and determination of permeability and rheological properties of obtained particulate systems

Soutenue le 12 avril 2011

Spécialité : Génie des Procédés Industriels

D1933

Compiègne University of Technology Institute of Biocolloidal Chemistry of NAS of Ukraine Preparation of concentrated mineral and bio-suspensions by filtration with alternative pretreatments, and determination of permeability and rheological properties of obtained particulate systems by Maksym LOGINOV Directors: prof. Eugene VOROBIEV (Compiègne University of Technology, France), prof. Nikolai LEBOVKA (Institute of Biocolloidal Chemistry, Kiev, Ukraine) and dr. Olivier LARUE (Compiègne University of Technology, France) Defended 12.04.2011 Examining board: Luhui DING (professeur des universités, Compiègne University of Technology, France),

Roger BEN AIM (rapporteur) (professor emeritus, INSA Toulouse, France),

Martine MEIRELES (rapporteur) (dr., directeur de Laboratoire de Génie Chimique, Université Paul Sabatier, Toulouse, France),

Valerii MANK (rapporteur) (professeur des universités, Chemical Faculty, National University of Food Technology, Kiev, Ukraine),

Eugene VOROBIEV (director) (professeur des universités, Compiègne University of Technology, France),

Olivier LARUE (director) (dr., maître de conférences en détachement, Compiègne University of Technology, France),

Nikolai LEBOVKA (director) (professeur des universités, Institute of Biocolloidal Chemistry, Ukraine)

Compiegne 2011

Abstract

Filtration is a mechanical operation used for solid-liquid separation. It is widely employed for preparation of concentrated mineral suspensions and for purification of biological suspensions. The efficiency of filtration is mainly determined by filtration rate, which depends on colloidal properties of initial suspension (size of particles and aggregation state). In order to improve filtration efficiency, initial suspensions are usually pretreated by flocculants. Flocculation decreases concentration of fine particles, enhances aggregation of particles, decreases specific cake resistance, and thus increases filtration rate. However, use of flocculants may also deteriorate required properties of the final suspension and filtrate. For example, flocculation of mineral suspensions results in undesirable decrease of filter-cake dryness and impedes filter cake liquefaction. Flocculation of bio-suspensions may decrease the transmission of valuable products from initial suspension to filtrate and may deteriorate filtrate quality. Consequently, pretreatment of suspension by flocculant may decrease the total efficiency of filtration.

Alternative pretreatment methods were proposed in order to improve filtration efficiency. For example, pretreatment of suspension with a dispersant is used for preparation of concentrated and flowable filter cakes. Pretreatment of bio-suspensions by high pressure homogenization and other disruption methods may be used for making higher the concentration of valuable intracellular components in filtrate. However, such pretreatment may decrease the filtration rate and the total efficiency of filtration due to increase of the membrane fouling or formation of denser filter cake.

Therefore, choice of the optimal pre-treatment method should account both for the filtration rate and the final properties of filtrate and filter cake. This optimisation requires the knowledge of colloidal properties of the feed suspension and dependence of these properties on intensity of various chemical and physical pre-treatments, and it creates a need in the simple method for determination of filterability. It also requires the knowledge of the mechanisms of filtration under various experimental conditions.

This thesis is focused on the influence of different pretreatment methods (use of dispersants, high voltage electrical disruption, and high pressure homogenization) on filtration of mineral (kaolin, calcium carbonate) and biological (yeast) suspensions. It also deals with determination of local compression-permeability properties of concentrated suspensions from the centrifugal settling experiments.

Investigation of the influence of a dispersant on preparation of flowable and concentrated suspension of kaolin has shown that preparation of kaolin suspensions with concentrations above 70 % wt is unreasonable due to low fluidity of the concentrated suspensions. It was concluded that low fluidity of concentrated suspensions is related to morphology (high aspect ratio) of the kaolin particles. Increase of suspension’s concentration results in the percolation of stabilized kaolin particles and in abrupt decrease of fluidity.

It was shown that highly concentrated (> 75 % wt) and flowable suspension of calcium carbonate may be prepared by means of dynamic filtration with addition of sodium polyacrylate. The optimal dryness of suspension obtained by dynamic filtration with delayed addition of a dispersant was higher than the optimal dryness of initially deflocculated suspension after its dynamic filtration.

It was also observed that continuous treatment of yeast suspension by high voltage electric discharges (HVED) may be used for disruption of the cells and extraction of intracellular bio-products. However, it also results in formation of cell debris and decrease of filtration rate due to internal membrane fouling. Comparison of the novel method of HVED-treatment with classical method of high pressure homogenization (HPH) shows that HPH is more effective disruption method than HVED, since it results in higher extraction of proteins and other bio-products at the same value of disintegration index of yeast cells. However, if the value of disintegration index Z is above 0.9, filtration of HPH-disrupted yeast suspension is governed by pore blocking mechanism. It results in very low rates of filtration of the maximally HPH-treated suspensions.

Also, two independent methods for analysis of the experimental dependencies measured during the centrifugal consolidation were proposed. The dependencies of local compression and permeability characteristics versus solid pressure were estimated by these methods for aqueous suspension of calcium carbonate.

Keywords: dead-end filtration, dynamic filtration, centrifugal consolidation, concentrated suspension, kaolin, calcium carbonate, yeast, dispersant, flocculant, high pressure homogenization, high voltage electrical discharges, filter cake dryness and fluidity, specific filtration resistance, membrane fouling, coefficient of consolidation, extraction.

Résumé

Ce travail de thèse est axé sur l’effet de différentes méthodes de prétraitement (utilisation des dispersants, traitement électrique et homogénéisation à haute pression) sur la filtration des suspensions minérales (kaolin, carbonate de calcium) et biologiques (levure). Il traite également de la détermination des propriétés locales de compression-perméabilité de suspensions concentrées à partir d’essais de sédimentation centrifuge.

Une étude est menée sur l’influence de dispersants pour la préparation de suspensions de kaolin concentrées mais demeurant fluide. L’augmentation de la concentration de la suspension provoque une percolation des particules de kaolin stabilisées et une diminution brusque de la fluidité. Cependant, à partir d’une concentration massique de la suspension de 70 %, son caractère fluide devient faible. Cela s’explique par la morphologie des particules de kaolin (haut rapport hauteur/ largeur).

Une suspension de carbonate de calcium très concentrée (> 75 % massique) et fluide peut être préparée par filtration dynamique et addition d’un dispersant : le polyacrylate de sodium. L’étape à laquelle est introduit le polyacrylate de sodium influence la concentration de la suspension. Ainsi, l’ajout du dispersant au cours de la filtration permet d’atteindre une siccité optimale supérieure à celle obtenue si la suspension est défloculée par le dispersant avant filtration.

Une étude porte sur le traitement en continu des suspensions de levures par décharges électriques de haute tension (DEHT). Il est constaté que ce procédé peut être utilisé pour la destruction des cellules et l’extraction des bioproduits intracellulaires. Cependant, il provoque aussi une formation de débris cellulaires et une diminution du taux de filtration due au colmatage des membranes. La comparaison de la nouvelle méthode de DEHT avec celle classique d’homogénéisation à haute pression (HHP) met en évidence que le traitement par HHP est une méthode de destruction plus efficace que le DEHT. Ainsi, pour une même valeur de l’indice de désintégration des cellules de levure (Z), il permet une extraction supérieure des protéines et des autres bioproduits. Pourtant, si la valeur de l’indice de désintégration dépasse 0,9, la filtration de la suspension traitée par HHP est régie par un mécanisme de colmatage des pores, entraînant un très faible taux de filtration.

Enfin, deux méthodes indépendantes d’analyse des dépendances expérimentales obtenues durant la consolidation centrifuge sont développées. Les dépendances des caractéristiques locales de compression et de perméabilité en fonction de la pression de phase solide ont été estimées par ces méthodes pour la suspension aqueuse de carbonate de calcium.

Mots-clés : filtration frontale, filtration dynamique, consolidation centrifuge, suspension concentrée, kaolin,

carbonate de calcium, levure, dispersant, floculant, homogénéisation à haute pression, décharges électriques de haute tension, siccité et fluidité du gâteau de filtration, résistance spécifique du gâteau de filtration, colmatage de la membrane, coefficient de consolidation, extraction.

Table of contents

Introduction 1

I.1. Characterisation of cake formation and consolidation 5

I.2. Dead-end filtration of stabilized mineral suspensions 29

I.3. Dynamic filtration of concentrated mineral suspensions 68

I.4. Filtration of disrupted yeast suspensions 90

I.5. Conclusions from the literature review 105

I.6. Literature cited 106

I.6.1. Literature cited on the subject of Cake filtration and consolidation 106

I.6.2. Literature cited on the subject of Cake filtration of stabilized suspensions 108

I.6.3. Literature cited on the subject of Dynamic filtration 114

I.6.4. Literature cited on the subject of Filtration of disrupted yeast suspension 116

II. Materials and methods 119

II.1. Centrifugal consolidation of calcium carbonate suspensions 119

II.2. Fluidity of highly concentrated kaolin suspensions 121

II.3. Dead-end dynamic filtration of highly concentrated CaCO3 suspensions 126

II.4. Dead-end filtration of Saccharomyces cerevisiae yeast suspensions 130

II.5. Statistical analysis of experimental data 134

III.1 Paper I: “Fluidity of highly concentrated kaolin suspensions” 137

III.2. Paper II: “Dead-end dynamic filtration of highly concentrated CaCO3” 146

III.3 Paper III: “Effect of high voltage electrical discharges on filtration of S. cerevisiae

yeast suspensions”, Paper IV: “Dead-end filtration of S. cerevisiae yeast suspensions:

effects of high-pressure disruption, high-voltage electrical discharges and

flocculation” 160

III.4. Paper V: “Compression-permeability characteristics of mineral sediments evaluated

with analytical photocentrifuge” 176

IV. Concluding remarks and suggestions for future work 189

Introduction

1

Introduction

The introduction describes the challenges existing in the field of filtration and makes

short overview of the objectives of the thesis and its contribution to the field of filtration.

Filtration is a mechanical operation used for solid-liquid separation. It is defined as

separation of particles or soluble solids from a liquid medium on the surface of semi-

permeable membrane. Filtration is employed in many industries: from the paper making and

the mineral industry to the beverage industry and biotechnology.

Various filtration methods (e. g., dead-end filtration, cross-flow microfiltration, dynamic

filtration and ultrafiltration) are created in order to solve different practical problems. For

example, dead-end filtration is commonly used for preparation of concentrated filter cakes

from diluted suspensions; microfiltration is used for purification of different biological

suspensions (purification of fermentation broth, separation of soluble bio-products from the

processed cell suspension). Micro- and ultrafiltration of juices and plant extracts is employed

for separation of colloidal impurities, decrease of turbidity, coloration and concentration of

active components. Dynamic filtration is aimed at avoiding or reducing of the cake formation,

therefore, it is usually employed for filtration of various mineral and biological suspensions

forming low permeable filter cakes.

The effectiveness of filtration is determined by three parameters: the filtration rate, the

quality of filtrate and the quality of the final filter cake or of the concentrate. A number of

methods for the improvement of these parameters exist. They are based on the various

physical and chemical pre-treatments of the filtered suspensions.

Filtration rate may be improved by pre-treatment of suspension with a flocculant, which

enhances the attraction between the particles and increases the particle size. Dynamic

filtration may be improved by pre-treatment of suspension with a dispersant, decreases the

attraction of particles and facilitates the filter cake erosion.

Pre-treatment of suspension by a dispersant may be needed if the filter cake with high

dryness and high fluidity is required.

Treatment with a flocculant is also used in order to decrease the turbidity and increase the

filtrate quality in the microfiltration of biological suspensions.

Different physical (high pressure homogenisation, high voltage electrical discharges) and

chemical (enzymatic treatment) methods were proposed for improvement of the extraction of

bio-products from microbial cells (e.g., yeast cells) and, thus, for improvement of the filtrate

quality (concentration of intercellular bio-products) during the membrane-assisted extraction.

Introduction

2

In should be noted that the main parameters determining the filtration efficiency are

interdependent. Both filtration rate and the final product quality depend on the colloidal

properties and chemical composition of the filtered suspension (particles size, shape, surface

charge and aggregation state, concentration of particles, concentration of polymeric

molecules, etc.). For example, filtration rate is frequently limited due to membrane fouling

and formation of low-permeable deposit of fine particles on the membrane surface (during the

dead-end filtration of non-flocculated mineral suspensions). The negative impact of

membrane fouling and deposit formation on the filtration rate may be reduced by means of

chemical pre-treatment of feed suspension (flocculation). However, the feed suspension pre-

treatment with a flocculant may influence negatively on the filter cake properties (decrease

the final dryness and reduce the viscosity of the liquefied filter cake) and may contaminate the

filtrate. Therefore, choice of the optimal method of pre-treatment should account for its

influence on each factor, determining the filtration efficiency.

Optimisation of the total filtration process requires knowledge of colloidal properties of

the feed suspension, dependence of these properties on intensity of various chemical and

physical pre-treatments, and creates a need in a simple method for determination of

compression-permeability properties (cake resistance and solidosity). It also requires

knowledge of filtration mechanism under various experimental conditions (operational

parameters and colloidal properties of the suspension).

The influence of various physical and chemical factors on filtration was studied

intensively, and many methods for determination of filtration properties were developed.

However, some filtration-related problems remain unsolved. Here, determination of local

compression-permeability properties from the centrifugal settling experiments, preparation of

highly concentrated and flowable mineral filter cakes, and determination of the optimal pre-

treatment method for the filtration-assisted extraction of intercellular components of yeast can

be mentioned. These problems are discussed in the present thesis.

This thesis consists of four chapters. The Chapter I (Literature review) summarises the

theories of filtration (dead-end filtration, dynamic filtration and membrane fouling). It is

divided in four sections.

Section I.1 of the literature review discusses the method developed for determination of

the local compression-permeability properties of filter cakes.

Section I.2 of the literature review contains discussion of the dead-end filtration of a

deflocculated mineral suspension. The section considers different factors impacting the

permeability, dryness and viscosity of mineral filter-cakes (size and shape of mineral

Introduction

3

particles, their surface properties, presence of various chemical additives, and concentration

of suspension). Special attention is paid to the kaolin suspensions and to the influence of a

dispersant (polyacrylic acid) on their colloidal, structural and filtration properties.

Section I.3 of the literature review is devoted to dynamic filtration of mineral

suspensions. It discusses advantages of cake removal during filtration of concentrated and

deflocculated mineral suspensions. A review of dynamic filtration models and various effects

related to deposit formation during dynamic filtration is presented together with discussion of

the possibilities to reduce the deposit formation. Special attention is paid to dynamic filtration

of calcium carbonate suspensions and possibility of preparation of highly concentrated

calcium carbonate suspension by means of dynamic filtration in the presence of a dispersant.

Section I.4 deals with peculiarities of filtration of complex bio-suspensions (mixture of

cells, cell debris and bio-molecules). It starts with an overview of the membrane fouling

mechanisms and the methods that are used for flux analysis and determination of the fouling

mechanism. The causes of membrane fouling during filtration of bio-suspensions and

available methods of avoiding the fouling are discussed.

Chapter II describes materials and methods used in this study.

Chapter III of the thesis is based on the results of five papers devoted to filtration of the

chemically and physically pre-treated mineral and biological suspensions and to

determination of filtration-consolidation properties of mineral suspensions from

centrifugation experiments.

Paper I is devoted to the dead-end filtration of kaolin suspension in the presence of a

dispersant. It deals with an important challenge in mineral industry: preparation of highly

concentrated mineral suspensions with low viscosity. Influence of dispersant addition and

particle concentration on viscosity and filterability of kaolin suspension was studied and

relation between colloidal properties of kaolin particles, structural properties of kaolin

suspensions and structure of the filter-cake is discussed in this paper. The aim of this work is

to provide better understanding of the properties of highly concentrated suspensions and to

study the limiting effects, which prevent these suspensions from dewatering by filtration.

Paper II proposes an alternative way for preparation of concentrated mineral suspensions

with low viscosity. It presents the results of a lab-scale study of dynamic filtration of calcium

carbonate suspension in the presence of polyacrylic acid. Influence of operational parameters

(filtration pressure and shear rate) and dispersant concentration on effectiveness of filtration is

discussed.

Introduction

4

In Papers III and IV, the study of filtration of disrupted yeast suspensions is reported.

The aim of this study is to define conditions of filtration and method of disruption allowing

maximisation of the filtration rate and preservation of the quality of filtrated extracts. The

papers compare the influence of two methods of yeast disruption (mechanical homogenisation

and electrical treatment) on the filtration efficiency, mechanism of membrane fouling, and the

filtrate quality. The impact of flocculation of disrupted yeast suspension on filtration is also

discussed.

Paper V presents two independent methods for estimation of compression-permeability

properties of mineral suspensions (local specific filtration resistance and local consolidation

coefficient). The first method is based on analysis of ultimate compression at various

centrifugal speeds. The second method is based on analysis of kinetics of centrifugal

consolidation of the studied suspension.

The Chapter IV summarizes conclusions of the discussed papers and presents some

suggestions for further work.

I. Literature review 5

Notation for Section I.1 ..................................................................................................... 6

I.1. Characterisation of cake formation and consolidation ........................................... 8

I.1.1. Basic equations of cake filtration ............................................................................ 8

I.1.2. Pressure dependence of the filtration parameters. Constitutive equations ...... 10

I.1.3. Theoretical models of permeability ...................................................................... 11

I.1.4. Integration of the basic equations of cake filtration ........................................... 12

I.1.5. Consolidation of a filter cake ................................................................................ 14

I.1.6. Alternative formulation of filtration-consolidation problem ............................. 18

I.1.7. Determination of local compression-permeability properties ............................ 20

I.1.7.1. Compression-permeability cell .......................................................................... 20

I.1.7.2. Dead-end filtration .............................................................................................. 22

I.1.7.3. Gravity and centrifugal sedimentation and consolidation .............................. 24

I.1.8. Summary ................................................................................................................. 28

I.1. Cake filtration and consolidation of mineral suspensions 6

Notation for Section I.1

a particle size [m]

A membrane surface area [m2]

B parameter of Eq. (I.35)

cc solid weight fraction of filter cake [–]

Ce average consolidation coefficient [m2/s]

cs solid weight fraction of suspension [–]

D solid diffusivity [m2/s]

e void ratio [–]

Ei rigidity of the “spring”

f parameter defined by Eq. (I.41)

H height of the consolidate [m]

k permeability [m2]

k’ Kozeny constant

ko parameter of constitutive equation

L cake thickness, height of the sediment [m]

n parameter of constitutive equation

pa parameter of constitutive equation

pk parameter of constitutive equation

pl liquid pressure [Pa]

pn parameter of constitutive equation

ps solid pressure [Pa]

Δp filtration pressure [Pa]

Py compressive yield stress [Pa]

ql superficial liquid velocity [m/s]

qs superficial solid velocity [m/s]

R radial distance from the axis of rotation to the bottom of the sediment [m]

r(φ) hindered settling function [–]

Rm membrane resistance [m–1]

So specific surface area of particles [m2/m3]

t time [s]

U average consolidation ratio [–]

u settling velocity [m/s]


V volume of filtrate [m]

x distance [m]

Greek letters

α specific cake resistance [m/kg]

αav average specific cake resistance [m/kg]

αo parameter of constitutive equation

β parameter of constitutive equation

β parameter of Eq. (I.35)

β slope of the filtration curve presented in t versus (V/A)2 coordinates

δ parameter of constitutive equation

ε porosity [–]

η parameter of Eq. (I.35)

Θ viscosity of the “dashpot”

μ liquid viscosity [Pas]

ρl density of liquid [kg/m3]

ρs density of solid [kg/m3]

υ parameter of Eq. (I.37)

φ solidosity, solid volume fraction [–]

φg concentration of structure formation [–]

φo parameter of constitutive equation

ω material coordinate [m]

Ω centrifugal rotation speed [rad/s]

ωo total height of solids [m]


I.1. Characterisation of cake formation and consolidation

I.1.1. Basic equations of cake filtration

When solid particles of suspension are larger than the pore size of the filter medium, they

form a deposit known as filter cake. Filtration is then called cake filtration or dead-end

filtration (if the suspension flow is perpendicular to the filter surface). Filter cake may be

considered as a solid packed bed made up of contacting particles and interparticle pores where

interstitial liquid may flow (Fig. I.1.a).

filter medium

filter cake

suspension

L, ωo

(a) (b)

L

Δpps

pl

distance from the filter medium

pres

sure

ql

qs

Fig. I.1. Schema of a filter-cake (a), pressure distribution in a filter cake (b).

Driving force of filtration is the pressure difference between filtered suspension and filter

medium Δp.

In conventional theory of cake filtration, the process of cake formation is described by the

next set of equations [Vorobiev, 2006; Lee and Wang, 2000; Olivier et al., 2007; Wakeman

and Tarleton, 1999]:

material balance equations for liquid and particles, relating the superficial liquid (ql) and

solid (qs) velocities with local porosity (ε) and local solid volume fraction (φ)

∂ql/∂x = ∂ε/∂t (I.1)

∂qs/∂x = ∂φ/∂t (I.2)

where t is the time and x is the distance.

force balance equation, relating liquid pressure pl with solid pressure ps:

∂pl/∂x + ∂ps/∂x = 0 (I.3)

Liquid pressure pl presents the local hydraulic pressure in the pores: the value of pl is maximal

at the suspension-cake interface and decreases to zero at the membrane surface (Fig. I.1.b).


Solid pressure ps presents the cumulative drag force acting on the particles. During the

filtration, the drag force appears due to the friction between the flowing interstitial liquid and

the particles. The solid pressure builds up from particle to particle: it changes from 0 on the

surface of the filter cake to Δp on the membrane surface (Fig. I.1.b). At the same time, the

value of liquid pressure pl decreases from Δp to 0 due to the friction (Fig. I.1.b).

Darcy’s equation, relating pressure drop in the porous medium dpl/dx with the interstitial

liquid velocity:

dpl/dx = – μ ε(ul – us)/k (I.4)

where ul – us is the relative velocity of the interstitial liquid, ul = ql/ε, us = qs/φ, μ is the

viscosity, k is the permeability (in m2). For incompressible solids, us = 0.

Eq. (I.4) may be presented using the material coordinate ω:

dpl/dω = – αμ ερs(ul – us) (I.5)

where ω is the height of solid (ω = φx), α is the local specific resistance of the filter cake

(α = 1/(kφρs)), ρs is the density of the solid.

Darcy’s law is valid only for a laminar flow, which is characterised by a low Reynolds

number Re ≤ 1–10. For a packed bed, the Reynolds number is

Re = aρl(ul – us)/(μ ε) (I.6)

where l is the density of liquid, a is the particle size. In practice, a typical particle size in a

colloidal mineral suspension is 1 m. The porosity of a filter cake is normally close to 0.5 and

the volume flow rate during filtration is within 10–1000 lm–2h–1. Therefore, Reynolds

number characterising filtration through the filter cake is low enough (Re 10–3) and Darcy’s

law can describe the filtration of colloidal mineral suspensions.

Complete description of filtration process may be done on the basis of Eqs. (I.1–I.5). If we

assume that ul >> us and the liquid velocity ql is constant across the filter cake, then

integration of Eqs. (I.4) and (I.5) with consideration of Eq. (I.3) yields

0

d1

psl pkLq

(I.7)

0

o d11

ps

sl pq

(I.8)


where L is the cake thickness, and ωo is the total height of solids in the cake. Further

integration of Eqs. (I.7)–(I.8) requires information about the pressure dependence of the

parameters k and α.

I.1.2. Pressure dependence of the filtration parameters. Constitutive equations

All suspensions and filter cakes are compressible to a greater or lesser extent: application

of the pressure results in their compaction (increase of the solid concentration, decrease of the

permeability). Dependence of solid volume fraction on compression stress (solid stress, ps) is

frequently presented in the form of empirical constitutive equation [Tiller and Leu, 1980]

φ = φo(1+ps/pa)β (I.9)

where φo, β and pa are empirical constitutive parameters. Other empirical equations for

pressure dependence of solidosity may be found in the literature [Tiller, 1955; Murase et al.,

1980]:

φ = φo at ps < ps, min

φ = φ1(ps)β at ps > ps, min

(I.10.a)

(I.10.b)

(1-φ)/φ = φ2 – φ3 ln(ps) (I.11)

where φi are empirical constants.

Pressure dependence of other filtration parameters (k and α) also may be presented in the

form of power-law equations [Tiller and Leu, 1980; Tiller and Yeh, 1987]

k = ko(1+ps/pk)–δ (I.12)

α = αo(1+ps/pn)n (I.13)

where ko, αo, δ and n are empirical constants. More constitutive equations may be found in the

literature [Olivier et al., 2007; Vorobiev, 2006]. The values of constitutive parameters may be

calculated by fitting of the experimental pressure dependencies φ(ps), k(ps) and α(ps) using

Eqs. (I.9)–(I.11), (I.12), and (I.13). However, experimental determination of the local values

of solid pressure, solidosity and permeability is a difficult task (especially in a wide range of

pressure). Frequently, fitting of the experimentally measured average values of φ and α

plotted versus filtration pressure Δp by the constitutive equations are used for determination

of β and n and for evaluation of the level of compressibility.


I.1.3. Theoretical models of permeability

Two theoretical models are frequently used for prediction of the permeability of filter

cake: Kozeny-Carman’s model and Happel’s model [Happel and Brenner, 1965]. These

models relate the permeability with measurable properties of the filter cake: specific particle

surface area, particle shape, and solid volume fraction.

According to Kozeny-Carman’s approach, the liquid flow in pores of a filter cake is

equivalent to the laminar liquid flow in a cylinder with the hydraulic radius r equal to

r = ε/(Soφ) (I.14)

where So is the specific surface area of particles (in m2/m3).

Thus, Kozeny-Carman’s equation for the permeability of filter-cake is expressed as

22o

3

Sk

k

(I.15)

and the specific cake resistance is expressed as

s

Sk

3

2o (I.16)

where k’ is the empirical Kozeny constant, which depends on the shape and size of particles

and tortuosity of pores. For regular-shaped particles (spherical, elliptical, cubic), k’ usually

equals to 4–5. For irregular particles the value of k’ increases with the increase of the particle

anisotropy. Therefore, in general case the value of k’ is determined experimentally from the

data on filter cakes permeability.

Happel and Brenner [1965] calculated the filter cake permeability in the framework of the

cell model. According to this model, the filter cake permeability is equal to the integral

permeability of a number of regularly packed “cells” consisting of a particle and surrounding

liquid layer. The particle to the cell volume ratio corresponds to the volume fraction of

particles in the filter cake. For spherical particles, the permeability is equal to

)23(

699613/5

23/53/1

2o

Sk . (I.17)

and the specific resistance is equal to

23/53/1

3/52o

6996

23

s

S. (I.18)


Once pressure dependence of the solid volume fraction φ = φ(ps) is experimentally

measured, it may be used for calculation of the local permeability k = k(φ(ps)) and the local

specific resistance α = α(φ(ps)) using Eqs. (I.15–I.18). However, Eqs. (I.15–I.18) should be

used with a caution for description of real filtration: Kozeny’s equation is valid only for

concentrated filter cakes, while Happel’s equation was deduced for the case of monodisperse

system of regularly packed non-contacting spherical particles.

I.1.4. Integration of the basic equations of cake filtration

If pressure dependence of the local permeability and local specific resistance is defined

(e.g., by Eqs. (I.12–I.13)), integration of the basic equations of cake filtration (I.7–I.8) yields

0

o d)/1(1

psnsl pppkLq

=

p

pp

ppk

n

n

/)1(

1)/1( 1

o (I.19)

and

0

oo d

)/1(

11

psn

assl p

ppq

=

sn

n

n p

pp

ppn

1

1o 1)/1(

/)1( (I.20)

The bracketed expression in Eq. (I.19) equals to the average permeability kav, and the

bracketed expression in Eq. (I.20) corresponds to the average specific resistance of the filter

cake αav. Average value of the solidosity may be calculated from Eqs. (I.4) and (I.9) as

savavp

s

s

p

p

sl

s

p

s

p

sl

L

av kxk

p

xq

pp

Lqx

L

1

d

d1

d

d1

d11

d1

0

0

0

0

00

(I.21)

Using Eq. (I.20) one may obtain general equation describing the filter cake formation:

p

qtA

V

savl

o

1

d

d (I.22)

where V is the filtrate volume, t is the filtration time, A is the area of the filter medium.

Essentially, Eq. (I.22) is a Darcy’s equation with the specified value of the pressure-

dependent filter cake specific resistance. Resistance of the filter medium Rm may be

introduced and Eq. (I.22) may be rewritten as

p

RtA

V

msav

)(

1

d

d

o

(I.23)


where Rm = 1

d

d

tA

V

p

is constant.

The value of ωo may be determined from the volume of filtrate as

savcs

l

Acc

V

)( 1

,1o

(I.24)

where cs is the solid weight fraction in the filtered suspension, cc, av is the average solid weight

fraction of the filter cake. The value of cc, av may be calculated as

1, 1/)1/1( slavavcc . (I.25)

Substitution of Eq. (I.24) in Eq. (I.23) with subsequent integration of Eq. (I.23) over the

filtration time and filtrate volume yields classical equation of cake filtration (Ruth-Carman

equation):

pA

RVV

ccpAVV

tt m

avcs

avl

)(

)(2 o1,

12o

o (I.26)

where to and Vo are the time and volume of filtrate corresponding to the initial point of

integreation, , respectively.

Eq. (I.26) is commonly used for description of a dead-end filtration and determination of

αav. Once several values of αav are measured at various filtration pressures Δp, the constitutive

parameters for the local specific resistance may be determined. Though Eq. (I.26) was derived

for description of the filter cakes with the pressure dependent αav, it is not appropriate for

analysis of filtration with formation of highly compressible filter cakes. It was assumed

during derivation of Eq. (I.26) that the solid velocity is negligible (qs = 0), the liquid velocity

is constant through the filter cake (∂ql/∂x = 0), the pressure drop across the cake is constant

and the pressure drop across the filter medium is neglected (Δp = const). These assumptions

are not valid for filtration with formation of highly compressible filter cakes. More rigorous

analysis of cake filtration incorporating the effect of variable liquid velocity may be found in

the literature [Stamatakis and Tien, 1991; Lee et al., 2000]. The effect of filtration pressure

redistribution between the filter cake and filter medium on filtration was analyzed in

[Vorobiev, 2006]. The process of filter cake consolidation was thoroughly studied in the

literature, and it is discussed in the next Section.


I.1.5. Consolidation of a filter cake

Since solid content in a filter cake is constant during the cake consolidation, the material

coordinates are preferred for description of this process. The material balance equation in

terms of material coordinates is presented as [Shirato et al., 1970a]

)( sl eqq

t

e (I.27)

where e is the void ratio (e = ε/φ), ω is the material coordinate.

Introduction of Eq. (I.27) in Darcy equation yields the consolidation equation

s

s

p

t

e 1. (I.28)

Eq. (I.28) may be solved if rheological properties of the filter cake (linear elastic, linear

visco-elastic, non-linear elastic or visco-elastic) are defined.

When filter cake is assumed to behave as an elastic body (if the cake solidosity is a unique

function of solid pressure), left part of Eq. (I.28) may be presented as

t

p

p

e

t

e s

s

. (I.29)

Introduction of Eq. (I.29) in Eq. (I.28) yields consolidation equation for elastic bodies

s

ss

s p

pet

p 1

/

1. (I.30)

Eq. (I.30) contains the pressure dependent parameters α and ∂e/∂t, which may vary

significantly during the consolidation. In spite of this fact, Eq. (I.31) is frequently presented in

the simplified form

2

2

2

2

)/(

1

s

es

ss

s pC

p

pet

p. (I.31)

where Ce is the modified coefficient of consolidation [Shirato et al., 1970b]. It was stated by

Shirato that “since Ce changes throughout the consolidated cake and with consolidation time,

Eq. [I.31] may be used as an approximation with a proper mean value of Ce considered

constant during the whole consolidation period” [Shirato et al., 1970b]. If the constancy of Ce

is assumed and initial and boundary conditions are defined, Eq. (I.31) may be solved

analytically, and the time dependencies of solid pressure and porosity distribution in the filter

cake may be calculated. For the conditions of filter cake consolidation, solution of Eq. (I.31)

gives


t

Ci

iU e

i2o

22

122 4

)12(exp

)12(

81

(I.32)

where U is the average consolidation ratio defined as a relative change of the filter cake

height during the consolidation

)/())(( oo HHtHHU (I.33)

where H(t) is the filter cake height measured at consolidation time t, Ho and H∞ are measured

at t = 0 and t = ∞, respectively. Fitting of the experimentally measured curve U = U(t) by

Eq. (I.32) may be used for determination of the value of Ce.

When filter cake is assumed to behave as a visco-elastic body (the cake solidosity depends

both on the consolidation pressure and consolidation time), Eq. (I.30) is substituted by

s

s

s

s

p

t

e

t

p

p

e 1. (I.34)

The second term of the left part of Eq. (I.34) presents the rate of consolidation due to the

creep effect. Consolidation equation will depend on the model used to describe the filter cake.

Shirato [Shirato et al., 1974] modeled the filter cake as a Terzaghi and Voigt elements

connected in series (Fig. I.2).

E

Θ

ps ps

E0

Fig. I.2. Combined Terzaghi-Voigt model of

a linear visco-elastic filter cake [Shirato et

al., 1974]: E0 – the rigidity of Terzaghi

element, E – the rigidity of Voigt element,

Θ – the viscosity of Voigt element.

Shirato et al. [1974] assumed that the values of Ce, E and Θ remain constant during the

consolidation (i.e., mean values of Ce, E and Θ are not pressure dependent) and provided the

analytical solution of their model. They showed that if the rate of consolidation related to the

deformation of Terzaghi’s element (elastic consolidation) is much higher then the rate of

consolidation related to the deformation of Voigt element (creep), then the overall

consolidation process may be divided in two stages: primary consolidation and secondary

consolidation. Then, average consolidation ratio is presented as

tBtCi

iBU

i

e

exp1

4

)12(exp

)12(

81)1(

12o

22

22 (I.35)


where η = E/Θ, B = β/(1 + β),1

d

d

1

1

sp

e

e (B is the creep constant, representing the

fraction of the secondary consolidation). The first term of the right part of Eq. (I.35)

represents deformation related to the elastic (primary) consolidation, and the second term

represents the creep.

Eq. (I.32) and (I.35) were derived using the questionable assumption about the constancy

of filter cake properties during the consolidation. However, these equations are widely

employed due to their simplicity. Eq. (I.32) is well fitted by empirical equation proposed by

Sivaram and Swamee (cited in [Shirato et al., 1979])

8.2/5.08.22

o

5.02o

)4/(41

)4/(4

tC

tCU

e

e

. (I.36)

Eq. (I.37) was extended by Shirato [Shirato et al., 1979; Shirato et al., 1980] in order to

include the creep behaviour. Next empirical equation was proposed for simplified analysis of

the consolidation

vv

e

e

tC

tCU

/5.02o

5.02o

)4/(41

)4/(4

(I.37)

where v is the, so-called, consolidation behaviour index. Fitting of the experimentally

measured consolidation curve U = U(t) by Eq. (I.37) and determination of the consolidation

behaviour index v may be useful for evaluation of the secondary consolidation. If the

secondary consolidation is negligible, v is equal to 2.85. The lower is the value of v, the

higher is the influence of creep on the overall consolidation process. Though this approach is

useful for analysis of consolidation of sludge and other complex materials [Shirato et al.,

1980; Grimi et al., 2010], it does not elucidate the details of consolidation and can not be

related to the microscopic processes of filter cake deformation.

Recently, Iritani et al. [2010] proposed more complex model of consolidation (similar to

the model proposed by Lanoiselle et al. [1996]). In order to describe the complex creep

behaviour, the cake was modeled by a number of Voigt elements connected in series

(Fig. I.3).


E1

Θ1

ps ps

E2

Θ2

…

EK

ΘK

E0

Fig. I.3. The model of a visco-elastic filter cake employed in [Iritani et al., 2010]. Each of K Voigt elements is characterised by its value of EK and ΘK.

According to this model, the consolidation ratio is presented as

)exp(14

)12(exp

)12(

811

112o

22

221

tBtCi

iBU N

K

NN

i

eK

NN

.

(I.38)

The model of Iritani is linear: it assumes that the values of Ce, BN and ηN remain constant

during the consolidation. Therefore, utilization of this model for analysis of consolidation of

highly compressible materials is not justified. However, Iritani’s model is more useful then

the model of Shirato: each pair of BN and ηN values may be attributed to a certain

phenomenon of structure deformation during the consolidation (e.g., deformation of flocs,

orientation of particles, loss of the bounded water).

In the general case, a non-linear model with pressure dependent parameters is required for

the correct description of consolidation process. Usually, it is impossible to obtain analytical

solution of the consolidation equation with variable coefficients of consolidation. A non-

linear consolidation equation is to be solved numerically.

Shirato et al solved numerically the consolidation equation for Terzaghi’s model with

variable consolidation coefficient C(ps) for the case of gravity settling [Shirato et al, 1970a]

and filtration followed by consolidation [Shirato et al 1971] . The solution was obtained using

the experimentally determined values of local compression-permeability characteristics

(liquid pressure distribution, solid volume fraction and permeability). It was shown that the

local values of C increase significantly during the consolidation. The calculated consolidation

curves perfectly coincided with the experimentally measured curves. Some deviation between

the calculated and experimental data was observed only at the final stage of consolidation

(U > 0.9), probably, due to the neglected effect of creep.

La Heij [La Heij, 1994; La Heij et al., 1995] solved numerically the consolidation

equation for the material with non-linear visco-elastic behaviour. Standard solid model

(Fig. I.4) was used for description of material properties.


E1E1

Θ

psps

E0

Fig. I.4. Standard solid model used in [La

Heij, 1994] to describe the sludge

consolidation.

The standard solid model is more suitable for simulation than the model of Shirato presented

in Fig. I.2, because at the end of consolidation the stress is applied only to the spring E0 and

elastic modulus E0 can be simply determined from the equilibrium values of porosity [La Heij

et al, 1995]. It was shown that the proposed model is much more acceptable for description of

filtration and consolidation of highly compressible materials.

I.1.6. Alternative formulation of filtration-consolidation problem

The alternative approach to the modeling of filtration and consolidation processes was

elaborated by the scientific group from University of Melbourne [Buscall and White, 1987;

Green et al, 1996; Landman and White, 1997; Green et al., 1998; Landman et al., 1999;

Stickland et al., 2005]. This approach is based on the conceptions of the compressive yield

stress Py(φ), the hindered settling function of solids r(φ), and the filtration diffusivity D(φ).

Determination of Py(φ) is equivalent to determination of ps(φ): Py(φ) is the maximum

stress of solids that may be applied to the suspension at a certain value of φ. As soon as the

applied stress exceeds Py(φ), the consolidation begins and φ starts to increase.

The hindered settling function r(φ) accounts for the hydrodynamic interactions between

the particles in the consolidating suspension. It is defined by the following equation [Green et

al., 1998]

2o )1()(/)( uur (I.39)

where u(φ) is the settling (or compaction) velocity, uo is the settling velocity of the individual

particle in diluted suspension. Hindered settling function is an inverse function of the

permeability [Olivier et al., 2007]:

)1(

)()(

rf

k (I.40)

where f is the constant related to the particle size and shape

pVf / . (I.41)


Here λ is the Stokes drag coefficient (for spherical particles λ = 6πμrp), rp is the particle

radius, Vp is the volume of a single particle. The value of r(φ) may be determined, for

example, from the dead-end filtration experiment [de Kretser et al., 2001]

2

o2

)1(11

d

2)(

pdrf (I.42)

where φ∞ is the equilibrium volume fraction at the compaction pressure Δp, φo is the volume

fraction of the filtered suspension, β2 is determined as the slope of the filtration curve V = V(t)

presented in the coordinates t vs (V/A)2.

The filtration diffusivity D(φ) is defined as [Landman et al., 1999]

)(

d)(d)1()( 2

rf

PD y

(I.43)

D is the main parameter of the filtration-consolidation equation formulated by Landman and

White [1997]

t

L

xD

xt d

d)(

(I.44)

Eq. (I.44) is similar to Eq. (I.30), and the meaning of D(φ) is directly related to the

consolidation coefficient Ce.

Parameters Py(φ), r(φ) and D(φ) depends on the material properties and on the solid

volume fraction of suspension or filter cake (Fig. I.5).

Fig. I.5. Dependencies of Py(φ), r(φ), and D(φ) on volume fraction of particles (φg is the

concentration of structure formation) (from [Landman and White, 1997]).

Similarly to the basic filtration equation discussed in the Section I.1.1, solution of Eq. (I.44)

requires information about the constitutive equations for D(φ), r(φ) and Py(φ). These


constitutive equations are usually presented as power functions of φ and (1 - φ) [Olivier et al.,

2007; Stickland et al., 2005], e.g.:

g

pg

gy p

P

1)/(

0)(

21

(I.45)

2)1()( 1rrr (I.46)

g

ddg

dD

32 )1(

0)(

1

(I.47)

where pi, ri and di are parameters.

Determination of parameters of the constitutive Eqs. (I.45)-(I.47) (or, in other words,

determination of the local values of D(φ), r(φ), Py(φ)) as well as determination of the

parameters of constitutive Eqs.(I.9)–(I.13) (determination of the local values of ps, k, α, and

Ce) is an important problem of filtration-consolidation theory. Once the parameters are

determined, filtration or consolidation may be modelled using Eq. (I.30) or Eq. (I.44). Various

experimental methods elaborated for determination of the local properties of cakes and

suspensions are reviewed in the next Section.

I.1.7. Determination of local compression-permeability properties

Many methods were proposed for determination of the local properties of cakes and

suspensions. These methods are based on various experimental techniques available for the

measurement of compression and permeability. Three most commonly used techniques

(compression-permeability, dead-end filtration, gravity/centrifugal consolidation) are

discussed below.

I.1.7.1. Compression-permeability cell

The compression-permeability cell (CP) is sketched in Fig. I.6.

piston

cell

filter cake

filter medium

liquid outlet

liquid inlet

Fig. I.6. Schema of the compression-

permeability cell.


According to this technique, suspension is placed into the cell and uniform filter cake

forms under the constant pressure created by the piston. The piston is equipped with a

pressure sensor and displacement meter, therefore, the consolidating pressure and the height

of the filter cake may be measured continuously during the consolidation. Once filter cake is

formed (equilibrium height of the cake compressed at the certain constant pressure is

reached), the liquid flows through the cake under the fixed pressure. In this way, solidosity

and permeability of the filter cake at the certain pressure are determined. Then, increased load

is applied to the piston and new values of the solidosity and the permeability, corresponding

to the new value of compressive pressure, are determined. After the series of such

measurements, dependences of the local solidosity and local permeability (or specific

resistance) on solid compressive pressure is obtained [Teoh et al., 2002]. Then, appropriate

constitutive equations may be chosen for fitting of these dependencies [Sedin, 2003;

Johansson, 2005].

If initial concentration of the studied suspension is high enough, then consolidation occurs

from the very beginning of the CP experiment. In this case, filtration stage is practically

absent and the mean values of Ce, B, η, and υ parameters at various compressive pressures

may be estimated from the consolidation curves U = U(t) [Shirato et al., 1974; Shirato et al.,

1978; Grimi et al., 2010; Iritani et al., 2010].

If initial suspension is diluted below the structure formation concentration, filtration stage

followed by the consolidation stage occurs. The method of analysis of the experimental data

(height of the sample versus time curves) depends on the used filtration model. For example,

Wakeman et al. [1991] analyzed the filtration using the Ruth-Carman equation and

determined dependence of the average specific filtration resistance on the applied pressure

α = α(Δp). Teoh et al. [2001; 2002] showed that the local values of specific filtration

resistance, estimated for the CP measurements, were in a good correspondence to the values

estimated from the dead-end filtration experiments using Eq. (I.20). More recently they

proposed a new method for determination of the pressure dependence of the average specific

filtration resistance from a single filtration experiment [Teoh et al., 2006a]. According to this

method, instantaneous average of the specific resistance of the cake αav is determined from the

instantaneous value of filtration velocity

)1/(

)dd(

d

d1

1

savslav

m

cmcVA

tVARp

tA

V

(I.48)


where mav is the instantaneous value of the average wet-to-dry cake mass ratio, which is

expressed as

avsavlavm )1(1 (I.49)

Here, φav is the instantaneous average value of the filter cake solidosity. Teoh et al. [2006a]

determined φav from the value of the cake height L

)()( 1 LcLcLLVAc ssslsslav (I.50)

The filter cake height L(t) may be experimentally measured using the set of the pressure

sensors built-in into the CP cell wall [Murase et al., 1989a; Teoh et al., 2006a]. The authors

[Teoh et al., 2006a; Teoh et al., 2006b] noticed that the values of αa measured by this method

are close to the values estimated from the measurement of the permeability of compressed

filter cakes.

I.1.7.2. Dead-end filtration

The main advantage of the dead-end filtration compared to the CP experiment is

simplicity of the used experimental installation. A common dead-end filtration cell does not

comprise the piston with the system for a liquid flow (Fig. I.7.a). However, it may be

equipped with the pressure probes (Fig. I.7.b), special insertions used for decreasing the

filtration surface (Fig. I.7.c), and floating pistons* protecting the filter cake from cracking

during the compression stage (Fig. I.7.d).

filtrateoutlet

filtercake

suspension

suspension inlet(a)

pressuresensors

(b)

diskwith hole

(c)

floatingdisk

(d)

Fig. I.7. Various types of the dead-end filtration cells.

In the dead-end filtration, the local and average filtration characteristics of the filter cakes

are determined from analysis of the filtration curves V = V(t). Several methods of filtration

* Shirato et al. [1985; 1986] proposed to cover the cake surface with thin layer of bentonite slurry in order to protect the cake and avoid the friction between the piston and filter cell wall.


curves analysis were discussed above. Recently, Iritani et al. [2011] developed a new method

for determining the pressure dependence of the average specific cake resistance based on a

single dead-end filtration with a filtration medium having high hydraulic resistance. This

method is based on the fact that the average specific resistance of the filter cake αav varies

with time even during the constant pressure filtration because of the pressure drop variation

across the filter cake. The pressure variation period of filtration is longer when the filter

medium resistance is high compared to the cake resistance. The value of αav is calculated from

the following set of equations:

ncav p )(o (I.51)

m

n

m

nsl V

tV

V

t

V

t

V

tpc

V

t

**

***1

o* d

d

d

d

d

d

d

d)(

d

d (I.52)

*** d

d

d

d

d

d

V

t

V

t

V

tpp

mc (I.53)

Here, V* = V/A, Δpc is the pressure drop across the filter cake, (dt/dV*)m is the reciprocal

filtration rate in the absence of the cake. The method of Iritani et al. [2011] is more

advantageous as compared to the method of Teoh et al. [2006a], since it does not require

information about the filter cake thickness and the experiments may be carried out in a simple

filtration cell described in Fig. I.7.a. However, Eq. (I.52) is valid only for the filtration of

diluted suspensions (with cs << 1).

Murase et al. [1987] designed a dead-end filtration installation with a holed disk inserted

in the filter cell (Fig. I.7.c). The disk serves for filter cake height L determination during the

filtration. Once filter cake grows on the underside of the disk, filtration rate steeply decreases

due to the steep decrease of the filtration area. Using such filtration cell, one can calculate the

αav = αav(Δp) dependence from a series of the constant pressure filtration experiments with the

help of Eqs. (I.48)–(I.50) [Murase et al., 1987].

An interesting method for determination of αav(Δp) dependence from a single filtration

test was elaborated by Iritani et al. [2008a] on the basis of idea proposed by Murase et al.

[1989a]. It is based on the “step-up pressure filtration” tests, in which the applied pressure is

increased by increments several times during filtration. Filtration pressure is raised manually

rapidly as soon as the height of the cake L reaches the certain value. The height of the filter

cake is determined either with the help of the set of pressure probes (using the cell presented

in Fig. I.7.b) [Murase et al., 1989a] or using the filter cell, the internal surface of which is

decreased step-by-step (Fig. I.8) [Iritani et al., 2008a].


diskswithholes

filtercake

suspensionFig. I.8. Schema of the filter cell with

decreasing inner cross-sectional area, which

is proposed in [Iritani et al., 2008a] for

determination of αav(Δp) dependence from a

single filtration experiment.

Fathi-Najafi and Theliander [1995] used the filter chamber equipped with the set of

pressure sensors (Fig. I.7.b) for determination of local compressive-permeability properties of

filter cakes. They proposed three methods for determination of local values of solid

compressive pressure ps, solidosity φ, and specific filtration resistance α from the analysis of

filtration curves and liquid pressure profiles. The methods are based on the fitting of the

experimental dependencies αav = αav(Δp), φ = φ(Δp) and x/L = x/L(ps) by conventional

constitutive equations.

In several works [Theliander and Fathi-Najafi, 1996; Lu et al., 1998; Johansson and

Theliander, 2007] simulation of the filter cake growth was carried out and the results were

used for the prediction of local compression-permeability properties and filtration

performance. The input data required for the simulation method described in [Theliander and

Fathi-Najafi, 1996] are the known constitutive equation for solidosity, functional dependence

between α and φ (for example, Happel’s equation (I.18)) and V = V(t) data. Lu et al. [1998]

proposed the method which requires only t – V data and the values of porosity on the cake

surface (which is the gel point) corresponding to various filtration pressures and certain

equation connecting local values of α and φ (e.g., I.18). In the model of Johansson and

Theliander [2007] the input data are the certain constitutive equations for solidosity and

specific resistance (with unknown parameters) and the experimentally measured t – V

dependence. It was shown, that filtration performance may be predicted satisfactory, if the

optimal constitutive equations are used for the simulation [Johansson and Theliander, 2007].

The constitutive equations may be determined by fitting of the experimentally measured

pressure and solidosity profiles [Sedin et al., 2003].

I.1.7.3. Gravity and centrifugal sedimentation and consolidation

The pressure dependencies of local and average values of solidosity and specific

resistance of suspensions may be estimated from the experiments on gravity/centrifugal

settling and consolidation. The equipment used for these experiments is quite diverse: from


inexpensive settling tubes to analytical photocentrifuges. Regardless of the type of equipment

used in the experiment, main principle of the measurement remains the same: height of the

sediment L is registered during the settling (Fig. 9). Each infinitesimal layer of the sediment is

compressed under the solid pressure corresponded to the total relative weight of particles

situated above this layer. The compression and permeability data, obtained from the gravity

and centrifugal experiments, corresponds to the low and moderate region of the solid

pressure, which is not available in the CP and dead-end experiments.

centrifugal or gravitysedimentation cell

supernatant

sediment

L

t

sedimentation curve

Lo initial

L(t)

L∞ final

Fig. I.9. Schema of the

gravity/centrifugal settling

experiment.

Both diluted (φ < φg) and concentrated (φ ≥ φg) suspensions may be studied by these

techniques. Two types of experimental dependencies may be obtained and analyzed in order

to determine the compression-permeability properties:

dependence of the equilibrium sediment height on the centrifugal acceleration

(Fig. I.10.a);

and dependence of the sediment height on the sedimentation time (kinetics of

settling/centrifugation) (Fig. I.10.b).

Sed

imen

t hei

ght L

, [m

m]

Time t, [s]

Ω = 1000 rpm

2000 rpm

3000 rpm

(b)

Ult

imat

e he

ight

L∞, [

mm

]

Rotation speed Ω, [rpm]

L∞ = L(t →∞)

(a)

Fig. I.10. Typical dependencies obtained in centrifugal settling experiment: (a) ultimate

sediment height L∞ at various centrifugal rotation speed Ω; (b) sediment height L versus

centrifugation time t.

Below we will discuss separately the methods created for analysis of the first (L∞ vs Ω) and

the second (L vs t) types of the experimental data.


Murase et al. [1989b] proposed a simplified method for determination of parameters of the

constitutive equation for solidosity from the centrifugal consolidation data presented in

Fig. I.10.a. The analysis was developed for relatively thin sediments with L << R (where R is

the radial distance from the center of rotation to the bottom of the sediment). It starts with the

assumption of the certain constitutive equation for φ and yields the equation relating the final

sediment height L∞ with the centrifugal acceleration RΩ2. Fitting the set of the experimental

points L∞ vs. RΩ2 by this equation yields the values of parameters of the constitutive equation.

Recently, Curvers et al. [2009] proposed another method of analysis for assessing the

compressibility of suspensions from the data on ultimate sediment height. The analysis is

based on a numerical iterative algorithm relating the equilibrium solidosity profile with the

profile of solids pressure and equilibrium sediment height [Curvers et al., 2009]. The method

assumes variation of the centrifugal acceleration through the cake thickness, therefore, it is

appropriate for analysis of thick cakes (with L∞ ~ R). The input data for this method are the

certain constitutive equation φ = φ(ps) and the set of experimental points L∞ vs. Ω2. The output

data are the values of parameters of the chosen constitutive equation for solidosity. The

method also yields local values of solidosity and solid compressive pressure in a centrifugal

cell.

From the practical point of view, the sediment height versus sedimentation time

dependence is equivalent to the filtrate volume dependence on filtration time: it contains

information about suspension permeability. Similarly, kinetics of the gravity/centrifugal

compaction of concentrated suspension is directly related to the consolidation kinetics

measured in the CP cell.

Observation of the gravity settling/consolidation is simple and does not require any

special equipment. However, only low compressive pressures may be created in the gravity

consolidation experiments. The wide range of compressive pressure is available in the

centrifugal consolidation experiments. However, until recent times, studies on the kinetics of

centrifugal consolidation were rather rare, because equipment for continuous measurement of

the sediment height was scarce [Iritani, 1993]. Nowadays, such type of measurements may be

performed using the new device – analytical photocentrifuge [Lerche, 2007]. The creators of

this centrifuge used it for quantification of the hindered settling function of suspensions

[Lerche, 2007].

Iritani et al. [2007; 2008b] proposed a method for evaluation of specific resistance of

suspension from analysis of the centrifugal settling data. They used the fact that initial


sedimentation velocity of non-compressed suspension uo is proportional to its specific

resistance α:

o

2

u

r

s

ls

(I.54)

where r is the radial distance from the center of rotation to the surface of the sediment. The

value of α, determined from the initial sedimentation velocity, corresponds to the initial

concentration of the settling suspension. Using this point (α, φ), complete dependence

α = α(φ) may be determined with the help of Kozeny equation or Happel equation [Iritani et

al., 2007]. Thus, specific filtration resistance of suspension may be estimated in the wide

range of φ. However, it was noticed in the Section I.1.3 that Kozeny and Happel equations

should be used with caution, because they assumed the constancy of the properties of particles

during consolidation. The true dependence of permeability on compressive solid pressure can

not be obtained from the dependence of initial sedimentation rate of non-compressed

suspension. More reliable information about the permeability of suspensions may be obtained

only from analysis of its consolidation.

Iritani et al. [2009] developed the method of analysis of the gravity consolidation

behaviour. The analysis is based on the simplified analytical solution of consolidation

equation, derived using the Terzaghi’s model. The authors derived the equation, relating the

consolidation ratio U with the modified consolidation coefficient of suspension Ce:

m

em tCm

mU

2o

22

3

1

3 4

)12(exp

)12(

)1(321

(I.55)

where U is defined by Eq. (I.33) and Ce is defined by Eq. (I.31). Fitting of the experimentally

measured gravity consolidation curve U = U(t) by Eq. (I.55) yields the values of Ce. The

authors also have shown that the value of Ce may be estimated from a single point of

consolidation curve using the equation

Ce = 0.665(ωo)2/t80 (I.56)

where t80 is the time of U = 0.8 [Iritani et al., 2009]. This equation may be useful when the

initial part of the consolidation curve is not available.

Equations (I.55)–(I.56) are valid in approximation of Ce remaining constant during the

consolidation process. This assumption may be appropriate in the narrow range of solids

pressure ps appearing in the gravity consolidation experiment [Iritani et al., 2009]. However,

in the general case, the consolidation coefficient is pressure dependent (Ce = Ce(ps)) and

increases throughout the consolidation time [Shirato et al., 1970a]. The pressure dependence


seems to be especially important when centrifugal consolidation is studied instead of gravity

consolidation. As a result, application of Iritani’s method for analysis of the centrifugal

consolidation data is questionable and requires additional investigation. Strictly speaking,

only numerical solution of the consolidation equation is necessary when the centrifugal

coefficient is pressure dependent [Shirato et al., 1970a].

I.1.8. Summary

We can summarize that each technique available for determination of the local

compressibility and permeability of suspensions has its own advantages. The new technique

of analytical centrifugation seems to be very promising for determination of the pressure

dependence of compression-permeability parameters (solid volume fraction, specific filtration

resistance, consolidation coefficient). However, the appropriate method is needed for analysis

of centrifugal consolidation and for determination of local properties of suspensions.


Notation for Section I.2 ................................................................................................... 31

I.2. Dead-end filtration of stabilized mineral suspensions ........................................... 33

I.2.1. Flocculation of mineral suspensions ..................................................................... 33

I.2.2.1. Effect of pH .......................................................................................................... 34

I.2.2.2. Effect of multivalent ions .................................................................................... 34

I.2.2.3. Effect of polyelectrolytes .................................................................................... 35

I.2.3. Dual effect of flocculation on filtration ................................................................ 35

I.2.4. Relation between kinetics of dead-end filtration and dryness of filter cake ..... 36

I.2.5. Viscosity of flocculated suspensions ..................................................................... 39

I.2.5.1. Influence of particles concentration on viscosity of suspensions .................... 40

I.2.5.2. Influence of shear on viscosity of suspensions .................................................. 42

I.2.5.3. Computer simulation of viscosity ...................................................................... 43

I.2.5.4. Experimental investigations of the viscosity of kaolin suspensions ................ 44

I.2.6. Colloidal properties of kaoline: influence on viscosity ....................................... 44

I.2.7. Structure formation in suspensions of high-aspect-ratio particles .................... 49

I.2.8. Regulation of flowability of concentrated suspensions ....................................... 52

I.2.8.1. Mechanism of particles stabilisation with polyelectrolytes ............................. 53

I.2.8.2. Polyacrylic acid ................................................................................................... 54

I.2.8.3. Effect of pH and dose of PAA ............................................................................ 54

I.2.8.4. Comparison of PAA with other polymers ......................................................... 54

I.2.8.5. Measure of size of polymer layer on particle surfaces ..................................... 55

I.2.9. Influence of dispersants on stability of kaolin suspensions ................................ 56

I.2.9.1. Effect of polyanionic molecules .......................................................................... 56

I.2.9.2. Adsorption of PAA molecules. Effect of pH ..................................................... 56

I.2.9.3. Sites of adsorption of PAA on kaolin surface ................................................... 57

I.2.9.4. Influence of Ca2+ ions on adsorption of PAA .................................................. 57


I.2.9.5. Flocculation by neutralization of charge .......................................................... 58

I.2.10. Effect of PAA on kaolin rheology ....................................................................... 58

I.2.11. Shear-thickening of concentrated suspensions .................................................. 59

I.2.11.1. Description of the shear thickening mechanism ............................................. 59

I.2.11.2. Structural model of Quemada ......................................................................... 60

I.2.11.3. Dependence of shear-thickening on particles aspect ratio ............................ 60

I.2.11.4. Shear-induced ordering in concentrated suspensions ................................... 61

I.2.12. Dead-end filtration of deflocculated mineral suspensions ................................ 62

I.2.12.1. Dead-end filtration followed by cake mixing .................................................. 62

I.2.12.2. Dead-end filtration after suspension deflocculation ...................................... 62

I.2.12.3. Combined use of dispersant and flocculant .................................................... 63

I.2.12.4. Dead end filtration in presence of dispersant with precoat formation ........ 63

I.2.12.5. Action of PAA on filtration of CaCO3 suspensions ....................................... 65

I.2.13. Effect of particles aspect ratio and orientation on specific cake resistance .... 66

I.2.13.1. Theory: effect of particles orientation on permeability ................................. 66

I.2.13.2. Experimental data on particles orientation during dead-end filtration ...... 67

I.2.14. Summary ............................................................................................................... 69



a particle size [m]

af floc size [m]

DF fractal dimension of flocs [–]

h height of filter cake [m]

k’ barrier probability, defined by Eq. (I.78)

ke constant defined in Eq. (I.74)

kl lumped permeability factor, defined by Eq. (I.59

Ko Kozeny constant

kp shape factor, defined by Eq. (I.72)

pf liquid pressure [Pa]

py compressive yield stress [Pa]

Δp filtration pressure [Pa]

r smaller radius of particle [m]

R larger radius of particle [m]

So specific surface area of particles [m2/m3]

t time [s]

t’ tourtosity (defined by Eq. (I.77))

V volume of filtrate [m]

X parameter, defined by Eq. (I.68)

Z structural variable (in the model of Quemada) [–]

Greek letters

α specific cake resistance [m/kg]

β angle between two particles (explained in Fig. I.17) [°]

shear stress [s–1]

c

critical shear stress [s–1]

ε porosity [–]

ζ ζ potential [mV]

η viscosity of suspension [Pas]

ηl viscosity of liquid [Pas]


θ angle [°]

σ shear stress [Pa]

σB Bingham’s yield stress [Pa]


φf average volume fraction of particles in the flocs [–]

φp solid volume fraction at percolation point [–]

φs-g solid volume fraction at point of sol-gel transition [–]


I.2. Dead-end filtration of stabilized mineral suspensions

Dead-end filtration is a common method for preparation of concentrated mineral

suspensions. It follows from the Section I.1 that efficiency of dead-end filtration is

determined by the value of specific filtration resistance α: low value of is required for fast

filtration (Eq. I.26). The value of α depends on porosity of a filter cake (α decreases with the

increase of porosity) and structure of pores (pore size, tortuosity, number of opened pores

etc.) It is also proportional to the particle size a and the surface area of particles So (see

Eq. I.18) and depends on colloidal properties of the suspended particles (particle shape and

charge). These properties also determine viscosity and dryness of the filter cake. Therefore,

optimization of filtration rate is usually attained by adjustment of colloidal properties of

particles and structural properties of the filter cake.

In the Section I.2 we will discuss preparation of concentrated and low-viscous mineral

suspensions by means of dead-end filtration. We will consider relation between the properties

of mineral particles (their shape, size and surface charge) and colloidal properties of

suspensions (structure formation, rheological behaviour and filterability). The methods

available for adjustment of colloidal properties (use of flocculants and dispersants) will be

reviewed. We will pay special attention to kaolin suspensions, because kaolin particles have

peculiar colloidal properties, while concentrated and flowable kaolin suspensions are needed

in mineral industry.

I.2.1. Flocculation of mineral suspensions

According to equation (I.18), the specific cake resistance α decreases when the average

particle size a grows. So, when particles in suspension are too small (a < 1 m), a

conventional method of α reduction is to trigger off the flocculation.

Flocculation is a process of aggregation of the dispersed fine particles into larger units

(flocs). Flocculation involves [Hogg, 1999]:

destabilization of the suspended fine particles, i.e., elimination of interparticle repulsion.

formation and growth of flocs, i.e., development of aggregates through particle-particle

collision and adhesion.

Destabilization of particles is required, because mineral particles in an aqueous suspension

often repel one another due to their surface charges. A mineral particle dispersed in water

usually obtains surface charge from dissociation of surface groups or adsorption of ions from


the aqueous medium. This interaction results in formation of a double electric layer around

the charged surface with:

- an immediate layer of counter-ions strongly linked to the surface;

- a diffuse and extended layer made up mostly of counter ions.

This double layer compensates the opposite electrical surface charge so that the net charge of

the system (particle and double layer) respects the principle of electro-neutrality. Untreated

colloidal particles often exhibit stability against aggregation resulting from repulsion between

their electric double layers.

According to DLVO theory, this electrical repulsion is proportional to the surface charge

and length layer of outer counter-ions [Hunter, 2001]. Lowering of the surface charge reduces

the interparticle repulsion and provokes destabilization of suspension (coagulation). If the

suspension is stirred, the number of destabilized particles may grow due to particle-particle

collision and adhesion [Hogg, 1999]. This is the flocculation process. Surface charge of the

mineral particles may be controlled through adsorption of polyvalent ions, surfactants and

polymers in order to initialize the flocculation.

I.2.2.1. Effect of pH

For mineral particles the surface charge depends on pH of solution. Variation of pH

suppresses dissociation of the surface hydroxyl groups or results in adsorption of

protons/hydroxyls on the surface [Tombacz, 1999]. At certain pH (so-called, isoelectric point)

the particles lose their surface charge and aggregate easily.

I.2.2.2. Effect of multivalent ions

As an alternative to lowering of repulsion between particles, their charge may be screened by

addition of multivalent ions to suspension. It effectively reduces the length of the diffusive

counter-ion layer, decreases repulsion between the particles and allows them to approach

closely to form aggregates. Effectiveness of the action of ions depends on their electrical

charge zi and their concentration. The required concentration of ions usually depends on their

charge as ~ zi–6 [Kruyt, 1952].

Metal ions, such as Mn2+, Al3+, Fe3+, can be highly effective for aggregation of particles.

In addition to the above mentioned effect of screening, these ions readily adsorb on the

negatively charged particle surface and reduce its charge, or even can reverse the sign of

charge to positive [Hunter, 2001]. High binding ability of these ions also plays an important


role in adsorption of molecules, such as polymers, which can be further added to improve

flocculation [Tian, 2006].

I.2.2.3. Effect of polyelectrolytes

Polymeric substances, especially polyelectrolytes, are very effective as agents for

aggregation of fine mineral particles [Mpofu, 2003a; Yu, 2006]. Highly charged polymeric

molecules adsorb on the oppositely charged surfaces forming local charge irregularities.

Aggregation occurs through interaction of the tails and loops of the adsorbed molecules with

bare surface of other particles. Molecular weights of the order of 105 Da seem to be optimal

for flocculation of mineral suspensions [Hogg, 2000].

Finally, previous Sections show that different ways may be used for triggering off the

flocculation of particles. But effects of flocculations, induced by neutralization of charge,

screening and bridging, on the efficiency of subsequent solid-liquid separation by filtration

will not be the same. Their advantages and drawbacks are discussed below.

I.2.3. Dual effect of flocculation on filtration

It was shown in [Klimpel, 1991], that flocculation of mineral particles not only increases

the average particle size but also enlarges the porosity of flocs:

)/(1 faa (I.57)

where a is the individual particle size, af is the floc size; exponent γ varies between 0.7 and

1.3.

So, it is expected that flocculation of feed suspensions always yields dual results. Increase

of the particle size results in faster filtration, while increase of the aggregate porosity results

in higher water content in the filter cake.

This conclusion was verified in many experimental studies. Besra et al. [Besra, 2000]

have demonstrated the influence of pH on filterability and final dryness of kaoline, calcite and

quartz suspensions: all the three mineral suspensions exhibited improvement in flocculation

and filtration rate near their respective isoelectric points. Filtration of kaolin suspension was

also studied in [Addai-Mensah, 2005] at various concentrations of indifferent electrolyte. It

was shown that dewatering rate and consolidation degree of kaoline suspensions depended

strongly upon the ionic strength (indifferent electrolyte concentration).


Suspensions were reaching maximum of the settling rate, sediment compactness and yield

stress under conditions of flocculation near the isoelectric point of kaoline particles. Increase

of the ionic strength also increased the settling rate.

It was shown in the work of Besra et al. [Besra, 2002, 2003] that flocculation of kaoline

suspension by cationic and non-ionic polyacrylamides appreciably decreased specific cake

resistance. However, flocculation retained excess water in the flocs.

Mpofu et al. [Mpofu, 2003b] have investigated the influence of adsorption of the

hydrolysable metal ions (Mn2+ and Ca2+) on particle interactions, flocculation and dewatering

behavior of kaoline dispersions. It was shown that adsorption of Mn2+ and Ca2+ significantly

decreased zeta potential (hence, surface charge) and adsorption of anionic polyacrylamide–

acrylate flocculant. Kaoline flocculation by metal ions alone resulted in faster clarification

(higher settling rates), but had no detectable effect on dispersion consolidation. In [Addai-

Mensah, 2007], flocculation and dewatering of the kaoline suspension in the presence of non-

ionic polyethylene oxide and anionic polyacrylamide was studied. It was shown that

flocculation of kaoline resulted in faster dewatering, however, increased moisture content in

the final concentrated suspension. The moisture content has been increased twice after

mechanical agitation of the flocculated sediment, revealing loose packed and fragile structure

of flocs. According to [Nasser, 2007a], such loose packed flocs may collapse under

compression.

A number of different flocculants were tested in [Dussour, 2000] for dead-end filtration of

kaoline suspensions. Salts, acids and polymers were used as a flocculation agent and specific

cake resistance and final dryness of the filter cakes were compared. It was shown that pre-

treatment of the concentrated kaoline suspension with an optimal dose of the flocculating

spice reduces specific cake resistance in half at the most, while dryness of the cake remains

constant.

Different types of flocculants were used in the mentioned studies. However, different

experimental studies came to the common result: increase in the dead-end filtration rate after

flocculation is accompanied by decrease in dryness of the filter-cake. Importance of this result

is discussed in the next section.

I.2.4. Relation between kinetics of dead-end filtration and dryness of filter cake

Simplistically saying, filter cake formation comprises two processes: filtration and filter

cake consolidation. The filtration rate is determined by the specific cake resistance α (see

Eq. I.26). The process of filtration was discussed in Section I.1. Filtration lasts until the filter-


cell is filled by the filter cake. This filtration stage is followed by consolidation (or

compression) of the filter cake. The specific cake resistance rises during the compression.

During consolidation, the applied pressure Δp is a sum of particle network stress pp and fluid

pressure pf:

Δp = pp + pf (I.58)

The particle network pressure consolidates the cake if pp exceeds the cake yield stress py;

the fluid stress maintains a liquid flow through the cake pores. According to [Raha, 2006] the

rate of cake compression depends on the yield stress and lumped permeability of the cake (kl).

Consolidation stops when the applied pressure is counterbalanced by the compressive

yield stress of the cake py. Substitution of the permeability coefficient in Eq.(I.5) by its

expression in Eq. (I.16) gives an expression for the compression rate:

h

ppk

h

pp

SKt

h yl

y

l

2

3

2

3

200

)1()1(1

d

d

(I.59)

where h is the cake thickness, φ is the solid volume fraction in the cake (φc < φ < φmax). φc and

φmax are the solid volume fractions at the beginning and at the end of consolidation,

respectively. According to [Buscall, 1988], py ~ φμ, where μ ≈ 4. Eq. (I.59) shows that the rate

of compression drops with the increase of cake dryness.

According to Eqs. (I.23) and (I.59), cake formation may be characterized by three

parameters: α, kl and φmax. It was mentioned above that each separate parameter depends on

the particle-particle interaction. Fig. I.11 shows the results of alumina suspension filtration at

different pH. The alumina particles become aggregated near the point of zero charge

pHpzc,alumina = 7.5. The surface charge of alumina increases in absolute value with distance

from p.z.c. both in acidic and basic directions, which leads to stabilisation of suspension.


4 6 8 100

1

2

3

4

0.4

0.45

0.5

0.55

0.6

0.65

0.7

pH

filt

rati

on α

-1an

d co

mpr

essi

on k

l

rate

par

amet

ers,

a. u

.

kl

equi

libr

ium

cak

e dr

ynes

s φ m

ax

φmax

α-1

4 6 8 100

1

2

3

4

0.4

0.45

0.5

0.55

0.6

0.65

0.7

4 6 8 100

1

2

3

4

0.4

0.45

0.5

0.55

0.6

0.65

0.7

pH

filt

rati

on α

-1an

d co

mpr

essi

on k

l

rate

par

amet

ers,

a. u

.

kl

equi

libr

ium

cak

e dr

ynes

s φ m

ax

φmax

α-1

Fig. I.11. Effect of pH on the specific cake resistance α and lumped permeability kl and

equilibrium cake dryness φmax for dead-end filtration of alumina suspension (adapted from

[Raha, 2005, 2006]).

It is clear that the filtration rate increases while the equilibrium cake dryness decreases, and

vice versa. A similar tendency was observed during filtration of alumina suspensions

flocculated by polyacrylic acids with different molecular weight [Raha, 2007]. The increase

of polymer molecular weight results in a more effective flocculation and faster filtration, but

the cake dryness decreases simultaneously. Studies on the cake filtration of flocculated

mineral suspensions cited in Section I.1.3 also confirm this trend.

Raha et al. [2007] have demonstrated that this trend is rather general for all the colloidal

suspensions. Fig. I.12 shows experimental data on the cake permeability (defined in Eq. I.59

as 23 /)1( lk ) and equilibrium cake dryness φmax for alumina suspensions under various

conditions of pressure, flocculation or stabilization [Raha, 2007].


equilibrium cake dryness φmax

perm

eabi

lity

kl(1

–φ

)3 /φ2

, a. u

.alumina,a = 0.2 μm


perm

eabi

lity

kl(1

–φ

)3 /φ2

, a. u

.


perm

eabi

lity

kl(1

–φ

)3 /φ2

, a. u

.alumina,a = 0.2 μm

Fig. I.12. Pareto profile for the dead-end filtration

followed by consolidation: permeability of

growing cake plotted versus cake dryness at the

end of consolidation. Symbols are experimental

data for different conditions of cake formation

(filtration pressure, pH and concentration of

flocculant). After [Raha, 2007].

All data follow one single curve. This curve is seemingly independent of the suspension

chemistry and physical process variables. Pareto profile was observed for all the suspensions

studied (filtration pressure, pH and concentration of flocculant) [Raha, 2007]. But the profile

depends on geometry of the particles (shape and size).

The Pareto behaviour puts in evidence of interrelation between the cake dryness and

filterability, which is based on importance of the cake structure for these two parameters. It

appears that it is not possible to improve the filtration kinetics without paying a penalty in

terms of lower extent of cake dewatering. It should be noted that improvement of cake

dewatering is more complicated if additional structure-sensitive parameter (viscosity of the

final suspension) is important.

I.2.5. Viscosity of flocculated suspensions

In some cases, fast filtration of a mineral suspension is not the only thing that is needed,

but physical properties and chemical composition of the filter cake are also of great

importance. For example, concentrated mineral suspensions with low viscosity are required in

ceramic industry, manufacture of pigments and paper coating [Jepson, 1984, Murray, 2005].

Same as maximal cake dryness and filtration rate, viscosity is also sensitive to the particle-

particle interactions and the structure of suspension. Therefore, flocculation of suspension

may deteriorate rheological properties of the final filter cake. In the next three sections, the

influence of flocculation on the rheology of concentrated suspensions will be briefly

discussed.


I.2.5.1. Influence of particle concentration on viscosity of suspension

In a concentrated colloidal suspension, motion of particles is hindered by the presence of

the other ones. Certain “tagged” particle can only move in the particle-free volumes, which

decrease with the increase of the volume fraction of particles.

If the particles are aggregated, the volume of liquid available for motion of particles is

reduced, because lots of liquid is entrapped by the flocks structure. Starov et al. [2002]

defined the relation between the viscosity of a flocculated suspension and the volume fraction

of particles:

A

fl

5.2

1

(I.60)

where is the viscosity of suspension, l is the viscosity of liquid, φ is the volume fraction of

particles, φf is the average volume fraction of particles in aggregates (packing density). A is a

coefficient related to friction between the liquid and aggregate surface. Since the volume of an

aggregate of n particles (Vf,n) is greater than the total volume of n individual particles (nV1),

φf < 1 in an aggregated suspension. In a non-aggregated suspension, φf = 1. Then, as it is

shown in Eq. (I.60), the viscosity is higher when the suspension is flocculated. The value of φf

depends on arrangement of particles in the floc, their shape and size distribution. For spherical

particles of same diameter, φf 0.74 for a close sphere packing and φf 0.63 for a random

sphere packing [Sigworth, 1996]. However, the theoretical prediction of φf in a real

suspension with particles of irregular shape and size is quite difficult.

In such a case, it is useful to consider flocs as fractal objects, implying that they are self-

similar and scale invariant [Chakraborti, 2000; Glover, 2004; Li, 2007, Gregory, 1998; Tang,

1999; Waite, 2001; Wu, 2002; Bushell, 2002; Li, 2006]. According to this approach the floc

structure is characterised by the fractal dimension DF

FD

f

a

an

(I.61)

where n is the number of particles in a floc, and a and af are the particle and floc sizes,

respectively [Turchiuli, 2004]. From Eq. (I.61), aggregates with looser structure have lower

fractal dimension. The packing density of particles in a floc is expressed through the fractal

dimension as [Rahmani, 2005]:


3

FD

ff a

a (I.62)

Experimental methods available for measurement of the fractal dimensions of aggregates

are indirect [Li, 2007; Soua, 2006a]. For example, substitution of f in Eq. (I.60) by Eq. (I.62)

enables DF estimation through measurement of suspension viscosity. Also, Eqs. (I.60) and

(I.62) suggest that decrease of floc fractal dimension increases viscosity of suspension. So, the

floc structure plays an important role in the rheology.

Equation (I.60) almost coincides with the Dougherty-Krieger’s equation [Krieger, 1972]

showing the relation between viscosity, volume fraction of particles and their maximum

packing fraction max

max][

max

1

l

(I.63)

where [] is the intrinsic viscosity. According to many authors []max 2 [Quemada, 2006].

Eq. (I.63) was empirically formulated for concentrated suspension of non-aggregated

particles. Soua et al. [Soua, 2006a] had proposed the modified Dougherty-Krieger’s equation

for aggregated suspensions in order to calculate the maximum volume fraction of flocs in

suspension. They replaced max in Eq. (I.63) by more appropriated max, flocs = maxf . This

modified equation makes it possible to assess the influence of flocculation (floc size and

fractal dimension) on viscosity in a highly loaded suspension via Eq. (I.62).

Eq. (I.60) gives the next relation for non-aggregating spherical particles

5.21/ l (I.64)

It coincides with well-known Einstein’s equation in case of diluted suspensions taking into

account that is close to zero and first order Taylor expansion of Eq. (I.64):

5.21/ l (I.65)

The models listed in this section, as well as models of Mooney, Dabak-Yucel, Liu and

others (referred in [Yuanling, 2004]), consider only geometrical factor in prediction of

viscosity of a concentrated suspension. They do not inquire into the influence of shear on the

floc structure and maximal volume fraction and, therefore, on viscosity. Influence of shear on

the structure and viscosity of flocculated suspensions is discussed in next section.


I.2.5.2. Influence of shear on viscosity of suspensions

If hydrodynamic perturbations exceed interparticle attraction, the floc structure collapses

[Tadros, 1990]. Hence, the structure and viscosity of flocculated suspension depends on the

shear stress and shear rate (so, exhibits non-newtonian flow behaviour). Many

researchers (referred in [Quemada, 2002] and [Carreau, 1999]) have simulated the

rheological behaviour of flocculated suspensions and estimated dependency ).,(

Different types of rheological behaviour of a suspension are predicted by the structural

model of Quemada [2002]. Quemada’s model discusses the relation between viscosity and

cumulative structure of suspension. The model assumes that:

(a) the structure of suspension may be characterised using structural variable Z;

(b) the structure may be perturbed under shearing, but restored by Brownian forces and

attraction between particles . Kinetics equation with single variable Z accounts for the

structure evolution;

(c) the viscosity is a function of Z;

Z increases with formation of, so-called, structural units: flocs, aggregates, or network of the

particles. Z decreases with disruption of structural units: deflocculation, disaggregation,

damage of a network of particles, etc. It is important that Quemada’s theory does not

postulate disintegration of structure with increase of the shear rate. Values of Z range from Z0

for

0 to Z for

. Kinetic equation for Z is expressed as:

)()( 0 ZZZZdt

dZc

(I.66)

where first term of equation accounts for structure disruption, second term of equation

accounts for structure recovery. Here, c

is the constant, c

~ ( kBT + U ), where U is the

energy of interaction between particles and term kBT accounts for Brownian motion.

Quemada’s theory leads to the following general equation for viscosity:

2

/

/1)(

c

c

X

(I.67)

where σ is the shear stress, (

) is the viscosity of suspension when its structure reaches the

steady-state at the given shear rate

, is the viscosity of suspension for

, X is the

rheological index given as


/ 1

/1 0X (I.68)

[Quemada, 2006]. The rheological index X accounts for the volume occupied by flocs and

particles at different shear rates. Here, φ is the volume fraction of solids, φ is the maximal

volume fraction of structural units (flocs) and particles when

, φ0 is the maximal

volume fraction of flocs and particles when

0.

Though Quemada’s model is based on simple assumptions, it predicts different types of

rheological behaviour [Quemada, 2006]. According to Eqs. (I.67)–(I.68), rheological

behaviour of suspensions mainly depends of the value of X, i.e., on ratio of φ and φ0. The

theory predicts that:

(a) steady-state viscosity increases with flocculation (inasmuch as flocculation increases the

energy of interparticle attraction U and thus increases c

);

(b) if 0 < X < 1, the viscosity of flocculated suspension drops from 0 to with increase of

shear stress of suspension (so-called shear-thinning behaviour);

(c) if X = 0, undisturbed suspension exhibits infinite viscosity (hence, yield stress develops);

(d) if X > 1, viscosity of suspension increases with shear stress (shear-thickening behaviour);

(e) if X = 1, viscosity is shear-invariable (Newtonian liquid).

It is seen that the rheological behaviour of suspension depends on organisation of particles

upon shear. Observation of shear-thinning (or shear-thickening) suggests that maximal

volume fraction of structural units decreases (or increases) with shear However, explanation

of such decrease (or increase) is required.

I.2.5.3. Computer simulation of viscosity

Computer simulation of concentrated suspensions may predict new rheological

phenomena. Barthelmes et al. [2003] have developed computer simulation for prediction of

the viscosity of concentrated aggregating suspensions knowing the intensity of interparticle

attraction and fractal dimension of flocs . It was shown that increase of interparticle attraction

results in formation of large flocs with low fractal dimension. According to Eqs. (I.60)–(I.62),

decrease of floc fractal dimension DF and increase of floc size af should increase viscosity of

suspension. However, it was observed that the viscosity does not vary much as DF decreases

from 2.7 to 2.1. This result is rather surprising with regard to concept of viscosity discussed in

Section I.2.5.1. The authors [Barthelmes et al., 2003] have shown that large and voluminous


flocs are more sensitive to the action of shear. The shearing of flocculated suspensions results

in disruption of large flocs. Therefore, decrease of the floc fractal dimension in the flocculated

non-sheared suspension results in decrease of the floc size in the sheared suspension. It results

in lower viscosity of the flocculated suspension.

An interesting result was reported in the theoretical study of Silbert et al. [1999], where

rheological behaviour of concentrated aggregating suspensions was simulated. It was

observed that at high shear rate particles may order in the direction parallel to the shear flow.

The ordering increased with increase of concentration of the particles. As soon as ordering

appeared, the suspension displayed shear thickening.

I.2.5.4. Experimental investigations of the viscosity of kaolin suspensions

The negative effect of flocculation on fluidity of kaoline suspensions was reported in

numerous experimental studies [Stenius, 1990; Johnson, 1998a; Conceicao, 2003; Conceicao,

2005; Tombacz, 2006; Nasser, 2007b; Kim, 2009]. However, the rheological behaviour of

kaoline displays some surprising features: non-monotonous effect of the particle charge on

viscosity of kaoline suspensions [Johnson, 1998b], and unexpected decrease of viscosity after

flocculation in the presence of some cations [Mpofu, 2003b]. In addition, concentrated kaoline

suspensions have high viscosity compared to other minerals [Yuan, 1997; Conceicao, 2005].

In summary of Section I.2.5: according to theoretical predictions and many experimental

results, viscosity of mineral suspensions increases after their flocculation. Viscosity is

sensitive to floc geometry (size, pacing density, fractal dimension). It should be noted that

rheological behaviour of kaolin suspensions is more complicated and viscosity is higher as

compared to other minerals. These phenomena are related to peculiarities of the crystalline

structure, morphology and surface charge distribution of kaoline particles, which is briefly

discussed in the next paragraph.

I.2.6. Colloidal properties of kaoline: influence on viscosity

Clay mineral kaolinite is a basic component of the kaoline powder. Kaoline may also

contain impurities of feldspar, quartz, mica and occasionally montmorillonite, anatase and

iron oxides [Raghavan, 1997; Chandrasekhar, 2002; Gamiz, 2005]. The chemical

composition of kaolinite is Al2Si2O5(OH)4 with substitutional impurities of Fe, Mg and Са

[Mpofu, 2003b; Ferris, 1975]. The kaolinite particle is a batch of alternate two-dimensional

arrays


tetrahedral sheet

octahedral sheetOH

O, OHAl

SiO

O face

T face

edgeH-bonds

tetrahedral sheet

octahedral sheetOH

O, OHAl

SiO

O face

T face

edgeH-bonds

Fig. I.13. Structure of kaolinite particle (the upper picture is adopted from [Barak, 2003]).

of silicon-oxygen tetrahedrons (tetrahedral silica sheet) and aluminium octahedrons

(octahedral alumina sheet) with the oxygen atoms shared between octahedrons of alumina and

tetrahedrons of silica (that is so called 1:1 or TO structure) [van Olphen, 1963; Bish, 1993;

Tombacz, 2006]. Particles of kaolinite have two different basal planes: O faces bearing

hydroxyl groups (Al)–OH and T faces bearing oxygen atoms, which are bounded to silicon

atoms (Fig. I.13).

(a)

0.5 m

(b)

2 m

(c)(a)

0.5 m

(b)

2 m

(c)

Fig. I.14 (a), (b) SEM images of kaolin particles, (c) AFM image of 3 kaolin particles with

edge surface area 13% (particle A), 33% (B) and 47% (C) of the total surface area.

Images (a), (b), (c) are from [Wan, 2002], [Murray, 2005] and [Brady, 1996], respectively.

Kaoline particles are plate-like in shape with the aspect ratio (diameter to thickness ratio)

varying between 2 and 10 [Brady, 1996] or even 50 [Jepson, 1984] depending on the type of

kaolins (Fig. I.14). Therefore, the surface area of edges varies from 5 to 50 % of the total

surface area (e.g., Fig. I.14.c). The average particle diameter equals to 0.5–5 m and specific

surface area makes only 10–20 m2/g [Herrington, 1992; Wan, 2002; Teh, 2009].


In aqueous suspensions, kaolin particles may exhibit surface charge heterogeneity [van

Olphen, 1963; Johnson, 1998b; Tombacz, 2006; Konan, 2007]. Kaolin particles have negative

charge sites on the T faces owning to substitution of Si4+-ions in the crystal lattice for lower

positive valence ions Al3+ and Fe3+ and that on the O faces owning to the substitution of Al3+

for Ca2+, Mg2+ and Fe2+ [van Olphen, 1963; Bolland, 1980]. This excess of negative charge is

compensated by the exchangeable cations forming the outer part of double electric layer. The

degree of isomorphic substitution is low for all types of kaolins and results in a relatively low

layer charge density (cation exchange capacity) of ~ 0.1–1 mEq/100 g [Ma, 1999; Tombacz,

1999]. The negative surface charge of the face lattice is independent of pH and electrolyte

concentration.

Some authors [Brady, 1996; Carty, 1999; Tombacz, 2006] highlight the difference in the

chemical nature of siloxane T faces and hydroxyl O faces and concede pH-independent

negative charge only for T faces. Carty suggests that in an aqueous suspension over a broad

range of pH values alumina surfaces are positively charged. Tombacz and Szekeres had

proposed a kaolin surface charge model taking into account ionization of basal (Al)–OH

‘gibbsite’ hydroxyls. Though basal (Al)–OH hydroxyls have low reactivity [Brady, 1996],

pH-dependent charges, either positive or negative, may develop on these amphoteric sites

[Tombacz, 2006]:

(Al)–OH + H+ –– (Al)–OH2+ (in acidic medium) (I.69)

(Al)–OH + OH+ –– (Al)–O – + H2O (in alkaline medium). (I.70)

Other charged groups are situated on the edges of the particles. The octahedral alumina

and tetrahedral silica sheets are disrupted at the edges of the particles, where the broken

bounds, exposing aluminol (Al)–OH and silanol (Si)–OH hydroxyls, occurs. Due to

hydroxyls, ionization edges are positively charged at low pH, but pass through the point of

zero charge and become negative at high pH [van Olphen, 1963]. Electrical charge of the

edges is formed due to reactions (I.69), (I.70) and due to dissociation of silanol hydroxyls

(Si)–OH + OH+ –– (Si)–O – + H2O (in alkaline medium). (I.71)

Brady et al. [Brady, 1996] had shown that only participation of edges is required for

explanation of pH-dependent surface charge of kaoline, while contribution of O basal faces is

low. Additionally, it was shown that aluminol hydroxyls of the edges display appreciably

higher Brønsted acidity than acidity of pure Al2O3 surface hydroxyls, while silanol sites differ

minimally from those of pure SiO2. It was concluded in [Tombacz, 2006], that acid-base


4 5 6 7 8 9 10

-30

-20

-10

0

10

20

30ζ edges,mV

pH

– –––––

– ––+

+ +

T face, charge = const, < 0

edges, pH < pHpzc,edge

charge > 0edges, pH > pHpzc,edge

charge < 0

4 5 6 7 8 9 10

-30

-20

-10

0

10

20

30ζ edges,mV

pH

– –––––

–– –––––––––

– ––+

+ +

–– ––––++

++ ++

T face, charge = const, < 0

edges, pH < pHpzc,edge

charge > 0edges, pH > pHpzc,edge

charge < 0

Fig. I.15. Development of patch-wise surface charge heterogeneity of kaolin particles.

ζedges data were taken from [Williams, 1978] for 1:1-electrolyte concentration of 10–3 M.

properties of the amphoteric sites of kaolinite lie between those of the surface hydroxyls of

pure alumina and silica; the kaolin edges have point of zero charge at pHpzc,edge 6–6.5.

Kaolin particles display patch-wise surface charge heterogeneity only at pH < pHpzc,edge.

Another reported values of kaolin pHpzc,edge are 3–4 [Appel, 2003], 3.8 [Brady, 1996], 4–5.5

[Coppin, 2002], 5.9 [Kretzschmar, 1998], 5–7 [Herrington, 1992] and ~ 7 [Williams, 1978;

Johnson, 1998b].

Such difference in the nature of edge and face surface charges of kaolin particles causes

heterogeneity of pH-dependent surface charge (Fig. I.15) and results in pH-dependence of the

particle-particle interaction of kaolin. In aqueous suspensions, kaolin particles are

electrostatically stabilized at pH > pHpzc,edges, when both faces and edges possess negative

charge; particles can form aggregates only at high concentration of electrolyte, when the

surface charge is screened [Tombacz, 2006]. Decreasing of pH below pHpzc,edges recharges

edges and causes electrostatic attraction between oppositely charged edges and faces. At low

pH, kaolin particles strongly aggregate forming ‘card house’ structures, where particles are

held together through edge-to-face contacts [van Olphen, 1963; Johnson, 1998b; Taylor,

2002]. Some authors suggests possibility of edge-to-edge contacts between particles in

vicinity of pHpzc,edges and formation of spacious ‘Bandermodel’ aggregates [Rand, 1977;

Taylor, 2002] (Fig. I.16). Formation of both ‘house of cards’ and ‘Bandermodel’ structures

was confirmed recently by means of scanning electron microscopy [Źbik, 2009].


pH increase

‘house of cards’ ‘Bandermodel’ ‘face-to-face’

pH increase

‘house of cards’ ‘Bandermodel’ ‘face-to-face’

Fig. I.16. Kaolin particles arrangement a different pH.

The pH-induced aggregation significantly exerts on rheological behaviour of kaolin

suspensions. In alkaline medium, the uniformly charged particles repel each other, and stable

kaolin suspensions exhibit slight shear-thinning flow with the yield stress equal to zero.

Decrease of pH promotes aggregation that results in increased viscosity [Tombacz, 2006]. In

concentrated suspensions, appearance of a ‘card house’ structure leads to formation of semi-

solid pastes with plastic flow behaviour [Johnson, 1998b]. At sufficiently high concentration

of kaolin, strong attractive gel arises with a network of edge-to-face heterocoagulated

particles. The elasticity of gel increases in acidic medium [Tombacz, 2006], however, gel

liquefies as the shear stress approaches the yield stress value. It was shown that in colloidal

suspensions the yield stress value is proportional to the concentration of contacts between the

particles and strength of the contact [Kapur, 1997]. Electrostatic attraction between the faces

and edges of kaolin particles are proportional to the edges charge, which increases as pH

decreases. Therefore, shear yield stress of kaolin suspension increases as concentration of

particles increases and pH decreases from pH = 10 to 3–5, in accordance with the theory’s

prediction. However, in contrast to spherical particulate systems shear yield stress of kaolin

suspensions passes through the maximum and decreases at pH < 3 [Johnson, 1998b; Addai-

Mensah, 2005; Teh, 2009]. This feature of kaolins rheology may reflect partial rearrangement

of particles from ‘edge-to-face’ to ‘face-to-face’ geometry [Johnson, 1998b]. In very acidic

medium O faces of the particles may be re-charged to positive due to basal (Al)–OH

hydroxyls dissociation, equation (I.69) [Tombacz, 2006]. This drives formation of ‘T face to

O face’ lamellar structured tactoids and, hence, decreases a number of particles in ‘edge-to-

face’ contact. The result is a decrease in the suspension shear yield stress [Schofield, 1954].

Due to the particularities of structure particles arrangement flocculation of kaolin

suspensions with hydrolysable metal ions also decreases shear yield stress. Specific


adsorption of positively charged hydrolyzed metal complexes leads to significant reductions

of particles zeta-potential, that decreases edge to face attraction and yields face to face

attraction. This results in particle ‘house of cards’ network breakdown and a marked decrease

of yield stress [Lagaly, 1989; Addai-Mensah, 2007].

Same as arrangement of particles and the number of interparticle contacts, the particle

size, shape and aspect ratio determine peculiarities of the rheological behaviour of kaolin

suspensions. At the same particle volume fraction, viscosity of diluted suspension of the

kaolin particles is higher than that of spherical or grain-like mineral particles due to larger

effective volume fraction occupied by rotating plate-like plates. For the plate-like particles,

Einstein’s equation for viscosity of non-interacting spheres (I.65) grades into

pl k5.21/ (I.72)

where constant kp > 1 (kp increases with increase of the particle aspect ratio and decreases

with increase of orientation of particles in the shear flow [Quemada, 2006]). However, shape

factor kp introduction in the equations for spherical particles is not sufficient to describe in

details the rheological behaviour of more concentrated suspensions [Yuan, 1997].

Since rheology of kaolin is associated with formation of a network of particles, below we

discuss briefly the influence of the particle shape on the structure formation and viscosity.

I.2.7. Structure formation in suspensions of high-aspect-ratio particles

Suspensions of kaoline and other clays with plate-like particles are often referred as

Bingham plastic bodies. They behave as a rigid body at low shear stress but become fluid at

higher stress [Luckham, 1999; Abend, 2000; Tombacz, 2006]. The Bingham equation for

plastic behavior is given as

plB (I.73)

where pl is the plastic viscosity and B is the Bingham yield stress. B is the minimum or

critical stress that should be imposed for triggering off the transition from solid state to liquid

and, thus, for triggering off the flowing of the suspension. This concept of yield stress is used

in several rheological models (Hershel-Bulkley, Casson [Quemada, 2006]).

The yield stress can be obtained from a rheological curve by means of equation (I.73).

The physical meaning of the yield stress is as follows: a concentrated suspension in absence

of stress is constituted of a network of particles; the yield stress of suspension represents the


mechanical force required for breaking this network, disconnection of particles and generation

of the flow.

The network formation may be discussed in the framework of percolation theory [Brinker,

1990; Sahimi, 1998; Walsh, 2008]. This theory forecasts the specific percolation volume

fraction φ ≈ φp (also named percolation threshold), when particles start to establish some

connections with their neighbors. Rather moderate changes in viscosity take place both below

φp and above φp, but strong discontinuity occurs at the vicinity of φp. Above φp, a continuous

network exists due to the contacts between particles.

A contact between three particles is possible when a particle penetrates into ‘excluded

volume’ of the other two particles (Fig. I.17). For particles with high aspect ratio (2R/r), the

excluded volume is much higher than the particle volume. Here, 2R is the particle diameter

and r is its thickness.

Hence, the percolation threshold is not related directly to the volume fraction of particles

but rather to the volume fraction of excluded volume [Celzard, 1996]. For 3D network, φp is

related to the excluded volume as

)exp(1 eep VVk (I.74)

where Ve is the excluded volume and V is the volume of particle. ke is a constant: ke = 2.8

and 1.8 for parallel and random orientation of particles, respectively [Celzard, 1996; Walsh,

2008]. For disk-like particles, the mean excluded volume equals to

0

23 sin4 dRVe (I.75)

where β is the angle between the two disks in contact and represents the angle of the

greatest disorientation of disks in the system (– β + ); = 0 and π/2 for parallel and

randomly arranged particles, respectively.

β

2R

rB

A

C

β

2R

rB

A

C

Fig. I.17. Sketch of excluded volume (e.v.).

When centers of particles A and C penetrate

into e.v. of particle B, it can be considered

that particles are in contact (β : angle

between two particles).


10 20 30 40 50 60 70 80 90

0.2

0.4

0.6

0.81

0.05

0.1

φp

, degree

aspectratio =

2

10

20

10 20 30 40 50 60 70 80 90

0.2

0.4

0.6

0.81

0.05

0.1

10 20 30 40 50 60 70 80 90

0.2

0.4

0.6

0.81

0.05

0.1

φp

, degree

aspectratio =

2

10

20

Fig. I.18. Percolation threshold of kaolin particles φp calculated for different aspect ratio

values as a function of maximum angle between particles (solid lines: ke = 1.8, dashed lines:

ke = 2.8).

Kaolin particles can be simulated by disks with aspect ratio varying from 2 to 10–50

[Jepson, 1984; Brady, 1996]. The percolation threshold φp of kaolin particles was estimated

using Eqs. (I.74) and (I.75). Fig. I.18 shows that both particle shape and orientation impact a

lot the percolation threshold.

For instance, φp strongly increases as decreases. So, φp is maximal for parallel ordering

of kaolin particles. Theoretically, suspension of plate-like particles may reach 50% vol.

concentration without gel formation if the maximum angle between two neighbour particles is

less than 30 degrees.

In suspensions with chaotic orientation of particles, φp drops with increase of particle

aspect ratio. For well delaminated kaoline particles, formation of gel may occur at volume

fraction below 0.05.

Meanwhile, for usual grain-like mineral particles (less anisotropic), structure arises at φ ~

0.5. Therefore, transition from Newtonian to plastic behaviour (sol-gel transition) in a kaoline

suspensions takes place at lower concentration of particles than in usual mineral suspensions

[Bundy, 1991; Yuan, 1997; and Fig. 4 in Lu, 2005].

And vice versa, concentration of Na-montmorillonite suspensions (having aspect ratio >

100) is much lower than that for thicker kaolin particles [Abend, 2000]. So, we can conclude


that the calculated percolation threshold (φp = 0.05–0.1) is close to experimentally measured

sol-gel transition concentration for kaolin suspensions (0.04 in [Kislenko, 2001], 0.13 in

[Addai-Mensah, 2005]).

It is worthwhile noting that there is a difference between sol-gel transition (that is the

volume fraction of steep increase in rigidity φs-g) and percolation threshold (that is the volume

fraction of steep increase in connectivity φp). According to [Celzard, 2001; Moraru, 2004],

the sol-gel transition point is higher than the percolation threshold:

12

12

D

D

p

gs

(I.76)

where D is the system dimension (D = 3). According to Eq. (I.32) φs-g/φp = 1.6.

In summary, electrostatic attraction exists between edges and faces of the kaolin particles

in neutral and acidic media. This attraction results in formation of aggregates having ‘house

of cards’ structure. At certain concentration of particles, the aggregates do connect into

percolating 3D network, which accounts for poor flowability of suspension. The percolation

concentration may be noticeably low in systems of attracting particles having high aspect

ratio. In natural form the kaolin suspensions are slightly acidic, and kaolin particles are plate-

like, kaolin suspensions are flocculated and their viscosity is elevated. So, in order to reduce

the viscosity of concentrated kaolin suspensions, it is necessary to decrease interparticle

attraction and deflocculate the suspension.

Next paragraph briefly discusses the methods used to improve the flowability of

concentrated suspensions.

I.2.8. Regulation of flowability of concentrated suspensions

Better flowability may be obtained from a mechanical crushing and thus an

homogenisation of particle sizes in the suspension [Garrido, 1990; Baudet, 1999; Conceicao,

2003; Murray, 2005]. However, it is quite energy-consuming. The easier way to improve

flowability of suspensions is to add chemicals called dispersants [Stein, 1995]. All the

chemicals having stabilizing effect on particles can be considered as dispersants: ions,

polyelectrolytes, non-ionic polymers and surfactants. Most commercial molecules used for

minerals stabilization are polyelectrolytes with low molecular weight (< 20 000 Da).


I.2.8.1. Mechanism of stabilisation of particles by polyelectrolytes

The mechanism of stabilization of particles in presence of polymeric dispersant is

described in this Section. Adsorption of dispersant on the particles increases the energy

barrier of their aggregation. According to the extended-DLVO theory [Israelachvili, 1992;

Quemada, 2002], the energy barrier is determined by attractive van der Waals forces and

repulsive electrostatic and steric forces. Electrostatic forces originate by the surface charge of

particles. Steric forces may be determined by two factors [Solomon, 1983; Israelachvili, 1992,

Tobori, 2003]:

osmotic factor (increase in polymer concentration in the gap between two polymer-

covered particles causes an increase in disjoining osmotic pressure);

entropic factor (compression of the adsorbed layer during collision of particles confines

conformation of polymer chain and, thus, also increases disjoining pressure);

The factors are sketched in Fig. I.19.

Adsorption of charged polymers changes both electrostatic and steric interaction forces. It

provides more effective electrosteric stabilisation of particles. Effectiveness of electrosteric

stabilization is influenced by the polymer charge. Polymer charge and conformation depends

on ionic composition of the medium: cation adsorption, pH changes and increase of ionic

strength may reduce electric charge of ionizable polymer groups. Decrease of the polymer

charge results in a more compact conformation of the polymeric molecule. Therefore,

decrease of the polymer charge results in lower repulsion between adsorbed polymer layers

and lower disjoining pressure. Conformation of non-ionic polymer molecules is less sensitive

to these factors. Therefore, different types of single polymers and polymer mixtures may

render an optimal stability of suspensions having different chemical nature [Kong, 2006]. In

the next Sections we will pay our attention to the widely used dispersant: polyacrylic acid.

polymer tailsand loops

counter-ion’slayer

polymer tailsand loops

counter-ion’slayer

Fig. I.19. Mechanism of steric

stabilization.


I.2.8.2. Polyacrylic acid

Polyacrylic acid (PAA) salts are widespread in mineral industry as dispersing agents

(calcium carbonate, ceramics, oxides, aluminosilicate clays, etc) [Shih, 1999; Sjöberg, 1999;

Tobori, 2003; Shen, 2004a; Labanda, 2005; Binner, 2006]. Polyacrylate-ions easily adsorb on

mineral surfaces either because of electrostatic attraction, or because of formation of a

complex between carboxylic groups and cations at the particle surface (Ca, Ba, Al). It

increases the surface charge in absolute value. So, PAA provides electrostatic and, to some

extent, steric stabilization. For example, ammonium polyacrylate can reduce significantly the

viscosity of suspensions of barium titanate microparticles [Tseng, 2002] and nanoparticles

[Shen, 2004a; Shen, 2004b].

I.2.8.3. Effect of pH and dose of PAA

It was shown that the value of pH and dose of PAA are important parameters determining

the efficiency of stabilization of particles [Shen, 2004a; Shen, 2004b]. Adsorption of PAA is

alters in neutral and acidic media. In a very alkaline medium, PAA is dissociated and has a

large negative charge. Therefore, at high pH electrostatic repulsion between negatively

charged particle surface and free PAA– prevent PAA– molecules from adsorption. With the

barium titanate, the highest PAA efficiency occurred at pH = 10 (2.0% w/w of PAA), while

dissociation of polyacrylic acid was moderate at this pH.

Usually, there exists some optimal dose of dispersant. [Zhang, 2006] has shown that the

viscosity of hydroxyapatite dispersion decreases with addition of sodium polyacrylate until

adsorption of dispersant reaches a maximum. Then, further addition of dispersant deteriorates

the flowability.

At optimal conditions of pH and dispersant dose, mineral suspensions often display a

shear-thinning behavior in a wide range of shear rates ( = 1–103 s–1) and maintain their

fluidity up to 55% volume fraction of particles [Shen, 2004a].

I.2.8.4. Comparison of PAA with other polymers

Here we discuss efficiency of PAA in comparison to other polymers. [Tobori, 2003] has

studied the rheological behaviour of concentrated calcium carbonate suspensions in the

presence of PAA and comb-grafted copolymer. Last one was made of a backbone of sodium

methacrylate and polyethylene oxide ‘tails’. It was observed that viscosity of suspensions

stabilized by a comb-grafted copolymer is lower than with PAA, and does not depend on at

high shear rates, while suspensions stabilized by 0.4% wt PAA (optimum dose) were shear-


thinning in the studied range of shear rates : = 10–3–103 s–1. [Tobori, 2003] have concluded

that the particles with PAA were still flocculated to some extent. Papo and Piani [2004] had

noted better flowability of cement paste with PAA than with lignosulfonate. In addition, they

have reported, as well as [Shih, 1999; Tobori, 2003], that viscosity increases again when PAA

is overdosed.

Farrokhpay et al. [2005] have compared the effects of dispersants containing different

functional groups (carboxylic, hydroxylic, amide) on titania pigment particles. The study was

carried out at pH = 6.0 and 9.5. These pH values correspond to low positive and low negative

surface charge of titania, respectively. It was observed that the most efficient are pure PAA

and modified polyacrylamide containing 10% of carboxylic groups and 10% of hydroxy

groups. Dispersant adsorption and particle zeta-potential were lower, while the shear stress of

suspension was better, for pure polyacrylic acid. At the same time, copolymeric dispersant

yields better fluidity despite of lower absolute value of particle zeta-potential. [Farrokhpay,

2005] have concluded that highly charged polymer chains of pure PAA provide better

electrosteric stabilization. Thickness of adsorbed PAA layer was assessed at 0.9 nm.

Copolymer molecules provide rather a steric barrier. Thickness of the adsorbed copoymer was

assessed at 1.2 nm.

It was observed in [Leong, 1995] that addition of PAA in a concentrated suspension of

mineral particles with pH-dependent surface charge (ZrO2 particles) decreases the value of

yield stress at the given pH. [Leong, 1995] has shown that adsorbed PAA molecules adopt a

flat conformation on the uncharged metal oxide surface.

I.2.8.5. Measure of size of the polymer layer on particle surfaces

Direct measurements of the adsorbed layer were performed in [Fukuda, 2001] by means

of AFM (atomic force microscopy). Highly loaded dispersant-containing alumina suspensions

were studied. Three dispersant concentrations were tested: below, at, and above the optimal

dispersant dose. The optimal dose was previously determined from viscosity analyses. It was

shown that at low dispersant doses alumina surface coverage by dispersant molecules is

patch-wise. In this case repulsion between alumina particles is low. Repulsion between

alumina particles increases significantly at optimal dispersant concentration. Overdosing of

dispersant reduces the repulsive force. [Fukuda, 2001] has deduced that unadsorbed PAA

molecules compress the adsorbed polymer layer above the critical dispersant concentration.


This short review concerning the effect of dispersant (PAA) on the stability of mineral

suspensions reveals importance of the surface properties for particle – polymer interaction. As

for kaolin, heterogeneity of the surface must play a determinant role in its interaction with the

polymer molecules. The adsorption of polymers on the kaolin particles and its effect on

viscosity of suspension are discussed in next Section.

I.2.9. Influence of dispersants on stability of kaolin suspensions

I.2.9.1. Effect of polyanionic molecules

Some recent papers show that polyanionic molecules are able to eliminate heterogeneity

of the kaolin surface charge and, hence, decrease viscosity of the kaolin slurries. It was

evidenced for phosphate [Ioannou, 1997; Penner, 2001], silicate, tripolyphosphate and

polyphosphate [Papo, 2002] and their mixtures [Romagnoli, 2007], hexametaphosphate

[Andreola, 2006] and citrate anions [Teh, 2009].

Adsorption of the said small polyanion molecules on positively charged edges of kaolin

particles increases their overall negative surface charge, thus intensifying electrostatic

repulsions between particles.

I.2.9.2. Adsorption of PAA molecules. Effect of pH

Sastry et al. [1995] have tried to understand how PAA adsorbs on kaolin at different pH.

They analyzed the isotherms of PAA (Mw = 250 000 Da) adsorption on kaolin particles. The

amount of adsorbed PAA was clearly decreasing at basic pH values. So, adsorption decreases

with increase of the negative surface charge of kaolin and negative charge of highly ionized

PAA molecules.

At high pH values, electrostatic repulsion between PAA anions and kaolin edges and faces

is expected. However, the relatively large amount of PAA adsorbed at high pH values

indicates that not merely an electrostatic interaction should be considered. Formation of

chemical bonds between aluminol sites of kaolin surface and polyacrylic acid may increase

the adsorption.

The authors deduced that the binding sites for PAA carboxylic groups are situated only at

~ 10% of the BET surface area of kaolin. Most probably, these sites are situated on the edges

of particles. Strong interaction of PAA and kaolin infer existence of a chemical reaction

between carboxylic groups and aluminol hydroxyls. It should be noted that chemical reaction

between PAA and surface of pure Al2O3 was evidenced by means of IR spectra analysis in

[Santhiya, 2000].


I.2.9.3. Sites of PAA adsorption on kaolin surface

Zaman et al. [, 2002] have assumed that mimics of alumina and silica active sites are

present on the surface of kaolin particles. They also have compared adsorption of low

molecular weight PAA (Mw = 3400 Da) on kaolin, alumina and silica. Adsorption isotherms

were analysed in diluted suspensions at pH = 7. The adsorption density (in mgm–2) of PAA

on kaoline surface was about 10 times lower than on alumina, while adsorption on the silica

surface was negligible. The authors have concluded that adsorbing PAA occupies only about

10% of the kaolin surface, which is the alumina-like surface of the edges. The infrared

spectroscopy of PAA-alumina and PAA-kaolin complexes has revealed similarity in the

polymer – surface interactions.

Adsorption of charged PAA– anions on the kaolin surface results in increase of the

negative surface charge of particles. Therefore, zeta-potential of the kaolin particles increases

with addition of polyacrylic acid. It was observed in [Zaman, 2002] that optimal dose of PAA

yielding the lowest viscosity of kaolin suspension and the highest absolute value of zeta-

potential corresponds to commencement of the plateau region in adsorption isotherm.

Adsorption of sodium polymethacrylate on alumina and silica was also studied in [Boufi,

2002]. Same as in [Zaman, 2002], it was observed that maximal amount of polymer adsorbed

on silica is much lower than that of polymer adsorbed on alumina. However, the non-zero

adsorption of PAA on silica surface was observed (~ 0.1 mgm-2 and 0.75 mgm-2 for SiO2 and

Al2O3, respectively). So, the results of this study do not discard possibility of PAA adsorption

on basal faces of kaolin particles.

I.2.9.4. Influence of Ca2+ ions on adsorption of PAA

Järnström and Stenius [Järnström, 1990] have measured adsorption of sodium

polyacrylate (NaPAA) on kaolin. They have defined also the hydrodynamic radius of PAA in

bulk of solution at different pH. They have shown that PAA partially adsorbs on the kaolin

basal surface. About 20% of adsorbed PAA is localized on the basal sites. However, they are

less favourable for adsorption than the sites on the edges. The Ca2+ ions present in the

suspension were pointed out as responsible for adsorption on the basal surfaces. Ca2+ ions

actually form a complex with PAA molecules, thus lowering the polymer charge. [Järnström,

1990] have concluded that only Ca2+ saturated polyacrylic acid molecules may adsorb on the

basal surfaces.

However, it was observed that good adsorption of PAA saturated by Ca2+ on the kaolin

particles does not correlate with better stabilization of these particles. PAA with Ca2+ ions acts


rather as a flocculant. It aggregates the particles causing significant increase of both the yield

stress and the plastic viscosity [Stenius, 1990].

Santhiya et al. [1998] have shown that isotherms of PAA adsorption on Al2O3 exhibit

high-affinity Langmuirian behaviour. The adsorption density decreases as pH increases. This

is similar to data obtained on kaolin that were reported by [Sastry, 1995] . The electrokinetic

study has shown that even low amount of PAA adsorbed at high pH may increase

significantly the absolute value of zeta-potential.

I.2.9.5. Flocculation by neutralization of charge

Das et al. [Das, 2001; Das, 2003] have shown that PAA may cause flocculation of

alumina particles if added at ultra-low concentration. The dose used was ~ 0.1% of the

optimal dose needed for stabilization of particles.

I.2.10. Effect of PAA on kaolin rheology

Influence of PAA (Mw = 10 kDa) on rheological behaviour of concentrated alumina

suspensions was investigated in [Palmqvist, 2006],. The authors reported that it was possible

to increase the solid content up to 59% vol with PAA as a dispersant, while the suspension

remained shear-thinning and maintained low viscosity. Progressive addition of PAA to

suspension resulted only in a downward (at dispersant concentration below optimal one) or

upward (at concentrations above the optimum) shift of the linear log – log flow curves.

In study of Davies and Binner [2000], ammonium polyacrylate with molecular weight

3500 Da was found to be effective in lowering of viscosity of the concentrated (up to

57% vol) alumina. Shear-thickening was noticed for suspensions with the dispersant

concentration below optimal. Also, maximum particle concentrations φmax were calculated

from the flow curves of the stabilized and non-stabilized suspensions [Binner, 2006]. It was

concluded that increase in repulsion of highly charged stabilized particles notably decreases

φmax. Therefore, the optimal dispersant concentration is required for preparation of low

viscous and concentrated suspension.

In [Sjöberg, 1999; Marco, 2004; Marco, 2005] viscosity of kaolin suspensions was

measured at different dispersant concentrations. It was observed that even low adsorbed

amount of the dispersant decreased viscosity of 60% wt kaolin suspension. Only shear-

thinning behaviour of the dispersed suspension was observed in the studied range of shear

rates = 10–1–103 s–1. In [Conceicao, 2003], shear-thickening of 63% wt kaolin suspensions


dispersed with NH4PAA was observed, while diluted suspensions ( 53% wt) were shear-

thinning at = 0–1300 s–1.

In summary, the rheology of kaolin suspensions with PAA is not related to the ‘edge-to-

face’ structure. As well as for other minerals, the fluidity of kaolin slurries is maximal for an

optimal dose of dispersant. This dose depends on the adsorption properties of the particles.

The above-mentioned works have demonstrated that the kaolin suspensions with optimal

PAA dose display a shear-thinning behaviour and low viscosity at solid loadings up to

60% wt. However, mineral suspensions with even higher solid loadings, used, for instance, as

paper coatings, or in ceramics for slip casting, may exhibit completely different rheological

behaviour. They are briefly discussed below.

I.2.11. Shear-thickening of concentrated suspensions

Most concentrated suspensions exhibit a shear-thickening behaviour that is an increase of

viscosity with increasing shear rate [Carreau, 1999; Quemada, 2006]. An onset point may be

defined as the critical shear rate c , over which the viscosity begins to increase. The onset

and thickening depend on the volume fraction of particles, their shape and size distribution

and the degree of their stabilization [Barnes, 1989; Quemada, 2006]. The onset of shear-

thickening marks the point, where the hydrodynamic forces start to dominate and re-organise

the particles.

According to Barnes [1989], all the suspensions may display shear-thickening if the shear

rate is high enough. Onsets at c ~ 10–100 s–1 are commonly reported for concentrated

suspensions > 50% wt. It was also observed that c shifts to lower values at higher

concentrations of particles.

I.2.11.1. Description of the shear thickening mechanism

There are two microstructural explanations for shear-thickening. According to Hoffman

(cited in [Barnes, 1989; Quemada, 2006]), the increase of viscosity is attributed to transition

from an easy flowing state, where the particles are ordered into two dimensional layers, to a

disordered state. This mechanism was confirmed by Hoffman’s experiments on light

scattering in flowing suspensions of spherical particles.

Another explanation implies that shear-thickening results from formation of shear-induced

clusters. Formation of clusters results in decrease of the volume available for motion of

particles. A natural increase of viscosity follows. This may result even in discontinuity of


viscosity if a percolation network of clusters is formed. This mechanism description does not

require to assume existence the layer-ordering of particles at shear rates c [Raghavan,

1997].

I.2.11.2. Structural model of Quemada

Quemada had used structural model for estimation of the influence of different parameters

(particles size and size distribution, concentration and suspension stability) on the cluster

formation and shear-thickening [Quemada, 1998a, 1998b]. Formulation of this model is the

same as for the structural model of viscosity of the flocculated suspensions. However, kinetics

equation for Z contains kinetic constant, which accounts for probability of shear-induced

aggregation. The model fits experimentally data well and predicts different behaviour for

suspensions of weakly aggregated and wholly stabilized particles:

1. At low shear rates, the shear-thinning is predicted for the weakly aggregated

suspensions.

2. The viscosity plateau is predicted for strongly stabilized suspensions.

3. In the weakly aggregated suspensions, the onset of shear-thickening becomes less

obvious: the low shear rate viscosity increases with increase of aggregation of the particles.

4. In both types of suspensions, viscosity reaches maximum with increase of shear rate

and further increase of results in disruption of clusters and decrease of viscosity.

It is also deduced in [Quemada, 1998b] that dilatancy is reduced for suspensions with

broader particle size distribution.

I.2.11.3. Dependence of shear-thickening on particle aspect ratio

Increase of dynamic viscosity with increase of shear rate was reported for a number of

mineral suspensions [Barnes, 1989]. In [Chadwick, 2002] dilatancy of anatase suspensions

with particle volume fraction near φ = 0.33 was registered by means of three methods: steady

state viscosity measurements, creep-recovery tests and oscillatory measurements.

Viscosity of moderately concentrated silica suspensions was studied in [Raghavan, 1997].

The studied suspensions exhibited shear-thickening behaviour even at low particle

concentration (5% wt), which should be the result of strong anisotropy of the studied

particles.

The data of Clarke, cited in (Fig. 8 in [Barnes, 1989]), Yuan [1997], Bergström [1998]

and [Curcio, 1998], suggest that at the certain volume concentration of particles the effect of

shear rate on the dilatancy dramatically increases with increase of the aspect ratio of particles.


This was deduced from experiments with mineral grain-like, needle-like and plate-like

particles with different aspect ratios.

Beazley [1972] has studied rheological behaviour of deflocculated kaolin suspensions at

different concentrations of particles. The suspension behaviour ( vs. suspension

concentration) was linear at low concentrations (with proportionality constant higher than

2.5), and nonlinear at intermediate concentration. At higher particle concentrations,

suspensions were shear-thickening. For monodispersed samples with high aspect ratio, the

dilatancy was observed at much lower particle concentrations (ckaol ≥ 33% wt) than in low

aspect ratio samples (ckaol ≥ 64% wt).

Such rheological difference between near-spherical and anisotropic suspensions of

particles is often attributed to the difference in excluded volumes of particles [Jogun, 1996].

An increase in particle anisotropy results in motion of geometrically hindered particles at

concentrations significantly less then the maximum particle fraction.

I.2.11.4. Shear-induced ordering in concentrated suspensions

Though transition from the ordered to disordered state of suspension is not required for

explanation of the shear-thickening, the shear-thinning of suspensions formed by anisotropic

particles at shear rates below c may be attributed to alignment of particles with flow [Egres,

2005]. The possibility of flow-induced orientation of particles in concentrated kaolin

suspensions was suggested, e. g., in [Champion, 1996] (from the data of light scattering),

[Jogun, 1996] (from conductivity measurement), [Brown, 2000] (from neutron diffraction

experiments).

In [Brown, 2000], symbasis between the extent of particle alignment and shear rate was

reported for concentrated kaolin. Surprisingly, reduction in alignment was observed after

concentration of particles exceeded the critical value φ = 0.13.

Jogun and Zukoski [Jogun, 1996] has reported that alignment of the kaolin particles was

also preserving in more concentrated shear-thinning suspensions (φ = 0.43). The authors

suggested that the particles experience a tumbling/shear aligning transition with increase of

the shear rate.

It was measured in [Egres, 2005] that alignment of long axis kaolin particles is preserved

at the shear-thickening regime. According to this result, hypothesis of order-disorder

mechanism of dilatancy in suspensions of anisotropic particles must be discarded. The authors

explained dilatancy in such suspensions as percolation of shear-oriented particles in shear-


induced clusters. Naturally, the percolation threshold for the clusters decreases as the particle

aspect ratio increases.

In summary of Section I.2.11, shear-thickening is possible in highly concentrated mineral

suspensions. Though the exact mechanism of shear-thickening is unclear, it follows from

increase of excluded volume in the suspension. The onset shear rate of shear-thickening c

decreases with increase of particle concentration and aspect ratio. Therefore, shear-thickening

is achievable in kaolin suspensions because of high aspect ratio of kaolin particles.

Addition of dispersant to kaolin suspension decreases the viscosity and helps attaining of

a high concentration of particles. However, viscosity of highly concentrated suspensions may

increase due to the shear-thickening. So, special study is required for elucidation of the

influence of particle and dispersant concentrations on rheological behaviour of kaolin

suspensions.

I.2.12. Dead-end filtration of deflocculated mineral suspensions

In this Section we discuss the ways for preparation of concentrated and low-viscous

suspensions based on the dead-end filtration method.

I.2.12.1. Dead-end filtration followed by cake mixing

[Wiekmann, 1980], [Bleakley, 1997] and [Willis, 1998]) have proposed to filtrate diluted

suspension and grind the filter-cake after discharge in a tank with an appropriate amount of a

dispersant. This process has some disadvantages.

The diluted suspensions, even untreated, are usually naturally flocculated. That’s why the

obtained filter cakes have high porosity and, thus, insufficient dryness (for instance < 60% wt

for CaCO3 suspensions). It is possible to break this high porous cake by grinding and to

release some water. However, the additional dewatering of the mixed filter cake is required in

order to reach the higher concentration (for instance 65–75% wt for CaCO3 suspensions).

Grinding and homogenizing with special equipment like jaw crushers and blade mixers is

energy-consuming and can alter the properties of the minerals (breakage of the particles). This

is a consequence of high viscosity of an aggregated concentrated mineral suspension.

I.2.12.2. Dead-end filtration after suspension deflocculation

[Purdey, 1976; Chamberlain, 1977; Story, 1990; Morreno, 1998, Hansen, 2000, Garrido,

2001] have proposed to add the dispersant before filtration. Filtration of deflocculated

suspension results in formation of a filter cake with lower porosity and, hence, with higher


dryness. It was demonstrated that despite of high dryness it is usually easier to homogenize

the final filter cake saturated with dispersant. However, this method has serious drawbacks.

The filter cake with low porosity has high specific resistance (see Eq. I.16). Thus, its

filtration requires either extended time or elevated pressure. Moreover, unadsorbed molecules

of dispersant contained by suspension get flushed out from the filter cake and contaminate the

filtrate.

I.2.12.3. Combined use of dispersant and flocculant

[Parker, 1997] has proposed preliminary mixing of diluted suspension with a dispersant

and a flocculant. According to this method, particles are stabilised by a dispersant before

filtration. The stabilised particles are flocculated with addition of a small quantity of

flocculant. Preliminary addition of dispersant facilitates fluidizing of the concentrated

suspension. Correctly chosen dose of flocculant accelerates solid-liquid separation, but does

not decrease viscosity at high shear rate. Approach of [Parker, 1997] is interesting, but it is

rather difficult to find proper flocculant-dispersant mixture, because when mixed, flocculant

and dispersant usually neutralize each other.

I.2.12.4. Dead end filtration in the presence of a dispersant with precoat formation

For preparation of a concentrated suspension, one must deals with controversial effects.

Flocculation gives better filtration speed, while stability gives better dryness and flowability.

It is however possible to avoid this controversial effects.

In [Soua, 2004; Vorobiev, 2004] two processes of filtration of diluted calcium carbonate

suspensions in the presence of a dispersant (polyacrylic acid) were compared. In the first

process, the dispersant is added to diluted suspension before filtration and filtration is carried

out in a single stage. The second process is based on two-stage filtration described in

[Mouroko-Mitoulou, 2002; Husson, 2003]. This process involves precoat filtration of

deflocculated suspension [Mouroko-Mitoulou, 2002; Husson, 2003].The first stage of the new

process is an ordinary filtration with formation of cake precoat from diluted suspension

(naturally flocculated) without any dispersant (Fig. I.20.a). At the second stage, the diluted

suspension is mixed with the dispersant and then filtered on the precoat (Fig. I.20.b–c). The

new layer of cake, deposited on the surface of precoat, consists of particles covered by the

dispersant. The filtrate from deflocculated suspension (enriched with dispersant) displaces the

dispersant-free interstitial liquid remaining in the pores of precoat (Fig. I.20.c–d). Precoat

absorbs and retains the dispersant molecules coming from the deflocculated suspension and,


thus, prevents the filtrate from contamination. Finally, the particles of precoat adsorb the

dispersant, which uniformly imbues the whole filter cake .

suspensionwithout

dispersant

suspensionwith

dispersant

suspensionwith

dispersant

suspensionwith

dispersant

precoat

precoat precoat

precoat

final cake saturatedwith dispersant

(a)

(c) (d)

(b)

suspensionwithout

dispersant

suspensionwith

dispersant

suspensionwith

dispersant

suspensionwith

dispersant

precoat

precoat precoat

precoat

final cake saturatedwith dispersant

(a)

(c) (d)

(b)

Fig. I.20. Schema of the two-stages dead-end filtration process (after [Soua, 2006a])

It was shown that such two-stage dead-end filtration have noticeable advantages

compared to a simple cake filtration. As shown in Fig. I.21.a, duration of two-stage filtration

is shorter than that of simple filtration of deflocculated suspension. Filtration curve of the

two-stage filtration is smooth and has not breakpoint. The slopes of the curve at the first

(filtration of aggregated suspension) and at the second stage (filtration of deflocculated

suspension) are equal. As shown in Fig. I.21.b, this implies a relative constancy of the specific

cake resistance during the two stages. On the contrary, for simple filtration of deflocculated

CaCO3 suspension, Fig. I.21.b shows a rise in specific cake resistance with the dispersant

dose.

CaCO3 filter cakes were becoming fluid at a low shear rate (Fig. I.21.c) whatever the

process was used. Moreover, the two-stage filter cake was more fluid. There was no

dispersant loss in filtrate in the two-stage filtration.


0 0.1 0.2 0.3 0.4 0.5 0.6 0.767

68

69

70

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

1

2

3

4

5

6

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

1

2

3

cdisp, % wt

cdisp, % wt

Vis

cosi

ty, P

a·s

(γ=

13

s–1 )

Spec

ific

cak

e re

sist

ance

, 10

12m

/kg

simple filtration

two-stage filtration

simple filtration


(b)

(c)

·

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

1

2

3

4

5

6

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

1

2

3

cdisp, % wt

cdisp, % wt

Vis

cosi

ty, P

a·s

(γ=

13

s–1 )

Spec

ific

cak

e re

sist

ance

, 10

12m

/kg

simple filtration


simple filtration


(b)

(c)

·

0 0.2 0.4 0.6 0.8 1 1.2 1.40

2

4

6

8

10

(t–

t 0)/

(V–

V0)

, 10

–6

s/m

3

V + V0, 10 – 4 m3

simple filtration

first stage

(a)

second stage

0 0.2 0.4 0.6 0.8 1 1.2 1.40

2

4

6

8

10

(t–

t 0)/

(V–

V0)

, 10

–6

s/m

3

V + V0, 10 – 4 m3

simple filtration

first stage

(a)

second stage

cdisp, % wt

Dry

ness

, % w

t

simple filtration


(d)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.767

68

69

70

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

1

2

3

4

5

6

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

1

2

3

cdisp, % wt

cdisp, % wt

Vis

cosi

ty, P

a·s

(γ=

13

s–1 )

Spec

ific

cak

e re

sist

ance

, 10

12m

/kg

simple filtration


simple filtration


(b)

(c)

·

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

1

2

3

4

5

6

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

1

2

3

cdisp, % wt

cdisp, % wt

Vis

cosi

ty, P

a·s

(γ=

13

s–1 )

Spec

ific

cak

e re

sist

ance

, 10

12m

/kg

simple filtration


simple filtration


(b)

(c)

·

0 0.2 0.4 0.6 0.8 1 1.2 1.40

2

4

6

8

10

(t–

t 0)/

(V–

V0)

, 10

–6

s/m

3

V + V0, 10 – 4 m3

simple filtration

first stage

(a)

second stage

0 0.2 0.4 0.6 0.8 1 1.2 1.40

2

4

6

8

10

(t–

t 0)/

(V–

V0)

, 10

–6

s/m

3

V + V0, 10 – 4 m3

simple filtration

first stage

(a)

second stage

cdisp, % wt

Dry

ness

, % w

t

simple filtration


(d)

Fig. I.21. Comparison of simple (empty symbols) and two-stage (full symbols) filtration.

(a) filtration curves in Ruth-Carman’s coordinates, total dispersant dose cdisp = 0.5% wt;

(b) cake specific resistance versus dispersant concentration;

(c) viscosity of filter cakes versus dispersant concentration;

(d) final dryness of the filter cake.

After [Vorobiev, 2004].

It should be noted, that viscosity of the concentrated suspension of calcium carbonate

decreases significantly after addition of the dispersant, while specific resistance of the filter

cake prepared in the simple dead-end filtration increases only in ~ 4 times (Fig. I.21.b–c).

I.2.12.5. Action of PAA on filtration of CaCO3 suspensions

[Soua, 2006b] has shown that zeta-potential of CaCO3 decreased from approx. + 4 mV to

– 40 mV with increase of PAA dose. But dry matter of the filter cake remaining after simple

filtration (Fig. I.21.d) did not vary much: from ~ 68.5 % wt at cdisp = 0% to 69.5 % wt at

cdisp = 0.7%. So, porosity of the filter cake did not vary much with the dose of dispersant.

Meanwhile, viscosity of suspension was dropping with the dispersant. This suggests that

hydrodynamic forces, which structure the filter cake during filtration, dominate over the

repulsive forces created by the dispersant. Therefore, there is only low effect of a dispersant

on the filter cake formation and structure.


One can explain such a moderate influence of the dispersant on arrangement of particles

in a concentrated suspension by dense structure of aggregates and grain-like shape of the

particles of CaCO3.

[Brinker, 1990] indicated that the structure of filter cakes made up of particles with

regular shape and uniformly charged surface may be less sensitive to repulsion and

orientation of particles than when the particles are plate-like or needle-like. Therefore, the

influence of a dispersant on filtration should be much more important for plate-like kaolin

particles than for grain-like CaCO3 particles. Next Section discusses why the structure and

specific resistance of a concentrated suspension of plate-like particles is more sensitive to the

mutual orientation of particles and cites some experimental results on orientation of particles

during dead-end filtration.

I.2.13. Effect of aspect ratio and orientation of particles on specific cake resistance

I.2.13.1. Theory: effect of particle orientation on permeability

[Lu, 2005] reported a theory of “barrier properties of composites” that can be used for

depiction of the influence of aspect ratio and orientation of particles on specific resistance of a

filter cake. The theory considers permeability coefficient of a system filled with plate-like

particles. The permeability estimation is based on calculation of two parameters: tortuosity

factor and ‘barrier probability’. ‘Barrier probability’ is the probability of formation of

completely non-permeable portion of the system. Both parameters are functions of the particle

aspect ratio (2R/r), orientation and volume fraction of particles (φ). The authors give the

following formulas for estimation of ‘barrier probability’ k' and tortuosity t'

rRt /21 (I.77)

rRS

k /23

12 (I.78)

where S is orientation parameter depending on the maximum angle between particles : S = 1

for parallel ordering of particles, S = 0 for random particles distribution.

Fig. I.22 presents influence of the shape and arrangement of particles on barrier properties

of suspension at the given concentration of particles estimated by means of equation I.78.

In a system of randomly oriented particles (S = 0), the barrier probability and, therefore,

resistance to flow, increases with the increase of particle aspect ratio.


1 2 3 4 5 6 7 8 9 10

0 1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

aspect ratio, 2R/r

orientation parameter, S

k'/φ S = 0

asp. ratio = 1

asp. ratio = 10

1 2 3 4 5 6 7 8 9 10

0 1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

aspect ratio, 2R/r

orientation parameter, S

k'/φ S = 0

asp. ratio = 1

asp. ratio = 10

Fig. I.22. Influence of particle aspect ratio and orientation on the barrier probability.

For high aspect ratio particles, the cake resistance will increase even more with alignment

of particles (perpendicularly to the flow). This factor is absent in a system of regular shape

isometric (e.g., spherical) particles. Other theories of “barrier properties” lead to the similar

conclusions [Cussler, 1988; DeRocher, 2005].

In addition, according to Fig. I.18, parallel orientation of the plate-like particles increases

their percolation threshold. Therefore, it means that higher concentration of particles is

accessible in suspension with aligned particles. But it results in lower suspension porosity and

worse permeability.

I.2.13.2. Experimental data on orientation of particles during dead-end filtration

It is clear that existence of particle alignment may be quite an important factor in filtration

of anisotropic particles. Naturally, alignment of particles should increase at higher suspension

concentration [Onsager, 1949]. Ordering of platey colloidal mineral particles at high

suspension concentrations was observed in a number of studies referred in [Davidson, 2003].

Hence, one can expect that kaolin particles will be much more ordered than grain-like

particles. As a result, filter cakes of the kaolin particles are also much more impermeable.

[Moan, 2003] observed on SEM images the striated structure of particles in concentrated

suspensions (not filter cakes) of deflocculated kaolin (φ = 0.55). They have suggested that

kaolin plates were aligned parallel to each other. The local parallel order persisted in a

distance of only few micrometers. The overall chaotic orientation of the ordered domains of

particles was, probably, the consequence of mixing the suspension before the measurement.

Orientation of plate-like particles in filter cakes and dense suspensions was observed in

several studies. In [Perdigon-Aller, 2005] preferred orientation of kaolin particles was

observed by means of non-invasive neutron scattering technique and extent of particle


orientation was related to the cake dryness and permeability. It was shown that alignment of

particles enhances with increase of cake dryness (in the studied range of particle volume

fraction φ = 0.2–0.5). Weakly aggregated natural suspensions were found to form the cakes

with lower alignment of particles than suspensions deflocculated with polyacrylic acid. The

extent of the preferred orientation of particles was estimated by means of orientation

parameter S ; it reached the value of S = 0.5 at φ = 0.35. Influence of the orientational order on

permeability was compared for weakly aggregated and deflocculated suspensions. It was

observed that for both types of suspensions ordering of particles resulted in decrease of

permeability, however, the permeability of deflocculated filter cakes was much lower than

that of aggregated with the same value of orientation parameter S. Hence, orientation

parameter is not a single factor influencing permeability of the filter cakes.

In [Pignon, 2000], the structure of filter cakes formed during filtration of disk-like mineral

particles of Laponite (aspect ratio = 30) was studied. The authors had shown that Laponite

particles are packed with anisotropic arrangement parallel to the membrane. Addition of

dispersant (diphosphate) changes ordering of the particles for more regular; such ordered

arrangement of particles leads to lower cake permeability.

Influence of the particle (cell) shape on filtration of bacterial suspensions was reported in

[Mota, 2002]. It was shown that shear-induced mutual alignment of rod-like bacteria

pronouncedly reduced permeability of filter cakes prepared in cross-flow filtration as

compared to those obtained in dead-end filtration.

Influence of the concentration of particles on their orientation and durability of

concentrated kaolin suspension was studied in [Babak, 1986]. The study was based on

computer analysis of ESEM pictures of compressed suspensions and rheological

measurements. It was shown that increase of solid volume fraction resulted in a complex

transformation of particle orientation. Initial increase in the volume fraction of particles (φ)

was leading to only insignificant decrease of the mean angle between particles, while number

of interparticle contacts was increasing significantly until φ reached some critical value (and

the angle between particles reached ~ 70°). After the critical point, the angle between particles

was steeply decreasing with increase of particle concentration, while the number of

interparticle contacts remained constant. Observed complex behaviour should reflect

transformation between formation and compression of dense aggregates. Additionally, it was

deduced that durability of a compacted suspension increases with increase of particle

orientation, because the strength of single interparticle contact increases with decrease of the

angle between particles.


I.2.14. Summary

Due to high aspect ratio of particles and complex distribution of particle surface charge,

kaolin suspensions are highly viscous in natural state. So, preparation of flowable and

concentrated kaolin suspensions requires application of a dispersant. However, highly loaded

and stabilized kaolin suspensions may display shear-thickening and even shear-hardening at

high shear-rates. In addition, filtration of dispersed suspensions may results in ordering of

kaolin particles and decrease in the filter cake permeability. These phenomena are also related

to particularities of kaolin particle geometry.

It follows from the Section I.2 that preparation of a concentrated and flowable mineral

suspension by means of dead-end filtration requires optimization of pretreatment method. The

factors increasing flowability and dryness of the filter cake also increase the time of filtration,

and vice versa. Therefore, it is necessary to study all the properties of kaolin suspensions

(structural, rheological and filtration) in a single study.


Notation for Section I.3 .......................................................................................................... 69

I.3. Dynamic filtration of concentrated mineral suspensions ............................................. 70

I.3.1. Arguments for cake removal during filtration of concentrated suspensions .......... 70

I.3.2. Background on dynamic filtration .............................................................................. 72

I.3.3. Models of dynamic filtration ........................................................................................ 73

I.3.3.1. Macroscopic models of dynamic filtration .............................................................. 73

I.2.3.2. Microscopic models of dynamic filtration ............................................................... 75

I.3.3.3. Distribution of particles sizes in the deposit layer in cross-flow filtration ........... 77

I.3.3.4. About the irreversibility of particles deposition ..................................................... 79

I.3.3.5. Erosion of the deposit in cross-flow filtration ......................................................... 80

I.3.3.6. Effect of particles interaction on deposit ................................................................. 81

I.3.3. Dynamic filtration of concentrated and stabilized mineral suspensions ................. 84

I.3.4. Attempts to maximize the suspensions concentration ............................................... 86

I.3.5. Summary ....................................................................................................................... 89



a particle size [m]

b height of the cell [m]

c concentration of suspension

Cc parameter, defined by Eq. (I.86a)

Cg gel concentration

Co bulk concentration

D diffusion coefficient [m2/s]

FA force of adhesion between particles [N]

FD drag force of cross-flow [N]

FF friction force [N]

FL lift force [N]

FY sum of drag force of filtrate and force of interaction between particles [N]

J filtrate flux [m3/(m2s)]

kf parameter, defined by Eq. (I.86a)

Km parameter, defined by Eq. (I.80)

Δp filtration pressure, transmembrane pressure, TMP [Pa]

Q volume velocity of suspension [m3/s]

Rd resistance of deposit [m–1]

Rm membrane resistance [m–1]

t time [s]

tw wall shear stress [Pa]

x distance [m]

Greek letters

δ thickness of deposit [m]

ηl viscosity of liquid [Pas]

ρ density of liquid [kg/m3]



I.3. Dynamic filtration of concentrated mineral suspensions

I.3.1. Arguments for cake removal during filtration of concentrated

suspensions

It was shown in Section I.2 that use of chemical additives can not increase the rate of

dead-end filtration without paying a penalty in terms of lower dryness of the filter cake, and

vice versa. Addition of flocculants or dispersants to the feeding suspension always gives dual

results. Flocculation yields large and loosely packed flocs with voluminous pores, which are

beneficial for fast filtration. But such flocs retain an excess of water in the pores.

Deflocculation of suspensions reduces the pore volume and leads to higher dryness. However,

higher tortuosity of pores in a dispersed filter cake results in higher hydraulic resistance and

longer filtration.

A promising way to improvement of filtration kinetics and preparation of a concentrated

(and flowable) suspension is to avoid or to delay the cake formation. Raha et al. [2009] have

modeled the influence of periodic and continuous removal of a filter cake on kinetics of a

dead-end filtration. They have shown by results of simulation that the filtration time decreases

with increase of a number of successive homogenizations of the filter-cake with suspension.

The filtration time is minimal for continuous homogenization of the formed cake with

suspension (Fig. I.23). With continuous homogenization filtration rate depends more on the

membrane resistance Rm than on the properties of suspension.

average solid volume fraction φ

filt

rati

on ti

me

t, s

00.35φ

500

0.07 0.14 0.21 0.28

1000

1500

2000

t

conventionaldead-end

with continuoushomogenization


filt

rati

on ti

me

t, s

00.35φ

500

0.07 0.14 0.21 0.28

1000

1500

2000

t



500

0.07 0.14 0.21 0.28

1000

1500

2000

t



Fig. I.23. Influence of a number of successive homogenizations Nh = 0, 1…4 and

(continuous homogenization) on the time of dead-end filtration of alumina suspension

(modeling). Insert shows experimental data. After [Raha, 2009].


This prediction was examined via a lab-scale filtration test [Raha, 2009]. Alumina

suspensions were filtered with and without homogenization of the formed cake and

suspension. In this experiment, homogenization involved mixing of the formed cake with

suspension by spatula. In was observed that homogenization led to significant reduction in

filtration time. While the cake dryness was the same as in conventional dead-end filtration

(see insert in Fig. I.23).

It was also predicted in [Raha, 2009] that filtration of concentrated suspension can be

even more efficient if the suspension is deflocculated. Fig. I.24 shows the effect of

deflocculation and single homogenization on the dead-end filtration of alumina suspensions.

Deflocculation was carried out changing the pH, from pH 7.6 to pH 3.3. Fig. I.24.a shows

results of modeling while Fig. I.24.b shows experimental results. It was shown by

computation that simultaneous homogenization and deflocculation of suspension reduce the

filtration time by two and permit achieving of the solid volume fraction in the filter-cake (φ )

about 0.7. The experiments confirmed prediction of the model for the filtration time, but the

achievable dryness was substantially lower φ = 0.54.


filt

rati

on ti

me

t, s

simulation


filt

rati

on ti

me

t, s

experiment

a: pH = 3.3 (dead-end)b: pH = 7.6 (dead-end)c: pH = 7.6 (1st stage)

pH = 3.3 (2nd stage)

1st

2nd

1st2nd

a

b

c

a

bc



homog. homog.

(a) (b)


filt

rati

on ti

me

t, s

simulation


filt

rati

on ti

me

t, s

experiment



1st

2nd

1st2nd

a

b

c

a

bc



homog. homog.


filt

rati

on ti

me

t, s

simulation


filt

rati

on ti

me

t, s

experiment



1st

2nd

1st2nd

a

b

c

a

bc



homog. homog.

(a) (b)

Fig. I.24. Dead-end filtration of deflocculated suspension (curve a). Dead-end filtration of

aggregated suspension (curve b). Filtration with intermediate homogenization and

deflocculation (curve c). The moment of homogenization is shown by an arrow. After [Raha,

2009].

In summary, both continuous homogenization and deflocculation of suspension are

beneficial for filtration of concentrated suspensions. The experimental data show that

homogenization of the filter cake results in faster filtration, while deflocculation of

suspension results in higher final dryness. Unfortunately, the maximal dryness of the alumina

suspension was not achieved in the experiments carried out in [Raha, 2009]. Homogenization


was implemented by a simple, but not conventional method, which is difficult to realize in a

large scale. In practice, homogenization of suspension may be carried out by one of a number

of dynamic filtration methods. Obviously, further investigation is required to clear up the

question: “How to prepare a very concentrated but flowable mineral suspension in a short

time by means of conventional filtration technique?”

I.3.2. Background of dynamic filtration

Dynamic filtration comprises a number of methods developed for avoiding the filter cake

formation during pressure filtration. In those methods the particles are continuously swept

away from the surface of membrane by the high-shear fluid flow. Due to the fluid flow, the

cake does not form at all or only a thin layer of the residual cake deposits. Hence, the rate of

dynamic filtration may be much higher than the rate of dead-end filtration. The thickness of

the residual cake in a dynamic filter depends on the hydrodynamics of the flowing slurry

adjacent to the membrane surface. The shear flow may be created either by recirculation of

the processed suspension, or by rotating/vibrating disks and membranes [Wronski, 1989;

Ripperger, 2002].

pext

M1M2

M3M4

V2

V1

V3

tank withsuspension

pump

permeate

flow meter

filtrationcell

filtration cell

drainagefilter

permeate

deposit

flowingsuspension

pext

M1M2

M3M4

V2

V1

V3

tank withsuspension

pump

permeate

flow meter

filtrationcell

pext

M1M2

M3M4

V2

V1

V3

tank withsuspension

pump

permeate

flow meter

filtrationcell

filtration cell

drainagefilter

permeate

deposit

flowingsuspension

Fig. I.25. Schema of cross-flow filtration apparatus. M – manometers, V – valves.

Dynamic filtration is called cross-flow (or tangential) if the suspension flows is parallel to

the membrane surface. Membranes may be different in shape: flat, cylindrical, spiral. Fig. I.25

presents the schema of a common cross-flow filtration apparatus. The rate of cross-flow

filtration is mainly determined by two parameters: suspension velocity Q and transmembrane

pressure Δp.


Fil

trat

e fl

ux, l

·m–2

·h–1

Lay

er th

ickn

ess,

mm

Time, min

Fil

trat

e fl

ux, l

·m–2

·h–1

Lay

er th

ickn

ess,

mm

Time, min

Fig. I.26. Cross-flow filtration of diatomaceous earth (after [Altmann, 1997]).

Figure I.26 shows typical evolutions of the permeate flux and cake thickness during a

cross-flow filtration. At the beginning, the permeate flux steeply decreases due to deposition

of particles on the membrane surface. In addition, blocking of membrane pores may also

account for this decrease. If Q is high enough, the deposit does not grow anymore. So, it is

possible to get a quasi-steady permeate flux for a long time [Altmann, 1997; Li, 2002].

The deposition of particles and cross-flow filtration are influenced by a great number of

parameters, such as cross-flow velocity, transmembrane pressure, membrane resistance,

deposited layer resistance, concentration of suspension, particle shape and size distribution,

aggregation state of suspension and interaction between particle and membrane surface. The

deposit growth and compression is the main factor influencing dynamic filtration. A lot of

methods were proposed for in situ observation of this process [Chen, 2004] and many models

were created to describe deposition of particles [Ripperger, 2002].

I.3.3. Models of dynamic filtration

According to [Ripperger, 2002], the models created to describe the cross-flow filtration

(and dynamic filtration generally) can be of two types: macroscopic and microscopic. The

macroscopic approach considers the system of particles as a continuum, while the

microscopic models consider behaviour of a single particle during filtration. Both approaches

assume that the factors of deposit formation are hydrodynamics, diffusion of particles and

particle-deposit interaction.

I.3.3.1. Macroscopic models of dynamic filtration

Macroscopic models (e.g. [Porter, 1972]) assume that the profile of particle concentration

near the membrane surface is maintained by two opposite transport processes: convective


transport of filtrate flow toward the membrane and diffusive movement of particles away

from the membrane surface and back into the bulk stream. In the stationary state, both

transport mechanisms are in balance. If concentration of particles c depends only on the

distance from the membrane x, then

dx

dcDcJ (I.79)

where J is the filtrate flux, and D is diffusion coefficient. The left term of Eq. (I.79) is the

convective transport of particles. Right term represents diffusive transport.

Next boundary conditions may be taken:

- the concentration of particles in the deposit (or ‘gel layer’) is uniform and equal to Cg;

- once the deposit is formed, its thickness δ remains constant;

- the concentration of particles in bulk is supposed to be uniform and equal to C0.

Thus, the equation (I.36) gives

00

lnlnC

CK

C

CDJ g

mg

(I.80)

where Km is the mass transfer coefficient. Equation (I.80) suggests that the rate of dynamic

filtration drops to zero as concentration of particles approaches to Cg. The effect of shear flow

is contained in Km. According to Porter [1972]:

Km ~ Q0.33/b0.66 (for laminar flow in the filter cell) (I.81)

Km ~ Q0.8/b (for turbulent flow in the filter cell) (I.82)

where Q is the volumetric flow rate of suspension, b is the height of the filter cell. A review

of Eqs. I.80–I.82 shows that the flux J may be increased by increasing Q or decreasing b.

Filtration rate dependence on the fluid velocity Q is much more pronounced for the turbulent

flow. Therefore, different techniques were implemented for creation of turbulence and

acceleration of filtration: turbulence promoters [Gupta, 1995; Krstićś, 2004; Mori, 2008;

Li, 2009], pulsatile flow [Gupta, 1992; Howell, 1993; Jaffrin, 1994], helical filter cells [Al-

Akoum, 2002], membranes placed on rotating disks, vibrating systems (reviewed in

[Wakeman, 2002; Jaffrin, 2008]).


I.2.3.2. Microscopic models of dynamic filtration

Microscopic models of dynamic filtration (e. g. [Altmann, 1997; Sethi, 1997; Bowen,

2001]) consider hydrodynamic, adhesive and friction forces acting on a single particle.

Balance of these forces is sketched in Fig. I.27. Lift force FL and drag force FD are caused by

shear flow, while drag force FY is caused by filtrate flow. It was shown in [Altmann, 1997]

that the main forces, which determine whether or not the streaming particle attaches to the

deposit, are the lift force FL and the drag force FY.

cross-flow direction

lift forceFL

drag forceof cross-flow FD

friction forceFF

drag force of filtrate FY+ particle interaction

filtrate flow direction

cross-flow direction

lift forceFL

drag forceof cross-flow FD

friction forceFF

drag force of filtrate FY+ particle interaction

filtrate flow direction10-1 100 101

10-12

10-11

10-10 FL FY φ = 0.01J = 1000 l/(m2h)

FY φ = 0.30J = 100 l/(m2h)

For

ce, N

FY φ = 0.01J = 100 l/(m2h)

particle size a, μm10-1 100 101

10-12

10-11

10-10 FL FY φ = 0.01J = 1000 l/(m2h)

FY φ = 0.30J = 100 l/(m2h)

For

ce, N

FY φ = 0.01J = 100 l/(m2h)

particle size a, μm

Fig. I.27. Forces acting on a particle in cross

flow filtration (after [Ripperger, 2002]).

Fig. I.28. Lift force FL and filtrate drag force FY

acting on a streaming particle as a function of

particle size (at different filtration conditions).

Calculated by the author.

The drag force FY can be estimated by means of Stoke’s equation:

FY = 6 π l a J f(φ) (I.83)

where l is the viscosity of liquid, a is the particle size, J is the velocity of filtrate and f(φ) is a

correction function, which steeply increases with the increase of particle concentration

[Altmann, 1997]. Therefore, the particle deposition is much more probable in concentrated

suspension.

The lift force FL may be estimated as:

FL = l

w a

5.035.1

1.6 (I.84)

where τw is the shear stress in the vicinity of the membrane, ρ is the density of liquid

[Altmann, 1997].


Comparison of equation (I.83) with (I.84) suggests that the particle deposition depends on

the particle size a. Figure I.28 shows an estimation of the hydrodynamic forces acting on a

streaming particle at different filtration rates J = 100 and 1000 l/m2h for diluted (φ = 0.01) and

concentrated (φ = 0.3) suspensions. Other parameters: l = 10–3 Pas, ρ = 103 kgm–3,

τw = 100 Pa (typical values in cross-flow filtration). As Fig. I.28, shows, the lift force is higher

than the drag force in a wide range of particle sizes at low filtration rates and low

concentrations of particles.. It means that the particles will be transported away from the

deposit layer. At high filtration rates or at high concentration of suspension, FL > FY only for

large particles, while for small particles FL < FY. Therefore, particles with size a < 0.45 μm

will attach to the deposit layer (at J ≥ 1000 l/(m2h) in suspensions with φ = 0.01, and at

J ≥ 100 l/(m2h) in suspensions with φ = 0.3 (see Fig. I.28)). Deposition of small particles

increases specific resistance of the deposit. As a result, the filtration rate decreases.

Equations (I.83) and (I.84) consider only hydrodynamic effects. They suggest decrease of

filtration rate with increase of the particle size. However, for submicron particles,

consideration of diffusion factor is quite necessary. Consideration of a diffusion-induced

back-transport of particles away from the membrane suggests increase of filtration rate with

decrease of the particle size: in Eq I.80, J ~ 1/a, since D ~ 1/a according to Einstein-Stokes

equation. Combination of hydrodynamic effects (Eqs. (I.83–I.84)) and diffusion (Eq. (I.80))

suggests that the minimum of filtration rate exists in the particle size range between 0.05 and

0.5 μm [Ripperger, 2002], [Sethi, 1997]. If particle size a ≤ 0.1 μm, filtration is determined

mainly by the diffusion, filtration rate increases with decrease of a. If particles are larger than

1 μm, filtration is mainly controlled by hydrodynamics and filtration rate increases with

increase of a. If particle size equals to approx. 0.1 μm, the net back transport away from the

membrane attains the minimum, thus leading to the maximum cake growth [Sethi, 1997].

Once the particle is deposited, it is necessary to consider a new force FA (adhesion force)

in order to know whether this particle will leave the surface of the deposit or will remain

fixed. The estimation of the particle adhesion is complicated, since a lot of parameters are

involved, including the particle shape, the number of contact points and electrostatic

repulsion. If we assume that the particles are spherical and uncharged, FA may be estimated

according to van der Waals equation:

)12/( 2HAaFA (I.85)

where A is Hamaker’s coefficient and H is the distance between the particles.


Figure I.29 shows the values of FA, FY and FL calculated using Eqs. I.83–I.84, as a

function of particle size assuming H = 1 nm and A = 10–20 J. These last values stand for

calcium carbonate in saline water (after [Kosmulski, 2003]).

10-1 100 10110-11

10-10

10-9

10-8

10-7

FL

FY +FA

For

ce, N

particle size a, μm10-1 100 10110-11

10-10

10-9

10-8

10-7

FL

FY +FA

For

ce, N

particle size a, μm

Fig. I.29. Lift force FL and adhesion forces

FY + FA, acting on a particle attached to the

deposit, as a function of particle size.

Calculated by the author.

Fig. I.29 shows that the lift force exceeds the adhesive force only if the particle size is

large enough, i.e., a > 2.5 μm. It means that a small single particle is irreversibly attached to

the deposit and cannot return into the cross-flow. Only large particles or strong particle

aggregates can be swept away from the surface.

In summary, the sketch of forces acting on a particle during dynamic filtration allows to

make next conclusions:

the probability of particle deposition is higher for small particles than for large particles;

deposition of small particles is irreversible (in contrast to deposition of large particles).

I.3.3.3. Distribution of particle sizes in the deposit layer in cross-flow filtration

Numerous experimental studies revealed other peculiarities of particle deposition in a

cross-flow filtration.

Ripperger and Altmann [2002] have studied the growth of deposit during cross-flow

filtration of a polydisperse mineral suspension. They showed that the favored deposition of

small particles results in formation of more compacted and less permeable top layer of the

deposit. It decreases the drag force of the filtrate, which results in deposition of even smaller

particles and formation of even denser top layer. Such a ‘size classification’ of particles in the

top layer of the deposit makes its resistance rising as it is shown in Fig. I.30. It explains, why

deposit thickness in Fig. I.26 reaches a steady-state more quickly than the filtration rate.


laye

r re

sist

ance

, 1/m

deposited layer thickness, mm

laye

r re

sist

ance

, 1/m

deposited layer thickness, mm

depo

sit t

hick

ness

, mm

transmembrane pressure, bar

depo

sit t

hick

ness

, mm

transmembrane pressure, bar

Fig. I.30. Evolution of deposit layer

resistance with its thickness

(after [Ripperger, 2002]).

Fig.I.31. Variation of deposit layer thickness

during filtration of silica at constant Q and

increasing p (after [Altmann, 1997]).

In addition, electron microscopic images of the deposit cross section confirmed the

asymmetrical deposit structure [Ripperger, 2002].

The size selective deposition of particles was also studied in [Foley, 1995; Chellam, 1998;

Klein, 1999]. Simulation of cross-flow filtration by Foley et al. [1995] has demonstrated that

higher suspension velocity Q results in higher specific resistance of deposited layer. The

cause is in increase of FY and preferential deposition of the smallest particles. Nevertheless,

filtration rate was not much affected by increase in specific resistance because of the decrease

in deposit thickness at higher Q. It was found that the specific resistance of deposit decreases

with the increase of transmembrane pressure (TMP) [Foley, 1995]. The cause is in increase of

FY and preferential deposition of the largest particles. [Chellam, 1998] and [Klein, 1999] have

studied experimentally the size distribution of deposit particle in cross-flow filtration. They

observed that the percentage of small particles in the deposit (and its specific resistance) was

much higher if the shear is ntense. This effect was substantial even for suspensions with

narrow particle size distribution [Chellam, 1998]. They pointed out that the specific

resistances of deposits in cross-flow filtration were 5 to 132 times higher than those of cakes

in conventional dead-end filtration. Furthermore, [Meier, 2002] have added that the size

classification of deposited particles is more pronounced under turbulent flow than under

laminar flow. They have demonstrated in pilot scale experiments that dynamic filtration may

be used for wet classification of colloidal particles (separation of small particles from large

ones).


I.3.3.4. Irreversibility of particle deposition

Irreversible deposition of particles was evidenced in the experiments of Altmann and

Ripperger [1997]. They have carried out cross-flow filtration of monodisperse silica

suspensions . The suspensions were filtered at constant cross-flow velocity but variable TMP:

progression from 0 to 2.5 bar at the first stage and regression from 2.5 bar to 0 bar at the

second stage. They observed that at the first stage the filtrate flux was governed only by

membrane resistance until TMP of 0.5 bar. At TMP > 0.5 bar, the filtrate drag force exceeded

the lift force and the deposit started to grow (see Fig. I.31). Afterwards, during the descending

of TMP, the deposit thickness did not change significantly. Therefore, silica particles seem to

be irreversibly deposited on the membrane under these conditions of filtration.

0 1 2 3 40

0.4

0.8

TMP, bar

resi

stan

ce R

d, 1

011m

-1

1st TMP cycle

2nd TMP cycle

0 1 2 3 40

0.4

0.8

TMP, bar

resi

stan

ce R

d, 1

011m

-1

1st TMP cycle

2nd TMP cycle

velocity, m/s

resi

stan

ce R

d, 1

012m

-1

10.5 20 1.50

0.5

1

1.5

2A B

CD

velocity, m/s

resi

stan

ce R

d, 1

012m

-1

10.5 20 1.50

0.5

1

1.5

2A B

CD

10.5 20 1.50

0.5

1

1.5

2A B

CD

Fig. I.32. Deposit resistance under cyclical

variation of pressure at constant suspension

velocity v (after [Benkahla, 1995]).

Fig. I.33. Deposit resistance under cyclical

variation of v at constant TMP (after[Ould-

Dris, 2000]).

This question of irreversibility of the deposition was investigated in more details by

[Benkahla, 1995], [Ould-Dris, 2000] and [Huisman, 1998]. [Benkahla, 1995] and [Ould-

Dris, 2000] have tested diluted suspensions of calcium carbonate in demineralised water.

[Benkahla, 1995] performed several successive cycles of TMP ascending and descending at

constant suspension flow rate. They observed that the resistance and thickness of the deposit

formed during ascending of TMP remained constant during the descending step (see

Fig. I.32). At next step of TMP ascending, the deposit thickness and resistance also remained

constant until the maximum value of TMP of the previous cycle was attained. Then the

deposit grew again with ascending of TMP. Constancy of the deposit resistance during the

descending steps confirms irreversibility of deposition of CaCO3 particles. In addition, it was


shown in some separate dead-end filtration experiments that the ascending TMP causes an

irreversible compression of the filter cake.

In order to explain experimental results presented in Fig. I.32, [Benkahla, 1995] suggested

that deposit growth is limited by the shear stress on its surface τw

τw = kf Δp + Cc (I.86.a)

where Δp is TMP, kf and Cc are friction and cohesion, respectively. Parameters kf and Cc are

functions of the properties and concentration of surface particles. Cc is equivalent to the yield

stress of the deposit and increases with deposit’s compression. The value of shear τw is

proportional to shear rate

and, therefore, to the velocity of suspension v:

τw =

b

vss (I.86.b)

where s is the suspension’s viscosity, b is the channel height of the filtration cell, δ is the

thickness of the deposit. Eq. (I.86.a) presents Coulomb’s criterion for particles in the top layer

of the deposit. It means that at constant velocity of suspension and constant TMP, deposit

grows until τw reaches the value of the right term of Eq. (I.86.a). Further increase of TMP

results in increase of the deposit thickness: δ reaches a new equilibrium value. Increase of

TMP also results in compression of the deposit and strong increase of Cc. That is why, TMP

decrease causes only small decrease of the deposit resistance. Due to irreversible compression

of the deposited layer, the value of the right term of Eq. (I.86.a) remains high as compared to

τw even if TMP decreases.

I.3.3.5. Erosion of the deposit in cross-flow filtration

Eqs. (I.86.a–I.86.b) also indirectly show that the deposit may be eroded at shear stress

τ > τw (τw is the shear stress at which the deposit was formed).

[Ould-Dris, 2000] have investigated conditions for erosion CaCO3 deposit. Fig. I.33

shows the deposit resistance under cyclical variation of the suspension velocity v at constant

TMP. The deposit formed at relatively low velocity of 0.3 m/s (point A) remained undisturbed

until the velocity reached 1.1 m/s (point B). Above this point, erosion of the deposit started

and its resistance dropped until 1.75 m/s (point C). In the range between point C and D the

filtration rate was determined by membrane resistance since the deposit was practically

absent. This regime maintained until 0.8 m/s (point D). Then, the deposit was reconstituting

with the decrease of speed until point A.


According to Eq. (I.86.b), the shear stress effect on the deposit (at constant v) was higher

at higher suspension viscosity and concentration. So, it was logically found that the erosion of

deposit started at lower velocity under these conditions. However, [Ould-Dris, 2000] have

also shown that the filtration rate declined with the increase of particles concentration from 60

to 700 g/l, probably, due to an enhanced transport of particles to the membrane surface.

[Ould-Dris, 2000] have found that the erosion shear stress is a linear function of TMP. It

confirms the validity of equation I.86. This equation suggests that the deposition with lower

cohesion may get eroded at lower shear stress. Unfortunately, the effect of interaction

between particles was not studied in [Benkahla, 1995, Ould-Dris, 2000] .

I.3.3.6. Effect of interaction between particles on the deposit

A decrease of cohesion between particles (that is, an increase of particle repulsion) may

trigger off:

formation of a denser deposit with higher specific resistance. The mechanism is explained

in section I.2. Disaggregation of particles results in lower average particle size. The lift forces

become weaker which, which means an irreversible particle deposition.

higher sensitivity to shear stress than in deposit with aggregated particles. Increase of

repulsion between particles must decrease friction kf and cohesion Cc between the particles.

A beneficial effect of aggregation on dynamic filtration was demonstrated, for example, in

[Bacchin, 1996; Nguyen, 2002; Al-Malack, 2004; Zhao, 2005; Horčičková, 2009]. The

aggregation of particles was realized with a coagulant [Nguyen, 2002; Al-Malack, 2004]

[Ripperger, 2002; Šmidová, 2004]. In these articles, the flux improvement was attributed to

less compact and more porous deposit structure, which guarantees lower specific resistance

(see Fig. I.34).

a) b)a) b)b)

Fig. I.34. Structure of deposit in cross-flow filtration of diluted monodisperse silica

suspensions: a) stabilized, b) aggregated (after [Ripperger, 2002]).

[Bacchin, 1996] have analyzed separately the effect of aggregation of clay particles on

the deposit mass and filtrate flux. A salt was used for aggregation of particles. The mass of


deposit monotonously increased with the increase of salt concentration. Such behaviour was

explained by stronger adhesion of aggregates on the deposit. However, the filtrate flux did not

decrease monotonously. It was declining until critical concentration of coagulation (c.c.c).

Further addition of salt above the c.c.c results in increasing of the filtrate flux. This

phenomenon was explained by non-monotonous variation of the deposit specific resistance.

According to [Chang, 1995; Bacchin, 1996; Bowen, 2001] initial addition of salts results in

compression of the double electric layers of particles and decrease of interparticle distance. In

this case, the structure of deposit is similar to the structure of “repulsive gel” with narrow

pores. Further addition of salts results in destabilization of particles and triggers off their

aggregation. Under such conditions, the deposit consists of aggregated particles and has a

structure of “attractive gel” with wide pores and low specific resistance.

[Šmidová, 2004] have investigated the cross-flow filtration of kaolin suspensions at pH

around the isoelectric point of kaolin (i.e.p). They measured the filtrate flux in a steady-state

regime and observed that the curve of flux plotted versus pH was asymmetrical, with a peak

at i.e.p. The flux was significantly dropping above pHi.e.p. The kaolin particles were

aggregated at pH < pHi.e.p. and stabilized at pH > pHi.e.p. (see section I.2). So, it was assumed

that observed maximal flux can be explained by the lower resistance of the deposit of

aggregated particles. Increase of pH caused formation of an oriented structure of particles

with lower permeability. This assumption is reasonable if the deposit structure formed at

cross-flow filtration is similar to that formed at dead-end filtration. Unfortunately, specific

cake resistances of dead-end and dynamic filtrations were not compared in this article.

Importance of the shear effect on the structure of deposit composed from plate-like and

needle particles was evidenced in several studies [Mota, 2002; Perdigon-Aller, 2005;

Perdigón, 2007]. [Xu-Jiang, 1995] have reported some surprising results. For suspension of

talc, they have found lower specific resistance of deposit in cross-flow filtration compared to

that formed in dead-end filtration.

Beneficial effect of particle stabilization should be expected in dynamic filtration, since

repulsion between the particles facilitates erosion of the deposit [Huisman, 1998; Elzo, 1998].

[Elzo, 1998] have investigated the effect of particle zeta-potential on filtration of silica

suspension. At high absolute value of zeta-potential, the repulsive forces between the particles

dominate. It reduces the deposition, because repulsive forces act oppositely to the drag force

of the filtrate flow. Fig. I.35 illustrates that higher zeta potential modulus facilitates filtration.


25

20

15

10

–90 –70 –50 –30 –10

stea

dy-s

tate

flu

x, 1

0–6m

/s

particles zeta-potential, mV

25

20

15

10

–90 –70 –50 –30 –10

25

20

15

10

–90 –70 –50 –30 –10

stea

dy-s

tate

flu

x, 1

0–6m

/s

particles zeta-potential, mV

0 0.2 0.4 0.6 0.8 10

5

10

15

20

25

30

35

stea

dy-s

tate

flu

x, 1

0–6m

/s

TMP, bar0 0.2 0.4 0.6 0.8 1

0

5

10

15

20

25

30

35

stea

dy-s

tate

flu

x, 1

0–6m

/s

TMP, bar

Fig. I.35. Influence of stability of particles on

cross-flow filtration of silica suspensions

(after [Elzo, 1998]).

Fig. I.36. Reversible deposit formation

during cross-flow filtration of the stabilized

silica suspension (ζ = – 80 mV)

(after [Huisman, 1998]).

-100 -80 -60 -40 -20 00

0.2

0.4

0.6

0.8

1

reve

rsib

ility

of

depo

sitio

n R

I

zeta-potential, mV

-100 -80 -60 -40 -20 00

0.2

0.4

0.6

0.8

1

reve

rsib

ility

of

depo

sitio

n R

I

zeta-potential, mV

stea

dy-s

tate

flu

x, l/

(m2 ·

h)

concentration of suspension , %vol.0 10 20 30 40

0

5

10

15

20

25 0.4 m/s

0.8 m/s

1.2 m/s

stea

dy-s

tate

flu

x, l/

(m2 ·

h)

concentration of suspension , %vol.0 10 20 30 40

0

5

10

15

20

25

0 10 20 30 400

5

10

15

20

25 0.4 m/s

0.8 m/s

1.2 m/s

Fig. I.37. Influence of particles stability on

deposit formation: RI = 1 for completely

reversible, RI = 0 for completely irreversible

deposition (after [Huisman, 1998]).

Fig. I.38. Dependence of cross-flow

filtration rate on the concentration and

tangential velocity of titania suspension

(after [Mikulášek, 2004]).

[Huisman, 1998] observed formation of reversible deposits during cross-flow filtration of

stabilized (at high pH) silica suspensions of. Note that deposit was thicker at higher TMP. As

shown in Fig. I.36, The thickness of deposit either decreased (reversible deposition of

particles during filtration of stable suspension), or stayed constant (irreversible deposition

during filtration of aggregated suspension) with decrease of TMP, Fig. I.37 shows that

reversibility of deposition is a function of particle charge and, therefore, mutual repulsion of

particles.


Besides, Elzo [1998] and Huisman [1998] showed that cake deposition in dynamic

filtration may be reduced and the filtration velocity may be enhanced by stabilization of

suspension.

Vassilieff et al. [1994] showed that the deposit can be stagnant or flowing, depending on

the ratio between the shear stress and the deposit yield stress values. If the shear stress,

exerted on the deposit by the fluid, is lower than its yield stress, the deposit remains stagnant

and its thickness grows. If the shear stress exceeds the deposit yield stress, the upper layer of

the deposit starts flowing tangentially and the deposit stops growing, permitting the permeate

flux to reach a steady state.

These findings encourage the research of dynamic filtration methods for concentrating

mineral suspensions. Addition of a dispersant may substantially decrease the yield stress of

the concentrated suspension (deposit), and, therefore, reduce the cake formation and enhance

its erosion. In addition, the stabilized mineral suspensions may be processed (pumped and

stirred) even at very high concentrations of particles due to their low viscosity. Therefore,

combination of a dispersant and appropriate dynamic filtration technique represents an

interesting way for continuous preparation of concentrated and flowable mineral suspensions.

I.3.3. Dynamic filtration of concentrated and stabilized mineral suspensions

Dynamic filtration of concentrated suspensions requires very high shear rate. Mikulášek et

al. [Mikulášek, 1998; Mikulášek, 2004] carried out cross-flow filtrations of concentrated

titania suspensions (up to 48% vol.) in a tubular cross-flow filter. Suspensions were stabilised

with the help of a dispersant (sodium hexamethaphosphate). They observed the steep initial

flux decline at the beginning of filtration that was related to fast deposition of particles. So,

beginning of the cross-flow filtration was dead-end-like. After a while, the flux reached a

steady-state value. The deposit growth was terminated by the high shear exerted at its surface.

The steady-state flux is more pronounced at higher cross-flow velocity but gets reduced at

higher feed concentration (Fig. I.38). The authors proposed a simple equation relating the

total resistance of the deposited layer Rd with the concentration of suspension

w

d

ld

pR

max

2 (I.87)

where Δp is TMP, l is the viscosity of dispersion medium, d is the apparent viscosity of

deposit, τw is the shear stress acting on deposit surface, φ and φmax are volume fraction of

particles in the suspension and deposit, respectively. According to Eq. (I.87), the deposit

resistance decreases with the decrease of suspension viscosity. Intense cross-flow shear stress


may reduce the deposit resistance. However, concentration of suspension continues during

cross-flow filtration. The higher is the feed concentration, the stronger shear is needed for

reducing the deposition of particles. Eq. (I.87) shows that filtration drops to zero as φ tends to

φmax. [Mikulášek, 1998] reported that the filtrate flux tends to zero when the titania suspension

tends to φ = 0.6. This limit does not dependent on the shear rate and TMP.

Fig. I.38 shows that the filtration rate achievable in cross-flow filtration is too low even

for concentrations much lower than the limit. It seems that the shear stress value achievable in

cross-flow filtration is lower than that required for concentration of mineral suspensions.

[Wakeman, 2002] has reviewed numerous techniques for enhancing the shear flow and for

preventing cake formation. But most of them are restricted to cross-flow filtration of diluted

suspensions and clarification of fluids.

[Jaffrin, 2008] suggested that dynamic filtration with vibrating membranes or rotating

disks may be much better than cross-flow filtration (Fig. I.39). Its good performance is

determined by very high shear rates may be produced with a low inlet flow, and therefore, a

low pressure drop in the module. Consequently, very low TMP can be maintained, and

combination of high shear rates and low TMP facilitates reduction of deposit resistance (see

Eq. I.87). The very high shear rate created by shear-enhanced devices effectively reduces the

concentration polarization during ultrafiltration [He, 2007; Tu, 2009]

. Therefore, high TMP values are advantageous, as far as the permeate flux continues to

increase until higher pressure levels than in conventional cross-flow filtration. A number of

pilot-scale devices available for dynamic filtration are reviewed in [Bouzerar, 1999] and

[Tu, 2009].

Utilisation of rotating disk and rotating membrane systems was shown to be very effective

in microfiltration of moderately and highly concentrated mineral suspensions [Jönsson, 1996;

Bouzerar, 2003; Ding, 2006; He, 2007]. For instance, in [Ding, 2006; He, 2007] the CaCO3

suspension (without dispersant, mean particle size equals to 3 µm) reached concentration of

25 % wt. in a new pilot multishaft disk system (MSD) with overlapping ceramic membranes.

Filtrate flux was equal to 800 l/(m2h) at TMP = 200 kPa and disk rotation speed 1500 rpm.


inlet offeed suspension

outlet of filtrategap betweendisk and membrane

fixed membrane

outlet of retentate

manometer

rotating disk

inlet offeed suspension

outlet of filtrategap betweendisk and membrane

fixed membrane

outlet of retentate

manometer

rotating disk

Fig. I.39. Rotating disk filtration device used in [Bouzerar, 2000], [Bouzerar, 2003]).

In [Bouzerar, 2003], a CaCO3 suspension (without dispersant, mean particle size of

50 µm) was concentrated up to 50 % wt. in a dynamic filtration module with rotating disk.

Filtrate flux was 950 l/(m2h) at TMP = 1.5 bar at disk rotation speed 1500 rpm. The filtrate

flux was large, most likely, because of large mean size of CaCO3 particles. However,

suspension of small colloidal particles (50 nm) could also be concentrated from 5 to 32% at

high filtrate flux J = 245–300 l/(m2h), TMP = 1.6 bar and disk rotation speed of 1500 rpm.

[Bouzerar, 2000] have studied dynamic filtration of colloidal CaCO3 suspension (4.7 μm)

using the same rotating disk module. They observed that the total resistance of the deposit

increased logarithmically with the increase of CaCO3 concentration. However, the filtrate flux

remained substantial (~ 200 lm-2h-1) even at 50 % wt concentration of particles (disk rotation

speed of 2000 rpm). In [Bott, 2000], CaCO3 suspension reached 70 % wt. in a DYNO rotating

disk system.

I.3.4. Attempts to maximize concentration of suspensions

It should be noted that the works referred to above were not aimed at maximisation of

suspension concentration. Only few studies were focused on this subject [Trave, 2007;

Ochirkhuyag, 2008]. For instance, [Ochirkhuyag, 2008] has prepared concentrated sericite

suspension (particle size of 10 μm) in a system of cakeless continuous filtration with rotating

disk filter. Fig. I.40 presents a schema of this system.


vessel

inlet for feed suspension

filter mountedon rotated disk

concentrate

filtrate

drivingmotor

vessel

inlet for feed suspension

filter mountedon rotated disk

concentrate

filtrate

drivingmotor

0 5 10 15 20 25 30 350

50

100

150

200

250

300

filt

rate

flu

x J,

l/(m

2 ·h)

sericite concentration, % vol

100 200 300 4000

5

10

15

speed, rpm

flux

, l/m

2 ·h

0 5 10 15 20 25 30 350

50

100

150

200

250

300

0 5 10 15 20 25 30 350

50

100

150

200

250

300

filt

rate

flu

x J,

l/(m

2 ·h)

sericite concentration, % vol

100 200 300 4000

5

10

15

speed, rpm

flux

, l/m

2 ·h

Fig. I.40. Filtration system with rotating

disk filter used in [Ochirkhuyag, 2008].

Fig. I.41. Evolution of filtrate flux. Insert:

filtrate flux for 30 % vol. suspension at

different disk speeds [Ochirkhuyag, 2008].

The sericite slurry was stabilised prior to filtration by a dispersant (sodium aluminate). As

shown in Fig. I.41, suspension was concentrated up to 35 % vol. (60 % wt.) at the disk

rotation speed of 400 rpm and TMP = 0.2 bar. The filtration flux decreased gradually as the

volume fraction of sericite particles was increasing to 20 % vol. However, it became almost

constant after the level of 20 % vol. No cake was observed on the surface of the filter at the

end of experiment. The final concentrated suspension was simply poured out from the filter

cell. It was noted that the final concentration in dynamic filtration was higher than that in

dead-end filtration carried out under the same pressure (35 and 23 % vol, respectively).

[Ochirkhuyag, 2008] note that higher was the disk rotation speed, the higher was the filtrate

flux (insert in Fig. I.41). Unfortunately, this article does not discuss the effect of dispersant on

the filtration velocity and properties of the final concentrate.

[Trave, 2007] described the effect of dispersant addition (sodium polyacrylate DV 834) on

cross-flow filtration of CaCO3 suspension (1.81 μm). The purpose was the preparation of

highly concentrated and fluid suspension using a tubular ceramic membrane at constant cross-

flow velocity of 1 ms–1. Fig. I.42 shows that both in the absence and in the presence of a

dispersant, the filtrate flux decreased as suspension was becoming more concentrated and

drops to zero at certain concentration.


filtr

ate

flux

, l/(

m2 ·

h)

concentration of suspension , %wt.26 28 30 32 34 36 380

100

200

300 cdispersant = 0 %fi

ltrat

e fl

ux, l

/(m

2 ·h)


100

200

300

filtr

ate

flux

, l/(

m2 ·

h)


100

200

300 cdispersant = 0 %

dispersant concentration, %wt/wt

0 0.5 1 1.5 2 2.5

40

50

60

70

max

imal

con

cent

rati

on o

f su

spen

sion

obt

aine

d, %

wt

limit for cake obtainedin dead-end filtration

dispersant concentration, %wt/wt0 0.5 1 1.5 2 2.5

40

50

60

70

max

imal

con

cent

rati

on o

f su

spen

sion

obt

aine

d, %

wt

dispersant concentration, %wt/wt0 0.5 1 1.5 2 2.5

40

50

60

70

max

imal

con

cent

rati

on o

f su

spen

sion

obt

aine

d, %

wt

limit for cake obtainedin dead-end filtration

Fig. I.42. Evolution of filtrate flux during cross-

flow filtration of CaCO3 suspension without

dispersant (after [Trave, 2007]).

Fig. I.43. Influence of dispersant on

maximal retentate concentration obtained

in cross-flow filtration [Trave, 2007].

0 2 4 6 8 100

1

2

3

4

5

6

volume of filtrate V, ml

filt

rati

on ti

me/

volu

me

of f

iltr

ate

t/V

, s/m

l

cdispersant = 0 %1 %2 %

0 2 4 6 8 100

1

2

3

4

5

6

volume of filtrate V, ml

filt

rati

on ti

me/

volu

me

of f

iltr

ate

t/V

, s/m

l

cdispersant = 0 %1 %2 %

0 5 10 15 20

0

0.2

0.4

0.6

0.8

1

time of filtration, min

resi

stan

ce o

f de

posi

t Rd,

1012

m–1 dispersant addition

(1%)

suspensionwithout

dispersant

0 5 10 15 20

0

0.2

0.4

0.6

0.8

1

time of filtration, min

resi

stan

ce o

f de

posi

t Rd,

1012

m–1 dispersant addition

(1%)

suspensionwithout

dispersant

Fig. I.44. Comparison of the cross-flow

filtration with the Ruth-Carman’s equation

(after [Trave, 2007]).

Fig. I.45. Cross-flow filtration with delayed

addition of the dispersant

(after [Trave, 2007]).

Fig. I.43 shows that this limit concentration increases with the dispersant concentration.

Above 1.7 % wt. of dispersant, the final dryness of retentate is identical to the dryness of filter

cake obtained in dead-end filtration of CaCO3. Note that the final retentate remains fluid

(0.8 Pa·s at shear rate of 20 s–1).

Dispersant changes the properties of the particle surface. Though complete filtration

curves were not given in [Trave, 2007], Fig. I.44 shows that the filtration rate passed through

a maximum with the increase of cdispersant. It seems that addition of 1 % of dispersant

decreased the thickness of the deposit and enhanced filtration. However, the cause of drop in

filtration after addition of 2 % of dispersant is unclear.


The required amount of dispersant in [Trave, 2007] was high, much higher than in dead

end filtration of CaCO3 [Soua, 2006]. The cause is in loss of unabsorbed dispersant during

cross-flow filtration. For lowering the amount of dispersant in the filtrate, addition of

dispersant was delayed. Fig. I.45 indicates that the delayed dispersant addition in cross-flow

filtration is immediately followed by a drop in deposit resistance. This phenomenon can be

explained by weakening of contacts between the deposit particles, induced by the dispersant,

and detachment of some particles (aggregates) from the deposit. However, the deposit

resistance increased again during the cross-flow filtration.

In principle, the delayed dispersant addition may allow the precoat formation. This idea is

analogous to that described in [Soua, 2006] for dead-end filtration with preliminary

precoating. The precoat should maintain the filtration speed, while the concentration of the

flocculated suspension increases. Unfortunately, data in [Trave, 2007] show that the precoat

did not maintain after dispersant addition and was replaced by impermeable deposit.

I.3.5. Summary

Preparation of concentrated mineral suspensions by means of dynamic filtration has some

advantages compared to dead-end filtration. The filtration time is reduced in dynamic

filtration [Raha, 2009], [Ochirkhuyag, 2008] and there is no step of cake grinding after its

discharge. First works showed also that dry matter of retentate and suspension fluidity are

close to those in suspensions produced by dead-end filtration [Trave, 2007].

It seems interesting to clarify the role of dispersant in the process of dynamic filtration

(deposition of particles, specific resistance and thickness of deposit) and influence of the

dispersant concentration and time of dispersant addition on the properties of final suspension

(viscosity, dryness and amount of adsorbed dispersant).

I. Literature review

90

Notation for Section I.4 ................................................................................................... 91

I.4. Filtration of disrupted yeast suspensions ................................................................ 92

I.4.1. Background on membrane fouling ....................................................................... 92

I.4.2. Analysis of flux decline during membrane fouling ............................................. 94

I.4.3. Use of flocculation to avoid membrane fouling ................................................... 98

I.4.4. Using of precoat cell layer to avoid membrane fouling .................................... 100

I.4.5. Choice of an optimal method for disruption of yeast suspension .................... 102

I.4.6. Summary ............................................................................................................... 104

I.4. Filtration of disrupted yeast suspensions

91


Jo filtrate flux through the clean membrane

KA parameter of Eq. (I.89)

kb parameter of Eq. (I.88)

n parameter of Eq. (I.88)

t time [s]

V volume of filtrate [m3]


92


According to Darcy’s equation (I.23) the rate of filtration is inversely proportional to the

sum of cake and membrane resistances. In sections I.2 and I.3, the cake resistance was

discussed solely, while the resistance of membrane was not considered. Such an approach is

acceptable when the particles of filtered suspension are larger than the pores of membrane and

concentration of particles in suspension is high. However, in some cases resistance of the

membrane significantly increases during the filtration. This occurs due to, so-called, fouling

of the membrane pores by fine-sized particles. This phenomenon is especially important for

filtration of bio-suspensions that contain high concentration of fine particles. In this chapter,

the influence of different types of fouling on filtration of bio-suspensions (generally, yeast

suspensions) will be discussed.

I.4.1. Background of membrane fouling

If particles are smaller than the pores of membrane (or have same sizes), the particles may

plug the pores, enter into the pore volume and deposit on the internal surface of membrane.

This phenomenon is called membrane fouling or depth filtration [Wakeman, 1999]. The

membrane fouling significantly increases resistance of the membrane. In such a case, the

filtration rate is no longer regulated by the cake formed on the membrane surface, but rather

by resistance of the membrane itself. This is a serious problem, because the fouled membrane

considerably extends or even stops the filtration.

Therefore, it is usually required to know in advance the granulometry of particles in

suspension in order to make the right choice of membrane porosity. If so, the appropriately

selected membrane will retain most of the particles on its surface and its fouling will be

minimized. The intimate knowledge of the particle size distribution in suspensions is

important for membrane selection, since even small fraction of fine particles may cause

membrane fouling. Fine-sized particles may be an admixture, or they may appear after

vigorous shearing, mechanical or chemical disruption of suspension.

Because of this reason, membrane fouling is the main obstacle in microfiltration of bio-

suspensions: fermentation broths (wine, beer), cell suspensions and lysates, protein solutions

[Bailey, 2000; Czekaj, 2000; Gan, 2001]. Bio-suspensions consist of large particles (cells and

their aggregates) and small particles (cell debris, macromolecules and their aggregates)

[Saxena, 2009]. So, solid particles in bio-suspensions have wide size distribution (10 nm –

10 μm, from macromolecules to intact cells). Very small bio-particles easily plug membrane


93

pores and/ or form compressible gel layer with low permeability on the membrane surface. It

is very important to study the mechanisms of membrane fouling for better optimizasion of

filtration parameters and/ or colloidal properties of the feeding suspensions [van Reis, 2001].

Four mechanisms of membrane fouling are generally distinguished [Bowen, 1995;

Wakeman, 1999, Grenier, 2008]: (a) complete, (b) standard, (c) intermediate pore blocking

and (d) cake formation (or particles bridging). They are sketched in Fig. I.46.

Complete pore blocking (or pore blocking) assumes that the particle size is larger than the

pore diameter. In this case, the deposition of particles at pore entrance seals the pore

completely. Thus, any flow through the sealed pore and further deposition of particles become

impossible.

complete cake formationintermediate standardcomplete cake formationintermediate standard

Fig. I.46. Schema of membrane fouling mechanisms: complete blocking, standard blocking,

intermediate blocking and cake formation (after [Bowen, 1995]).

Intermediate pore blocking (or pore constriction) assumes that particles seal some pores

completely. However, deposition of particles on the blocked membrane surface remains

possible. Therefore, intermediate pore blocking assumes a probability of pore blocking by a

particle. This mechanism is sometimes regarded as a combination of complete pore blocking

and cake formation.

Standard blocking assumes accumulation of small particles mainly inside the membrane

pores. Hence, the cross-sectional area of pores decreases and the filtrate flux reduces.

Cake formation assumes that pores are not blocked by particles. The formation of cake

decreases the filtrate flow proportionally to the cake resistance. Cake formation was discussed

in previous sections.

According to Hermia [1982] and Bowen [1995], whatever is the mechanism of membrane

fouling, the filtrate flux obeys to the following characteristic equation

n

b dV

dtk

dV

td

2

2

(I.88)

where kb and n are constants. The exponent n characterizes the mechanism of fouling:


94

n = 0 for cake formation,

n = 1 for intermediate pore blocking,

n = 1.5 for standard pore blocking,

n = 2 for complete pore blocking.

Equation I.88 is valid only for filtration at constant pressure. Other similar exponent equations

were expressed for filtration at varying pressure and constant filtrate flux [Chellam, 2006].

Equation I.88 gives a simple and convenient method for determination of the fouling

mechanism by plotting log(d2t/dV2) versus log(dt/dV). It should yield a straight line with a

slope equal to n [Ho, 2000; Hwang, 2007; Yukseler, 2007; Mahesh Kumar, 2008]. This

equation is frequently used for characterisation of the membrane fouling during the entire

course of filtration. However, Wakeman [1999] stated that Eq. I.88 “does not describe the

physics of particle deposition beyond the initial few moments of filtration”. To clear up this

divergence, it is necessary to review the formulations of the different mechanisms of fouling

and the applicability of these equations for analysis of the flux decline.

I.4.2. Analysis of flux decline during membrane fouling

Specific equations for four classical mechanisms of membrane fouling are shown, for

example, in [Bowen, 1995]. For complete pore blocking, it is considered that the filtrate flux

decline is proportional to the fraction of blocked membrane surface per unit volume of

permeate (KA) and is proportional to the initial filtrate flux through the clean membrane (J0).

This formulation leads to:

dtJKJ

dJA 0 (I.89)

Transformation of Eq. (I.89) into the characteristic one yields

n

A dV

dtJK

dV

td

02

2

(I.90)

Hence, kb = KAJ0 is a constant (according to Eq. I.88), KA also remains constant during

filtration. Since KA depends on membrane properties, Eq. (I.90) is valid, as long as the

membrane surface remains clean from the layer of deposited particles.

Intermediate blocking also requires the constancy of surface properties. In such a case,

kb = KA. Standard blocking requires the constancy of pore sizes of the membrane and kb =

KB(J0)-1/2, where KB is a constant depending on the membrane properties.

In practice, the surface, on which the deposition of particles takes place, varies in the

course of filtration due to existence of size distribution of the pores and the particles. For

example, Bowen et al. [1995] described consecutive steps of the membrane fouling during


95

filtration of BSA solutions comprising small BSA molecules and large particles (BSA

aggregates). They stated that:

‘(i) in the initial moments of the blocking process, the smallest pores are blocked by all the

particles arriving on the membrane; (ii) Then the inner surfaces of bigger pores start to be

covered; (iii) Afterwards, some particles cover other pre-existing already arrived particles

while others directly block some of the pores; (iv) Finally a cake starts to build up.’.

So, according to Bowen et al., actual mechanism of membrane fouling may correspond to

none of the theoretical ones. Actual fouling process may be a combination of simple

mechanisms and may involve several stages. It results in quite a complex shape of the

characteristic filtration curve (see, for example, Fig.I.47).

107 1081011

1012

n = 1.7

n = 1.8

n = 0

(i)

(ii)

(iii)

(iv)

dt/dV, s/m3

d2 t/d

V2 ,

s/m

6

107 1081011

1012

n = 1.7

n = 1.8

n = 0

(i)

(ii)

(iii)

(iv)

dt/dV, s/m3

d2 t/d

V2 ,

s/m

6

1061010

1014

dt/dV, s/m3

d2 t/d

V2 ,

s/m

6

0

1011

1012

1013

107 108 109

8·1014

8·1015

α = 8·1016

n = 2

n = 0

1061010

1014

dt/dV, s/m3

d2 t/d

V2 ,

s/m

6

0

1011

1012

1013

107 108 109

8·1014

8·1015

α = 8·1016

n = 2

n = 0

Fig. I.47. Characteristic filtration curve for a

BSA solution (after [Bowen, 1995]).

Fig. I.48. Predictions of characteristic

filtration curve: effect of specific cake

resistance (after [Ho, 2000]).

Fig. I.47 shows that the value of exponent n was changing during filtration. It seems that

fouling mechanisms change successively: from complete blocking (i) to cake formation (iv).

Mahesh Kumar et al. [2008] also noted n variation during filtration. In their study of

living yeast suspension, the value of n calculated using (I.88), decreased from 2 to 0 and

finally reached negative value n = – 0.5. Iritani et al. [1995] reported even wider range of n

fluctuations during filtration of protein (BSA) solution. They have concluded that the

dominant filtration mechanisms were changing in the progress of filtration.

Hwang et al. [2007] have analysed filtration curves of suspensions with monodisperse

particles through a track-etched membrane. The particle size was 0.15 μm and membrane pore

size was 0.2 μm. It was evidenced that the initial pore blocking mechanism is always followed

by cake formation. Hence, the value of n decreases from 2 to 0. Each transition between

mechanisms depends on the rate of filtration and the concentration of particles.


96

Ho and Zydney [2000] have developed a model of filtration taking into account the initial

pore blockage and subsequent growth of filter cake above the fouled surface. They derived

simple equation for filtration flux through the fouled membrane at any given filtration time.

The equation contains two parameters: pore blocking constant and specific cake resistance.

This model predicts both decrease of n from 2 to 0 and negative value of the exponent for a

certain part of filtration curve, as it is shown in Fig. I.48.

Duclos-Orsello et al. [2006] have developed filtration model accounting for three basic

mechanisms of fouling. The model is based on assumption that the initial pore constriction is

followed by pore blocking and, finally, by cake formation. The equation for filtrate flux

through the fouled membrane was derived. This equation comprises three independent

characteristic parameters, where each parameter corresponds to one of the mentioned

mechanisms of fouling. Ratio of these parameters determines the relative effects of different

fouling mechanisms on filtration. The proposed filtration model was tested on suspensions

with particles of different size (and, therefore, with different expectable mechanisms of

membrane fouling). The theory showed excellent agreement with experimental data (see, for

example, Fig. I.49). In the experiment presented in Fig. I.49, the particle size in the

monodisperse suspension was 0.25 μm and the membrane pore size was 0.20 μm. Hence,

influence of pore constriction on filtration of this suspension was negligible. Indeed,

comparison of the characteristic parameters of the solid line presented in Fig. I.49 reveals that

filtration was influenced by pore blocking and cake formation. It was also noted that in the

given case the plot d2t/dV2 versus dt/dV did not yield a straight line with the slope value n = 2.

Therefore, the conventional method of flux decline analysis, based on application of Eq. I.88,

did not yield complete information about the fouling mechanism.

dt/dV, s/m3

d2 t/d

V2 ,

s/m

6

108107

1012

1011

1010

from pore blocking to cake formation

dt/dV, s/m3

d2 t/d

V2 ,

s/m

6

108107

1012

1011

1010

from pore blocking to cake formation

Fig. I.49. Flux decline analysis of particulate

suspension. Solid line represents the least-

square fitting of experimental data by the

equation of Duclos-Orsello et al.

After [Duclos-Orsello, 2006].

Another method for determination of fouling mechanisms was proposed in

[Grenier, 2008]. The method is based on fitting of the experimental data by linear forms of


97

characteristic equations of separate fouling mechanisms. These equations are listed in

Table I.1.

Table I.1. Fouling mechanisms and linear forms of corresponding

characteristic equations.

Fouling mechanism Corresponding linear form*

Cake formation dt/dV = a1V + b1

Intermediate blocking dt/dV = a2t + b2

Standard blocking (dV/dt)1/2 = a3V + b3

Complete blocking dV/dt = a4V + b4

*ai and bi are constants.

The method assumes that filtration may be divided into several successive steps with only one

prevailing fouling mechanism. Therefore, experimental curve may be divided into several

segments, which are described by one of the mentioned characteristic equations. Plotting of

the filtration curve in different coordinates corresponding to linear forms of equations yields

linear segments on filtration curve. Simultaneously, the values of n on the separate linear

segments of filtration curve can be determined from Eq. I.88. An example of data analysis is

presented in Fig. I.50.

0 2 4 60

1

2

3

4

0 2 4 60

1

2

V x104, m3V x104, m3

dt/d

V x

10-7

, s/m

3

dV/d

tx10

6 , m

3 /s

2nd stage of fouling:dt/dV = a1·V + b1,

n = 0

1st stage of fouling:dV/dt = a4·V + b4,

n = 2

0 2 4 60

1

2

3

4

0 2 4 60

1

2

V x104, m3V x104, m3

dt/d

V x

10-7

, s/m

3

dV/d

tx10

6 , m

3 /s

2nd stage of fouling:dt/dV = a1·V + b1,

n = 0

1st stage of fouling:dV/dt = a4·V + b4,

n = 2

Fig. I.50. Analysis of filtration according to Grenier at al. [2008].

Left: plotting of filtration curve in coordinates corresponding to the linear form of

characteristic equation of pore blocking mechanism (dV/dt – V). Right: plotting of filtration

curve in coordinates corresponding to the linear form of characteristic equation of cake

formation (dt/dV – V). Values of n on the linear segments were determined from Eq. (I.88).

Both linearity of the segments and the values of n suggest that pore blocking is followed by

cake formation.


98

Fig. I.50 shows that linearization may be useful for distinguishing the mechanisms of

fouling. Keskinler et al. [2004] used the same method for analysis of cross-flow filtration of

yeast suspension. They have concluded that the initial flux decline fits well to an intermediate

blocking mechanism, and after this stage they have identified the classical cake filtration.

Iritani et al. [1995] also showed that linearization yields information additional to that

obtained from representation of curves in coordinates of Eq. (I.88).

Zydney and Ho [2002] further examined the validity of linearization for prediction of

filtration. They studied filtration of different protein solutions and estimated duration of

filtration by two methods. The first method comprised linearization of initial segment of

filtration curve using the linearized form of the pore constriction model and it allows

extrapolation to a longer filtration time. The second method was based on fitting of the initial

segment by the two-parameter equation of Ho and Zydney (mentioned above). Contrary to

previous authors, they showed that analysis based on linearization can not predict adequately

the time of filtration. Their pore-blocking cake filtration model provides much better

description of filtration for different types of proteins.

In summary, each of the reviewed methods (use of general characteristic equation (I.88),

linearization of filtration curve or use of one of a number of combined filtration models) may

be applied efficiently for identification of the fouling mechanism and prediction of filtration.

Fitting of filtration data by the equations proposed in [Ho, 2000] and [Duclos-Orsello, 2006]

allows estimation of the relative effect of different fouling mechanisms on filtration. The

values of the characteristic parameters determined from fitting may be used for calculation of

suspension properties: pore blocking constants and specific cake resistance. Therefore, fitting

of experimental data by these equations gives the key to optimise suspension properties and

minimise fouling.

The methods available for adjustment of the particle sizes in bio-suspensions and

optimisation of filtration (flocculation, use of undisrupted cells as filer aids, reasonable

disruption of the suspension) are briefly reviewed in the following paragraphs.

I.4.3. Use of flocculation to avoid membrane fouling

Flocculation of bio-suspensions by inorganic salts in [Narong, 2006a, 2006b] or cationic

polymers [Kim, 2001; Wickramasinghe, 2002, 2004; Karim, 2008] is efficient for increasing

the average particle size and the filtration rate, and for decreasing the turbidity of suspensions.

Figs. I.51–I.52 show results of flocculation of the yeast suspensions at their cross-flow

filtration.


99

0 1000 2000 30000

100

200

300

400

time, s

flux

, m3 m

-2s-1

x 10

-6

a

b

a: untreated suspensionmean particle size = 10 μmturbidity = 200 NTU

b: flocculated suspensionmean particle size = 20 μmturbidity = 100 NTU

0 1000 2000 30000

100

200

300

400

time, s

flux

, m3 m

-2s-1

x 10

-6

a

b

a: untreated suspensionmean particle size = 10 μmturbidity = 200 NTU

b: flocculated suspensionmean particle size = 20 μmturbidity = 100 NTU

10 20 30 40 50 601

1.5

2

2.5

3

3.5

time, min

J flo

cc./J

nofl

occ.

a

b

10 20 30 40 50 601

1.5

2

2.5

3

3.5

time, min

J flo

cc./J

nofl

occ.

a

b

Fig. I.51. Influence of flocculation (by

Al2(SO4)3) on the particle size, turbidity and

cross-flow filtration of a model yeast

suspension. Membrane pore size = 0.2 μm.

(After [Narong, 2006b]).

Fig. I.52. Cross-flow filtration of a model

yeast suspension flocculated by different

cationic polymers: (a) mean particle size =

80 μm, with wide size distribution; (b) mean

particle size = 100 μm with narrow size

distribution

(After [Wickramasinghe, 2004]).

Baran [1988] have screened a number of polymers for flocculation of cells in suspension.

Cationic polymers appeared to be the most effective. Increasing of the molecular weight of

the polymer also improved flocculation, probably by promotion of “bridging”. Hughes et al.

[1990] have found that suspension of washed cells required less flocculant than cells in a

complex growth medium. This suggests interference between the flocculant and the ionic

species present in the growth medium.

Selection of a suitable flocculant for real bio-suspensions is complex. Industrial practice

often relies on a trial and error method, where a number of flocculants are tested under a

variety of flocculation conditions. For example, Aspelund et al. [2008] have screened several

cationic polyelectrolytes for real bacterial cell suspension consisting of cells, cell debris and

extracted proteins. The flocculated suspensions were submitted to an unstirred or stirred dead-

end filtration. It was found that polyelectrolytes with longer chains are able to form larger

flocs. The increase in particle size was decreasing specific cake resistance and increasing the

permeate flux, which is reasonable to expect. But there was an optimum in flocculent

concentration, as far as it was found that the largest flocs did not provide the greatest

permeate flux enhancement. Also, it was observed that flocculation reduced rejection of

proteins during filtration.


100

Shan et al. [1996] investigated the effect of different cationic polymers on the efficiency

of flocculation and solid-liquid separation of real bio-suspension. They observed that though

polymers have high efficiency for removal of inclusion bodies (cells and cell debris), they

also capture soluble proteins. Therefore, flocculation may reduce recovery of the target bio-

product. Agerkvist et al. [1990] investigated the influence of flocculation on purification of

protein solution from the cells and cell debris. They found have that flocculation of bio-

suspension by the optimal dose of polymeric flocculant (chitosan) removed 98% of the cell

debris. However, more than 40% of the target protein was rejected due to the flocculation.

So, though flocculation is efficient for solid-liquid purification, it may decrease

concentration of target soluble bio-products in the final filtrate. This finding encourages

seeking for ‘non-chemical’ methods for regulation of the particle size in bio-suspensions. It is

expected that ‘non-chemical’ methods will improve solid-liquid separation, but without

altering the recovery of proteins.

I.4.4. Using of precoat cell layer to avoid membrane fouling

It was noted in [Guell, 1999; Kuberkar, 2000; Hwang, 2006; Chupakhina, 2008] that

addition of undisrupted yeast cells to protein solutions improves the filtration rate. It also

reduces the membrane fouling and increases transmission of soluble protein into filtrate.

Guell et al. [1999] studied the effect of addition of the yeast cells on membrane fouling

during filtration of the mixture of proteins. Yeast cells were either added directly to protein

solution, or were used for forming pre-coat layer of undisrupted cells on the membrane

surface. It was observed that small concentration of yeast cells in suspension enhanced the

filtrate flux and maintained nearly 100% transmission of proteins, while without yeasts,

transmission of soluble proteins into the filtrate was only 40%. Formation of the pre-coat

layer of yeast cells on the surface of original membrane before filtration of the mixture of

proteins also enhanced the filtrate flux and increases transmission of proteins. A mechanism

was proposed for explanation of these results. According to [Guell, 1999], the yeast cells may

form a secondary membrane on the top of the original membrane. Though the yeast cell layer

has higher resistance than the original membrane, it screens the membrane from the fouling

fine-sized particles. Fig. I.53 shows that such secondary membrane entraps the protein

aggregates, which otherwise would be responsible for fouling of the original membrane and

decrease of transmission of the soluble proteins into filtrate.


101

(a) (b)

protein monomersmembrane pores blocked withprotein aggregates

yeast cells

protein aggregates

protein aggregates

(a) (b)

protein monomersmembrane pores blocked withprotein aggregates

yeast cells

protein aggregates

protein aggregates

Fig. I.53. Schema of the retention of protein aggregates by dynamic layer or precoat layer of

undisrupted yeast cells. After [Guell, 1999].

Influence of the yeast cells on filtration of the protein suspension was modelled in

[Kuberkar, 2000]. According to the model, the mixed suspension of yeast cells and protein

was regarded as a bimodal system consisting of small particles (protein aggregates) and large

particles (yeast cells). It was assumed that small particles foul the original membrane if they

reach the membrane surface. Large particles form the cake on the membrane surface. This

cake is treated as a deep-bed filter, which captures small particles. Thus, concentration of

small foulant particles in the vicinity of membrane decreases in the presence of large particles,

and fouling decreases too. Equation describing filtration of the mixture of small and large

particles was derived. It was shown that filtration flux depends on the ratio between

concentrations of small particles and large particles. At low concentration of large particles,

screening of the original membrane from small particles is ineffective and filtration quickly

stops due to membrane fouling. At high concentration of large particles, formation of thick

impermeable cake slows filtration. However, at optimum concentration of large particles, thin

and permeable pre-coat layer efficiently screens membrane from the fouling. This theoretical

finding was confirmed experimentally in [Kuberkar, 2000] and match well with experimental

observations of [Guell, 1999].

Chupakhina and Kottke [2008] investigated the effect of yeast addition on cross-flow

filtration of a fermentation broth. Filtration was investigated at different concentrations of

yeasts and different cross-flow velocities. It was observed that the steady-state filtrate flux

increases at optimal yeast concentration. In contrary to usual observations, the filtrate flux

was increasing with decrease of the cross-flow velocity. Lower velocity enabled formation of

the yeast cell layer, which acted as a secondary membrane. Thus, it protected the filter from


102

the fouling agent of the broth (proteins, polysaccharides). At higher velocity, the yeast cells

were swept away from the filter surface. As a result, the filter pores were blocked and the

filtration rate decreased.

In summary of this section, it may be concluded that it is possible to enhance filtration by

adjustment of the particle size distribution in a bio-suspension without addition of chemical

flocculants. Such optimisation of filtration requires balanced concentrations of the foulant

particles and large rigid particles (e.g., untreated cells).

I.4.5. Choice of an optimal method for disruption of yeast suspension

Filtration of bio-suspensions is widely used for purification of extracted bio-products

(usually, intracellular proteins) from cells and other insoluble particles. Preparation of the

extract involves physical or chemical treatment of cell suspension. Vigorous treatment results

in disruption of cell walls and liberation (extraction) of the target intracellular bio-products

(e.g., proteins). Cell disruption may also generate colloidal impurities (cell debris), which

block the pores of the membrane, slows filtration and decreases concentration of target

products in the filtrate. Consequently, it is necessary to find an adequate technique for

disruption of cells. Effectiveness of the disruption technique depends on the yield of target

bio-products (proteins). It depends also on the feasibility of further extract purification from

the solid phase. It is better to have moderate cell damage with lower content of cell debris.

Numerous techniques have been proposed for yeast cell disruption [Chisti, 1986; Geciova,

2002] (see Fig. I.54). The mechanical method of high-pressure homogenisation is most

appropriate for industrial-scale disruption. This method results in considerable breakage of

cells and high recovery of intracellular proteins. However, it generates a large quantity of cell

debris, which complicates the downstream purification. Other classical methods of cell

disruption are either less effective or expensive, or can not be realized in industrial scale. This

encourages seeking for a new methods of cell disruption.


103

Bead mill X-pressHughes press

Ultrasound HPHMicrofluidiserFrench press

ThermolysisDecompressionOsmotic shock

AntibioticsChelatesSolvents

Detergents

Lytic enzymesAutolysis

Solid shear Liquid shear Physical Chemical Enzymatic

Mechanical Non-mechanical

Classical methods of cell disruption

Bead mill X-pressHughes press

Ultrasound HPHMicrofluidiserFrench press

ThermolysisDecompressionOsmotic shock

AntibioticsChelatesSolvents

Detergents

Lytic enzymesAutolysis

Solid shear Liquid shear Physical Chemical Enzymatic

Mechanical Non-mechanical

Classical methods of cell disruption

Fig. I.54. Classical methods available for cell disruption (after [Chisti, 1986; Geciova, 2002]).

Treatment of yeast suspensions by high-intensity pulsed electric field was recently

proposed as a promising way for extraction of proteins [Ganeva, 2003]. High electric fields of

microsecond duration (typically, 5–10 kV/cm) may cause electroporation of membranes,

which seems to enhance release of the intracellular bio-products. Electroporation has some

advantages compared to homogenisation. It does not generate fine cell debris and does not

produce any significant temperature elevation. Nevertheless, effectiveness of the pulsed

electric field treatment as a method for extraction of proteins from yeast cells is still under

discussion [Shynkaryk, 2009].

Another alternative electrical method of extraction is based on application of the high

voltage electrical discharges (HVED). HVED of microsecond duration create shock waves

(pulsed high pressure) and powerful light radiation. These phenomena may results in

considerable disruption and homogenisation of colloidal particles in aqueous suspensions.

HVED has found applications for inactivation of microorganisms [Zuckerman, 2002] and

extraction of soluble materials from cellular tissues (seeds) [Gros, 2003]. HVED treatment of

an aqueous bio-suspension at 40–50 kV/cm can provoke a noticeable mechanical damage of

cells and rupture of cell walls. Recently, Shynkaryk et al. [2009] reported the effect of HVED

on disruption of a yeast suspension. It was shown that application of successive HVED pulses

results in a gradual disruption of yeast cells and extraction of intracellular proteins.

The degree of cell disruption and extraction of bio-products strongly depends on the

method used for cell treatment [Shynkaryk, 2009]. Also, conditions of the treatment determine

content the of cell debris in the treated suspensions. For example, it was shown in

[Kloosterman IV, 1988] that continuous disruption of a baker’s yeast suspension in a bead

mill leads to high level of protein extraction. However, continuous treatment substantially

increases the content of cell debris. It was observed that continuously milled yeast


104

suspensions are difficult to filter as compared with moderately treated suspensions

[Kloosterman IV, 1988].

I.4.6. Summary

It seems that more vigorous cell disruption may yield less of the target product than

moderate treatment. A reasonable choice of the treatment method (homogenization or

electrical treatment) and operating parameters for cell disruption will optimize all the stages

of solid-liquid purification, including extraction of target product and filtration of extract from

colloidal impurities. So, it is interesting to investigate thoroughly the effect of the novel

electrical methods of cell treatment on disruption of cells and filtration of the disrupted

suspensions and to compare them with the classical methods of cell disruption.

Conclusions from the literature review

105

I.5. Conclusions from the literature review

This Section summarises main conclusions following from the literature review.

The techniques, available for evaluation of the local compression-permeability properties

of suspensions, are presented in the Section I.1. The new technique of analytical

centrifugation may be used for determination of local properties of suspensions (solidosity,

specific filtration resistance, and compressibility coefficient) in the range of low and moderate

solids pressure. However, the appropriate method is required for analysis of the centrifugal

consolidation data. Therefore, it is necessary to develop a method for evaluation of local

filtration parameters from the data obtained using analytical centrifuge.

It follows from the Section I.2 that preparation of concentrated and flowable mineral

suspension by dead-end filtration requires optimal chemical pre-treatment of suspension and

optimal concentration of particles: the factors increasing flowability and dryness of the filter

cake also increase the time of filtration, and vice versa. The role of particle concentration in

permeability and fluidity is especially important for kaolin suspensions. Therefore, it is

necessary to study all the properties of kaolin suspensions (structural, rheological and

filtration) in a single work.

Preparation of concentrated mineral suspensions by dynamic filtration may be

advantageous as compared to dead-end filtration (Section I.3). The filtration time may be

reduced in dynamic filtration, and there is no step of cake grinding after filtration. Therefore,

it looks interesting to study the role of the dispersant in the process of dynamic filtration of

typical mineral suspension (calcium carbonate) and influence of dispersant concentration and

time of dispersant addition on the properties of final suspension (viscosity, dryness and

amount of adsorbed dispersant).

The more vigorous method of cell disruption may yield less target product than moderate

treatment (Section I.4). Reasonable choice of the treatment method (homogenization or

electrical treatment) and operating parameters for cell disruption will optimize all the stages

of solid-liquid purification, including both extraction of the target product and filtration of

extract from colloidal impurities. So, it is interesting to investigate thoroughly the effects of

novel electrical methods of cell treatment on cell disruption and filtration of the disrupted

suspension and to compare them with classical methods of cell disruption.

I.6. Literature cited

106

I.6.1. Literature cited on the subject of Cake Filtration and Consolidation Buscall and White 1987// R. Buscall, L. R. White, The consolidation of concentrated suspensions: Part 1. The

theory of sedimentation, J Chem. Soc. Faraday Trans., 83 (1987) 873–891 Curvers 2009// D. Curvers, H. Sayen, P. J. Scales, P. Van der Meeren, A centrifugation method for the

assessment of low pressure compressibility of particulate suspensions, Chemical Engineering Journal, 148 (2009) 405–413

de Kretser 2001// R. G. de Kreyser, S. P. Usher, P. J. Scales, D. V. Boger, K. A. Landman, Rapid filtration measurement of dewatering design and optimisation parameters, AIChE J., 47 (2001) 1758–1769

Fathi-Najafi and Theliander 1995// M. Fathi-Najafi, H. Theliander, Determination of local filtration properties at constant pressure, Separation Technology, 5 (1995) 165–178

Green 1996// M. D. Green, M. Eberl, K. A. Landman, Compressive yield stress of flocculated suspensions: determination via experiment, AIChE J., 42 (1996) 2308–2318

Green 1998// M. D. Green, K. A. Landman, R. G. de Krester, D. V. Boger, Pressure filtration technique for complete characterisation of consolidating suspensions, Ind. Eng. Chem. Res., 37 (1998) 4152–4156

Grimi 2010// N. Grimi, E. Vorobiev, N. Lebovka, J. Vaxelaire, Solid-liquid expression from denaturated plant tissue: Filtration-consolidation behaviour, Journal of Food Engineering, 96 (2010) 29–36

Iritani 1993// E. Iritani, K. Hattori, T. Murase, Analysis of dead-end ultrafiltration based on ultracentrifugation method, Journal of Membrane Science, 81 (1993) 1–13

Iritani 2007// E. Iritani, N. Katagiri, K. Aoki, M. Shimamoto, K.-M. Yoo, Determination of permeability characteristics from centrifugal flotation velocity of deformable oil droplets in O/W emulsions, Separation and Purification Technology, 58 (2007) 247–255

Iritani 2008a// E. Iritani, H. Nagaoka, N. Katagiri, Determination of filtration characteristics of yeast suspension based upon multistage reduction in cake surface area under step-up pressue conditions, Separation and Purification Technology, 63 (2008) 379–385

Iritani 2008b// E. Iritani, N. Katagiri, K. Aoki, M. Shimamoto, Acquisition of compression-permeability data of soft and hard colloids based on centrifugation experiments, Proceedings of the 10th World Filtration Congress (WFC10), Leipzig (Germany), I (2008) 51-55

Iritani 2009// E. Iritani, T. Hashimoto, N. Katagiri, Gravity consolidation-sedimentation behaviour of concentrated TiO2 suspensions, Chemical Engineering Science, 64 (2009) 4414–4423

Iritani 2011// E. Iritani, N. Katagiri, Y. Takaishi, S. Kanetake, Determination of pressure dependence of permeability characteristics from single pressure filtration test, Journal of Chemical Engineering of Japan, 44 (2011) 14–23

Johansson 2005// C. Johansson, Pressure and solidosity profiles in cake filtration, Ph. D. dissertation, Chalmers University of Technology (2005)

Johansson and Theliander 2007// C. Johansson, H. Theliander, Validation of predicted local profiles in cake filtration, Trans. IChemE, 85 (2007) 220–228

La Heij 1994// E. J. La Heij, An analysis of sludge filtration and expression, Ph. D. dissertation, Eindhoven University of Technology (1994)

La Heij 1995// E. J. La Heij, P. J. A. M. Kerkhof, A. J. M. Herwijn, W. J. Coumans, Fundamental aspects of sludge filtration and expression, Water Research, 30 (1995) 697–703

Landman and White 1997// K. A. Landman, L. R. White, Predicting filtration time and maximizing throughput in a pressure filter, AIChE J., 43 (1997) 3147–3160

Landman 1999// K. A. Landman, J. M. Stankovich, L. R. White, Measurement of the filtration diffusivity D(φ) of a flocculated suspension, AIChE J., 45 (1999) 1875–1882

Lanoiselle 1996// J.-L. Lanoiselle, E. I. Vorobiev, J.-M. Bouvier, G. Piar, Modeling of solid/liquid expression from cellular materialls, AIChE J., 42 (1996) 2057–2068

Lee and Wang 2000// D. J. Lee, C. H. Wang, Theories of cake filtration and consolidation and implications to sludge dewatering, Water Research, 34 (2000) 1–20

Lee 2000// D. J. Lee, S. P. Ju, J. H. Know, F. M. Tiller, Filtration of highly compactible filter cake: variable internal flow rate, AIChE Journal, 46 (2000) 110–118

Lerche 2007// D. Lerche, T. Sobisch, Consolidation of concentrated dispersions of nano- and microparticles determined by analytical centrifugation, Powder Technology, 174 (2007) 46-49

Lu 1998// W.-M. Lu, Y.-P. Huang, K.-J. Hwang, Methods to determine the relationship between cake propertiesand solid compressive pressure, Separation and Purification Technology, 13 (1998) 9–23

Murase 1987// T. Murase, E. Iritani, J. H. Cho, S. Nakanomori, M. Shirato, Determination of filtration characteristics due to sudden reduction in filtration area of filter cake surface, Journal of Chemical Engineering of Japan, 20 (1987) 246–251


107

Murase 1988// T. Murase, M. Iwata, I. Kato, W.-D. Lee, M. Shirato, Determination of specific resistance of highly compressed cake by expression data, Journal of Chemical Engineering of Japan, 21 (1988) 204–206

Murase 1989a// T. Murase, E. Iritani, J. H. Cho, M. Shirato, Determination of filtration characteristics based upon filtration tests under set-up pressure conditions, Journal of Chemical Engineering of Japan, 22 (1989) 373–378

Murase 1989b// T. Murase, M. Iwata, T. Adachi, L. Gmachowski, M. Shuirato, An evaluation of compression-permeability characteristics in the intermediate concentration range by use of centrifugal and constant-rate compression techniques, Journal of Chemical Engineering of Japan, 22 (1989) 378–384

Olivier 2007// J. Olivier, J. Vaxelaire, E. Vorobiev, Modelling of cake filtration: an overview, Separation Science and Technology, 42 (2007) 1667–1700

Sedin 2003// P. Sedin, On the determination and application of local filtration properties, Ph. D. dissertation, Lulea University of Technology (2003)

Sedin 2003// P. Sedin, C. Johansson, H. Theliander, On the measurement and evaluation of pressure and solidosity filtration, Trans. IChemE, 81 (2003) 1393–1403

Shirato 1970a// M. Shirato, H. Kato, K. Kobayashi, H. Sakazaki, Analysis of settling of thick slurries due to consolidation, Journal of Chemical Engineering of Japan, 3 (1970) 98–104

Shirato 1970b// M. Shirato, T. Murase, M. Negawa, T. Senda, Fundamental studies of expression under variable pressure, Journal of Chemical Engineering of Japan, 3 (1970) 105–112

Shirato 1971// M. Shirato, T. Murase, M. Negawa, H. Moridera, Analysis of expression operations, Journal of Chemical Engineering of Japan, 4 (1971) 263–268

Shirato 1974// M. Shirato, T. Murase, A. Tokunaga, O. Yamada, Calculations of consolidation period in expression operations, Journal of Chemical Engineering of Japan, 7 (1974) 229–231

Shirato 1978// M. Shirato, T. Murase, K. Atsumi, T. Nagami, H. Suzuki, Creep constants in expression of compressible solid-liquid mixtures, Journal of Chemical Engineering of Japan, 11 (1978) 334–336

Shirato 1979// M. Shirato, T. Murase, K .Atsumo, T. Aragaki, T. Noguchi, Industrial expression equation for semi-solid materials of solid-liquid mixture under constant pressure, Journal of Chemical Engineering of Japan, 12 (1979) 51–55

Shirato 1980// M. Shirato, T. Murase, K. Atsumo, Simplified computational method for constant pressure expression of filter cakes, Journal of Chemical Engineering of Japan, 13 (1980) 397–401

Shirato 1985// M. Shirato, T. Murase, E. Iritani, S. Nakatsuka, Filter cake dewatering by formation of bentonite skin layer on cake surface, Journal of Chemical Engineering of Japan, 18 (1985) 372–376

Shirato 1986// M. Shirato, T. Murase, E. Iritani, S. Nakatsuka, Analysis of consolidation pocess in filter cake dewatering by use of difficult-to-filter slurries, Journal of Chemical Engineering of Japan, 19 (1986) 587–592

Stamatakis and Tien 1991// K. Stamatakis, C. Tien, Cake formation and growth in cake filtration, Chem. Eng. Sci., 46 (1991) 1917–1933

Stickland 2005// A. D. Stickland, R. G. de Kretser, P. J. Scales, Nontraditional constant pressure filtration behavior, AIChE J., 51 (2005) 2481–2488

Teoh 2001// S. K. Teoh, R. B. H. Tan, D.He, C. Tien, A multifunction test cell for cake filtration studies, Trans. Filtr. Soc., 1 (2001) 81–90

Teoh 2002// S. K. Teoh, R. B. H. Tan, C. Tien, Correlation of C-P cell and filtration test data using a new test cell, Separation and Purification Technology, 29 (2002) 131–139

Teoh 2006a// S. K. Teoh, R. B. H. Tan, C. Tien, A new procedure for determining filter cake resistance from filtration data, Chemical Engineering Science, 61 (2006) 4957–4965

Teoh 2006b// S. K. Teoh, R. B. H. Tan, C. Tien, Analysis of cake filtration data – a critical assessment of conventional filtration theory, AIChE Journal, 52 (2006) 3427–3442

Theliander and Fathi-Najafi 1996// H. Theliander, M. Fathi-Najafi, Simulation of the build-up of a filter cake, Filtration and Separation. (1996) 417–421

Tiller 1955// F. M. Tiller, The role of porosity in filtration. Part II: Analytical equations for constant rate filtration, Chem. Eng. Prog., 51 (1955) 282–290

Tiller and Yeh1987// F. M. Tiller, C. S. Yeh, The role of porosity in filtration. Part XI: Filtration followed by expression, AIChE J., 33 (1987) 1241–1255

Tiller and Leu 1980// F. M. Tiller, W. F. Leu, Basic data fitting in filtration, J. Chin. Inst. Chem. Eng., 11 (1980) 61–70

Vorobiev 2006// E. Vorobiev, Derivation of filtration equations incorporating the effect of pressure redistribution on the cake-medium interface: a constant pressure filtration, Chemical Engineering Science, 61 (2006) 3686–3697

Wakeman 1991// R. J. Wakeman, M. N. Sabri, E. S. Tarleton, Factors affecting the formation and properties of


108

wet compacts, Powder Technology, 65 (1991) 283–292 I.6.2. Literature cited on the subject of Cake Filtration of Stabilized Mineral Suspensions Abend 2000// S. Abend, G. Lagaly, Sol–gel transitions of sodium montmorillonite dispersions, Applied Clay

Science 16 (2000) 201–227 Addai-Mensah 2005// J. Addai-Mensah, J. Ralston, Investigation of the role of interfacial chemistry on particle

interactions, sedimentation and electroosmotic dewatering of model kaolinite dispersions, Powder Technology 160 (2005) 35 – 39

Addai-Mensah 2007// Jonas Addai-Mensah, Enhanced flocculation and dewatering of clay mineral dispersions, Powder Technology 179 (2007) 73–78

Andreola 2006// F. Andreola, E. Castellini, J. M. F. Ferreira, S. Olhero, M. Romagnoli, Effect of sodium hexametaphosphate and ageing on the rheological behaviour of kaolin dispersions, Applied Clay Science 31 (2006) 56–64

Appel 2003// C. Appel, L. Q. Ma, R. D. Rhue, E. Kennelley, Point of zero charge determination in soils via traditional methods and detection of electroacoustic mobility, Geoderma 113 (2003) 77–93

Babak 1986// V. G. Babak, V. N. Sokolov, Influence of physicochemical factors on the contact interactions between kaolinite particles in solutions of electrolytes, Colloidal Journal (in Russian), 48 (1986) 218–225

Barak 2003// P. Barak, E. A. Nater, The virtual museum of minerals and molecules 1998-2003 [Online], available at http://virtual- museum.soils.wisc.edu/kaolinite/index.html, Univ. of Wisconsin-Madison, Madison, WI.

Barnes 1985// H. A. Barnes, K. Walters, The yield stress myth? Rheol. Acta 24 (1985) 323–326 Barnes 1989// H. A. Barnes, Shear-thickening ('dilatancy') in suspensions of nonaggregating solid particles

dispersed in Newtonian liquids, Journal of Rheology 33 (1989) 329–366 Barnes 1999// H. A. Barnes, The yield stress-a review or 'παντα ρει'-everything flows? Journal of Non-

Newtonian Fluid Mechanics 81 (1999) 133–178 Barthelmes 2003// G. Barthelmes, S. E. Pratsinis, H. Buggisch, Particle size distributions and viscosity of

suspensions undergoing shear-induced coagulation and fragmentation, Chemical Engineering Science 58 (2003) 2893–2902

Baudet 1999// G. Baudet, V. Perrotel, A. Seron, M. Stellatelli, Two dimensions comminution of kaolinite clay particles, Powder Technology 105 (1999) 125–134

Beazley 1972// K.M Beazley, Viscosity-concentration relations in deflocculated kaolin suspensions, Journal of Colloid and Interface Science, 41 (1972) 105–115

Besra 2000// L. Besra, D.K. Sengupta, S.K. Roy, Particle characteristics and their influence on dewatering of kaolin, calcite and quartz suspensions, Int. J. Miner. Process. 59 2000. 89–112

Besra 2002// L. Besra, D.K. Sengupta, S.K. Roy, P. Ay, Flocculation and dewatering of kaolin suspensions in the presence of polyacrylamide and surfactants, Int. J. Miner. Process. 66 (2002) 203– 232

Besra 2003// L. Besra, D.K. Sengupta, S.K. Roy, P. Ay, Influence of polymer adsorption and conformation on flocculation and dewatering of kaolin suspension, Separation and Purification Technology 37 (2004) 231–246

Binner 2006// J. G. P. Binner, A. M. McDermott Rheological characterisation of ammonium polyacrylate dispersed, concentrated alumina suspensions, Ceramics International, 32 (2006) 803–810

Binner 2006// J. G. P. Binner, A. M. McDermott, Rheological characterisation of ammonium polyacrylate dispersed, concentrated alumina suspensions, Ceramics International, 32 (2006)803–810

Bish 1993// D. L. Bish, Rietveld refinement of the kaolinite structure at 1.5 K, Clays and Clay Minerals, 41 (1993) 738–744

Bleakley 1997// I. S. Bleakley, P. M. McGenity, C. Nutbeem, C. R. L. Golley, Patent EP 0768344 (1997) Bolland 1980// M. D. A. Bolland, A. M. Posner, J. P. Quirk, pH-independent and pH-dependent surface charges

on kaolinite, Clays and Clay Minerals 28 (1980) 412–418 Boufi 2002// S. Boufi, S. Baklouti, C. Pagnoux, J.-F. Baumard, Interaction of cationic and anionic

polyelectrolyte with SiO2 and Al2O3 powders, Journal of the European Ceramic Society 22 (2002) 1493–1500

Brady 1996// P. V. Brady, R. T. Cygan, K. L. Nagy, Molecular controls on kaolinite surface charge, Journal of Colloid and Interface Science 183 (1996) 356–364

Brinker 1990// C. J. Brinker, G. W. Scherer, Sol-gel science. The physics and chemictry of sol-gel processing, Academic Press, London, 1990

Brown 2000// A. B. D. Brown, S. M. Clarke, P. Convert, A. R. Rennie, Orientational order in concentrated dispersions, of plate-like kaolinite particles under shear, Journal of Rheology 44 (2000) 221–233


109

Bundy 1991// W. M. Bundy, J. N. Ishley, Kaolin in paper filling and coating, Applied Clay Science 5 (1991) 397–420

Bushell, 2002// Bushell, G.C., Yan, Y.D.,Woodfield, D., Raper, J., Amal, R., 2002. On techniques for the measurement of the mass fractal dimension of aggregates. Adv. Colloid Interface Sci. 95, 1–50.

Carreau 1999// P.J. Carreau, P.A. Lavoie, F. Yziquel, Rheological properties of concentrated suspensions, Rheology Series. Advances in the Flow and Rheology of Non-Newtonian Fluids 8 (1999) 1299–1345

Carty 1999// W. M. Carty, Colloidal nature of kaolinite, Am. Ceram. Soc. Bull., 78 (1999) 72–76. Celzard 1996// A. Celzard, E. McRae, C. Deleuze, M. Dufort, G. Furdin, J. F. Marêché, Critical concentration in

percolating systems containing a high-aspect-ratio filler, Physical Review B - Condensed Matter and Materials Physics 53 (1996) 6209–6214

Celzard 2001// A. Celzard, M. Krzesiñska, J. F. Marêché, S. Puricelli, Scalar and vectorial percolation in compressed expanded graphite, Physica A: Statistical Mechanics and its Applications 294 (2001) 283–294

Chakraborti, 2000// Chakraborti, R.K., Atkinson, J.F., Van Benschoten, J.E., 2000. Characterization of alum floc by image analysis. Environ. Sci. Technol. 34, 3969–3976.

Chamberlain 1977// R. J. Chamberlain, Process for stabilizing lime mud, US patent 4026991 (1977) Champion 1996// J. V. Champion, L. F. Gate, G. H. Meeten, P. R. Wood, Rheo-optics of concentrated kaolinite

suspensions, Colloids and Surfaces A: Physicochemical and Engineering Aspects, 111 (1996) 223–229

Chandrasekhar 2002// S. Chandrasekhar, S. Ramaswamy, Influence of mineral impurities on the properties of kaolin and its thermally treated products, Applied Clay Science, 21 (2002) 133–142

Conceicao 2003// S.I. Conceicao, J.L. Velho, J.M.F. Ferreira, Influence of deagglomeration and carboxymethyl cellulose binders on rheological behaviour of kaolin suspensions, Applied Clay Science 23 (2003) 257– 264

Conceicao 2005//S. Conceicao, N.F. Santos, J. Velho, J.M.F. Ferreira, Properties of paper coated with kaolin: The influence of the rheological modifier, Applied Clay Science 30 (2005) 165– 173

Coppin 2002// F. Coppin, G. Berger, A. Bauer, S. Castet, M. Loubet, Sorption of lanthanides on smectite and kaolinite, Chem. Geol. 182 (2002) 57–68

Curcio 1998// F. Curcio, B. A. DeAngelis, Dilatant behavior of superplasticized cement pastes containing metakaolin, Cement and Concrete Research, 28 (1998) 629–634

Cussler 1988// E. L. Cussler, S. E. Hughes, W. J. Ward III, R. Aris, Barrier membranes, Journal of Membrane Science, 38 (1988) 161–174

Das 2001// K. K. Das, P. Somasundaran, Ultra-low dosage flocculation of alumina using polyacrylic acid, Colloids and Surfaces A: Physicochemical and Engineering Aspects, 182 (2001) 25–33

Das 2003// K. K. Das, P. Somasundaran, Flocculation-dispersion characteristics of alumina using a wide molecular weight range of polyacrylic acids, Colloids and Surfaces A: Physicochemical and Engineering Aspects, 223 (2003) 17–25

Davidson 2003// P. Davidson, J.-Ch. P. Gabriel, Mineral liquid crystals, Current Opinion in Colloid & Interface Science, 9 (2005) 377–383

Davies 2000// J. Davies, J. G. P. Binner, The role of ammonium polyacrylate in dispersing concentrated alumina suspensions, Journal of the European Ceramic Society, 20 (2000) 1539–1553

DeRocher 2005// J. P. DeRocher, B. T. Gettelfinger, J. Wang, E. E. Nuxoll, E. L. Cussler, Barrier membranes with different sizes of aligned flakes, Journal of Membrane Science, 254 (2005) 21–30

Dussour 2000// C. Dussour, P. Favoriti, E. Vorobiev, Influence of chemical additives upon both filtration and electroosmotic dehydration of a kaolin suspension, Separation Sci. Technol. 35 (2000) 1179-1193

Egres 2005// R. G. Egres, N. J. Wagner, The rheology and microstructure of acicular precipitated calcium carbonate colloidal suspensions through the shear thickening transition, Journal of Rheology 49 (2005) 719–746

Farrokhpay, 2005// S. Farrokhpay, G. E. Morris, D. Fornasiero, P. Self, Influence of polymer functional group architecture on titania pigment dispersion, Colloids and Surfaces A: Physicochem. Eng. Aspects 253 (2005) 183–191

Ferris 1975// A. P. Ferris, W. B. Jepson, The exchange capacities of kaolinite and the preparation of homoionic clays, Journal of Colloid and Interface Science 51 (1975) 245–259

Fukuda 2001// Y. Fukuda, T. Togahi, Y. Suzuki, M. Naito, H. Kamiya, Influence of additive content of anionic polymer dispersant on dense alumina suspension viscosity, Chemical Engineering Science, 56 (2001) 3005–3010

Gamiz 2005// E. Gámiz, M. Melgosa, M. Sánchez-Marañón, J.M. Martín-García, R. Delgado, Relationships between chemico-mineralogical composition and color properties in selected natural and


110

calcined Spanish kaolins, Applied Clay Science 28 (2005) 269–282 Garrido 1990// L. B. Garrido, J. Gainza, E. Pereira, Rheological properties of concentrated aqueous suspensions

of kaolin — application of the multiple ternary Bingham model, Applied Clay Science 5 (1990) 217–228

Garrido 2001// L. B. Garrido, E. F. Aglietti, Zircon based ceramics by colloidal processing, Ceramics International, 27 (2001) 491–499

Glover, 2004// Glover, S.M., Yan, Y.D., Jameson, G.J., Biggs, S., 2004. Dewatering properties of dual-polymer-flocculated systems. Int. J. Miner. Process.. 73, 145–160.

Gregory, 1998// Gregory, J., 1998. The role of floc density in solid–liquid separation. Filtr. Sep. 35, 367–371. Hansen 1998// C. W. Hansen, Production of concentrated carbonate suspensions, International patent

WO/2000/39029 (2000) Happel 1965// J. Happel, H. Brenner, Low Reynolds number hydrodynamics, Prentice-Hall, 1965 Herrington 1992// T. M. Herrington, A. Q. Clarke, J. C. Watts, The surface charge of kaolin, Colloids and

Surfaces 68 (1992) 161–169 Hogg 1999// R Hogg, The role of polymer adsorption kinetics in flocculation, Colloids and Surfaces A:

Physicochemical and Engineering Aspects 146 (1999) 253–263 Hogg 2000// R. Hogg, Flocculation and dewatering, Int. J. Miner. Process. 58 2000. 223–236 Hunter 2001// R. J. Hunter, Foundations of Colloid Science, Clarendon Press, Oxford (2001) Husson 2003// M. Husson, C. Jacquemet, E. Vorobiev, Method for producing aqueous suspensions of mineral

fillers, the thus obtained aqueous suspensions of mineral fillers and the use thereof, US Patent Application 20050249759 (2003)

Ioannou 1997// A. Ioannou, A. Dimirkou, Phosphate adsorption on hematite, kaolinite, and kaolinite–hematite (k–h) systems as described by a constant capacitance model, Journal of Colloid and Interface Science, 192 (1997) 119–128

Israelachvili 1992// Intermolecular and surface forces, Academic press, London, 1992 Järnström 1990// L. Järnström, P. Stenius, Adsorption of polyacrylate and carboxy methyl cellulose on kaolinite:

Salt effects and competitive adsorption, Colloids and Surfaces, 50 (1990) 47–73 Jepson 1984// W.B. Jepson , Kaolins: their properties and uses, Philosophical Transactions of the Royal Society

of London A311 (1984) 411-432 Jogun 1996// S. Jogun, C. F. Zukoski, Rheology of dense suspensions of platelike particles, Journal of Rheology

40 (1996) 1211–1232 Johnson 1998a// S. B. Johnson, A. S. Russell, P. J. Scales, Surface chemistry–rheology relationships in

concentrated mineral suspensions, Int. J. Miner. Process. 58 _2000. 267–304 Johnson 1998b// S. B. Johnson, A. S. Russell, P. J. Scales, Volume fraction effects in shear rheology and

electroacoustic studies of concentrated alumina and kaolin suspensions, Colloids and Surfaces A: Physicochemical and Engineering Aspects 141 (1998) 119–130

Kapur 1997// P. C. Kapur, P. J. Scales, D. V. Boger, T. W. Healy, A theoretical framework for the yield stress of suspensions loaded with size distributed particles, J. American Institute Chemical Engineers 43 (1997) 1171–1179

Kim 2009// S. Kim, A. M. Palomino, Polyacrylamide-treated kaolin: A fabric study, Applied Clay Science (2009) 270–279

Kislenko 2001// V. N. Kislenko, R. M. Verlinskaya, Rheological Behavior of Kaolin and Montmorillonite Suspensions at Low Concentrations, Journal of Colloid and Interface Science 244 (2001) 405–409

Klimpel 1991// R.C. Klimpel, R. Hogg, Evaluation of floc structures, Colloids and Surfaces Volume 55, 1991, Pages 279-288

Konan 2007// K. L. Konan, C. Peyratout, J.-P. Bonnet, A. Smith, A. Jacquet, P. Magnoux, P. Ayrault, Surface properties of kaolin and illite suspensions in concentrated calcium hydroxide medium, Journal of Colloid and Interface Science 307 (2007) 101–108

Kong 2006// H. J. Kong, S. G. Bike, V. C. Li, Electrosteric stabilization of concentrated cement suspensions imparted by a strong anionic polyelectrolyte and a non-ionic polymer, Cement and Concrete Research 36 (2006) 842–850

Kretzschmar 1998// R. Kretzschmar, H. Holthoff, H. Sticher, Influence of pH and humic acid on coagulation kinetics of kaolinite: a dynamic light scattering study, J. Colloid Interface Sci. 202 (1998) 95–103

Krieger 1972// I. M. Krieger, Rheology of monodisperse latices, Adv. Colloid Interface Sci. 3 (1972) 111-136 Kruyt 1952// H. R. Kruyt, Colloid Science, Vol. 1, Elsevier, Amsterdam, 1952 Kugge 2004// Christian Kugge, Vincent S.J. Craig, John Daicic, A scanning electron microscope study of the

surface structure of mineral pigments, latices and thickeners used for paper coating on non-absorbent substrates, Colloids and Surfaces A: Physicochem. Eng. Aspects 238 (2004) 1–11

Labanda 2005// J. Labanda, J. Llorens, Influence of sodium polyacrylate on the rheology of aqueous Laponite


111

dispersions, Journal of Colloid and Interface Science, 289 (2005) 86–93 Lagaly 1989// G. Lagaly, Principles of flow of kaolin and bentonite dispersions, Applied Clay Science 4 (1989)

105–123 Leong 1995// Y. K. Leong, P. J. Scales, T. W. Healy, D. V. Boger, Interparticle forces arising from adsorbed

polyelectrolytes in colloidal suspensions, Colloids and Surfaces A: Physicochemical and Engineering Aspects, 95 (1995) 43–52

Li 2007// J. Li, J.-K. Kim, Percolation threshold of conducting polymer composites containing 3D randomly distributed graphite nanoplatelets, Composites Science and Technology 67 (2007) 2114–2120

Li 2007// T. Li, Z. Zhu, D. Wang, C. Yao, H. Tang, The strength and fractal dimension characteristics of alum–kaolin flocs, Int. J. Miner. Process. 82 (2007) 23–29

Li, 2006// Li, T., Zhu, Z., Wang, D.S., Yao, C.H., Tang, H.X., 2006. Characterization of floc size, strength and structure under various coagulation mechanisms. Powder Technol. 168, 104–110.

Loginov 2008// M. Loginov, O. Larue, N. Lebovka, E. Vorobiev, Fluidity of highly concentrated kaolin suspensions: Influence of particle concentration and presence of dispersant, Colloids and Surfaces A: Physicochem. Eng. Aspects 325 (2008) 64–71

Lu 2005// C. Lu, Y.-W. Mai, Influence of aspect ratio on barrier properties of polymer-clay nanocomposites, Physical Review Letters 95 (2005) 088303-1–088303-4

Luckham 1999// P. F. Luckham, S. Rossi, The colloidal and rheological properties of bentonite suspensions, Advances in Colloid and Interface Science 82 (1999) 43–92

Ma 1999// C. Ma, R. A. Eggleton, Cation exchange capacity of kaolinite, Clays and Clay Minerals 47 (1999) 174–180

Marco 2004// P. Marco, J. Labanda, J. Llorens, The effects of some polyelectrolyte chemical compositions on the rheological behaviour of kaolin suspensions, Powder Technology, 148 (2004) 43–47

Marco 2005// P. Marco, J. Llorens, Adsorption of some linear copolymers onto kaolin particles in concentrated suspensions, Colloids and Surfaces A: Physicochemical and Engineering Aspects, 270–271 (2005) 291–295

Moan 2003// M. Moan, T. Aubry, F. Bossard, Nonlinear behavior of very concentrated suspensions of plate-like kaolin particles in shear flow, Journal of Rheology 47 (2003) 1493–1504

Moraru 2004// V. Moraru, N. Lebovka, D. Shevchenko, Structural transitions in aqueous suspensions of natural graphite, Colloids and Surfaces A: Physicochem. Eng. Aspects 242 (2004) 181–187

Moreno 1998// R. Moreno, A. Salomoni, S. M. Castanho, Colloidal filtration of silicon nitride aqueous slips. Part I: optimization of the slip parameters, Journal of the European Ceramic Society, 18 (1998) 405–416

Mota 2002// M. Mota, J. A. Teixeira, A. Yelshin, Influence of cell-shape on the cake resistance in dead-end and cross-flow filtrations, Separation and Purification Technology, 27 (2002) 137–144

Mouroko-Mitoulou 2002// Th.Mouroko-Mitoulou, Filtration des suspensions minérales avec formation d’un gâteau liquéfiable: cas d’une suspension de carbonate de calcium, Ph. D. Thesis, Université de Technologie de Compiègne (2002)

Mpofu 2003a// P. Mpofu, J. Addai-Mensah, J. Ralston, Investigation of the effect of polymer structure type on flocculation, rheology and dewatering behaviour of kaolinite dispersions, Int. J. Min. Proc. 71 (2003) 247–268

Mpofu 2003b// P. Mpofu, J. Addai-Mensah, J. Ralston, Influence of hydrolyzable metal ions on the interfacial chemistry, particle interactions, and dewatering behavior of kaolinite dispersions, Journal of Colloid and Interface Science 261 (2003) 349–359

Murray 2005// H.H. Murray, J.E. Kogel, Engineered clay products for the paper industry, Appl. Clay Sci. 29 (2005) 199-206.

Nasser 2007a// M.S. Nasser, A.E. James, Effect of polyacrylamide polymers on floc size and rheological behaviour of kaolinite suspensions, Colloids and Surfaces A: Physicochem. Eng. Aspects 301 (2007) 311–322

Nasser 2007b// M. S. Nasser, A. E. James, Compressive and shear properties of flocculated kaolinite–polyacrylamide suspensions, Colloids and Surfaces A: Physicochemical and Engineering Aspects 317 (2008) 211–221

Onsager 1949// L. Onsager, The effects of shape on the interaction of colloidal particles, Annals of the New York Academy of Sciences, 51 (1949) 627–659

Palmqvist 2006// L. Palmqvist, O. Lyckfeldt, E. Carlstrom, P. Davoust, A. Kauppi, K. Holmberg, Dispersion mechanisms in aqueous alumina suspensions at high solids loadings, Colloids and Surfaces A: Physicochem. Eng. Aspects 274 (2006) 100–109

Papo 2002// A. Papo, L. Piani, R. Ricceri, Sodium tripolyphosphate and polyphosphate as dispersing agents for kaolin suspensions: rheological characterization, Colloids and Surfaces A: Physicochemical and Engineering Aspects, 201(2002) 219–230


112

Papo 2004// A. Papo, L. Piani, Effect of various superplasticizers on the rheological properties of Portland cement pastes, Cement and Concrete Research, 34 (2004) 2097–2101

Parker 1997// A. Parker, A. Pich, Patent EP 0636578 (1997) Penner 2001// D. Penner, G. Lagaly, Influence of anions on the rheological properties of clay mineral

dispersions, Applied Clay Science, 19 (2001)131–142 Perdigon-Aller 2005// A. C. Perdigon-Aller, M. Aston, S. M. Clarke Preferred orientation in filtercakes of

kaolinite, Journal of Colloid and Interface Science, 290 (2005) 155–165 Pignon 2000// F. Pignon, A. Magnin, J.-M. Piau, B. Cabane, P. Aimar, M. Meireles, P. Lindner, Structural

characterisation of deposits formed during frontal filtration, Journal of Membrane Science, 174 (2000) 189–204

Purdey 1976// J. A. Purdey, Particulate solid materials, US patent 3954609 (1976) Quemada 1998a// D. Quemada, Rheological modelling of complex fluids: II. Shear thickening behavior due to

shear induced flocculation, The European Physical Journal. Applied Physics 2 (1998) 175–181

Quemada 1998b// D. Quemada, Rheological modeling of complex fluids: III. Dilatant behavior of stabilized suspensions, The European Physical Journal. Applied Physics 3 (1998) 309–320

Quemada 2002// D. Quemada, C. Berli, Energy of interaction in colloids and its implications in rheological modeling, Advances in Colloid and Interface Science 98 (2002) 51–85

Quemada 2006// D. Quemada, Modelisation rheologique structurelle, Tec & Doc, Paris, 2006. Raghavan 1997// P. Raghavan, S. Chandrasekhar, A. D. Damodaran, Value addition of paper coating grade

kaolins by the removal of ultrafine coloring impurities, International Journal of Mineral Processing 50 (1997) 307–316

Raghavan 1997// S. R. Raghavan, S. A. Khan, Shear-thickening response of fumed silica suspensions under steady and oscillatory shear, Journal of Colloid and Interface Science 185 (1997) 57–67

Rahmani 2005// N. H. G. Rahmani, T. Dabros, J. H. Masliyah, Fractal structure of asphaltene aggregates, Journal of Colloid and Interface Science 285 (2005) 599–608

Rand 1977// B. Rand, I. E. Melton, Particle interactions in aqueous kaolinite suspensions : I. Effect of pH and electrolyte upon the mode of particle interaction in homoionic sodium kaolinite suspensions, Journal of Colloid and Interface Science 60 (1977) 308–320

Romagnoli 2007// M. Romagnoli, F. Andreola, Mixture of deflocculants: A systematic approach, Journal of the European Ceramic Society, 27( 2007) 1871–1874

Sahimi 1998// M. Sahimi, Non-linear and non-local transport processes in heterogeneous media: from long-range correlated percolation to fracture and materials breakdown, Physics Reports 306 (1998) 213–395

Santhiya 1998// D. Santhiya, G. Nandini, S. Subramanian, K. A. Natarajan, S. G. Malghan, Effect of polymer molecular weight on the absorption of polyacrylic acid at the alumina-water interface, Colloids and Surfaces A: Physicochemical and Engineering Aspects, 133 (1998) 157–163

Santhiya 2000// D. Santhiya, S. Subramanian, K. A. Natarajan, S. G. Malghan, Surface chemical studies on alumina suspensions using ammonium poly(methacrylate), Colloids and Surfaces A: Physicochemical and Engineering Aspects, 164 (2000) 143–154

Sastry 1995// N. V. Sastry, J.-M. Séquaris, M. J. Schwuger, Adsorption of polyacrylic acid and sodium dodecylbenzenesulfonate on kaolinite, Journal of Colloid and Interface Science, 171 (1995) 224–233

Schofield 1954// R. K. Schofield, H. R. Samson, Flocculation of kaolinite due to the attraction of oppositely charged crystal faces, Discuss. Faraday Soc. 18 (1954) 135–145

Shen 2004a// Z.-G. Shen, J.-F. Chen, H. Zou, J. Yun, Rheology of colloidal nanosized BaTiO3 suspension with ammonium salt of polyacrylic acid as a dispersant, Colloids and Surfaces A: Physicochemical and Engineering Aspects, 244 (2004) 61–66

Shen 2004b// Z.-G. Shen, J.-F. Chen, H. Zou, J. Yun, Dispersion of nanosized aqueous suspensions of barium titanate with ammonium polyacrylate Journal of Colloid and Interface Science, 275(2004)158–164

Shih 1999// C.-J. Shih, M.-H. Hon, Electrokinetic and Rheological Properties of Aqueous TiN Suspensions with Ammonium Salt of Poly(methacrylic Acid), Journal of the European Ceramic Society 19 (1999) 2773–2780

Sigworth 1996// G. K. Sigworth, Rheological properties of metal alloys in the semi-solid state, Can. Metall. Q. 35 (1996) 101–122.

Silbert 1999// L. Silbert, J. R. Melrose, R. C. Ball, The rheology and microstructure of concentrated, aggregated colloids, J. Rheol. 43 (1999) 673–700

Sjöberg 1999// M. Sjöberg, L. Bergström, A. Larsson, E. Sjöström, The effect of polymer and surfactant adsorption on the colloidal stability and rheology of kaolin dispersions, Colloids and Surfaces A: Physicochemical and Engineering Aspects, 159 (1999) 197–208


113

Solomon, 1983// D. H. Solomon, D. G. Hawthorne, Chemistry of pigments and fillers, Wiley, New York, 1983 Soua 2004// Z. Soua, Th. Mouroko-Mitoulou, E. Vorobiev, Study of filtration/liquefaction of calcium carbonate

dispersions, Chemical Engineering Research and Design, 82 (2004) 105–109 Soua 2006// Z. Soua, O. Larue, E. Vorobiev, J.-L. Lanoiselle, Estimation of floc size in highly concentrated

calcium carbonate suspension obtained by filtration with dispersant, Colloids and Surfaces A: Physicochem. Eng. Aspects 274 (2006) 1–10

Soua 2006b// Z. Soua, Déshydratation mécanique de suspensions minérales en présence de dispersant : caractérisation physico-chimique et rhéologique des gâteaux obtenus par filtration avec formation de précouche (FAP), Ph. D. Thesis, Université de Technologie de Compiègne (2002)

Starov 2002// V. Starov, V. Zhdanov, M. Meireles, C. Molle, Viscosity of concentrated suspensions: influence of cluster formation, Advences in Colloid and Interface Science 96 (2002) 279-293

Stein 1995// H. N. Stein, The Preparation of Dispersions in Liquids, New York, Marcel Dekker (1995) Stenius 1990// P. Stenius, L. Jarnstrom, M. Rigdahl, Aggregation in concentrated kaolin suspensions stabilised

by polyacrylate, Colloids and Surfaces 51 (1990) 219–238 Stenius 1990// P. Stenius, L. Järnström, M. Rigdahl, Aggregation in concentrated kaolin suspensions stabilized

by polyacrylate, Colloids and Surfaces, 51 (1990) 219–238 Story 1990// P. M. Story, Process for preparing high solids slurries, International patent WO/1990/013606

(1990) Tadros 1990// Th. F. Tadros, Use of viscoelastic measurements in studying interactions in concentrated

dispersions? Langmuir 6 (1990) 28–35 Tang 2001// S. Tang, Y. Ma, C. Shiu, Modelling the mechanical strength of fractal aggregates, Colloids and

Surfaces A: Physicochemical and Engineering Aspects 180 (2001) 7–16 Tang, 1999// Tang, S., 1999. A model to describe the settling behavior of the fractal aggregates. Colloids Surf.,

A Physicochem. Eng. Asp. 157, 185–192. Taylor 2002// M. L. Taylor, G. E. Morris, P. G. Self, R. St. C. Smart, Kinetics of adsorption of high molecular

weight anionic polyacrylamide onto kaolinite: the flocculation process, Journal of Colloid and Interface Science 250 (2002) 28–36

Teh 2009// E.-J. Teh, Y. K. Leong, Y. Liu, A. B. Fourie, M. Fahey, Differences in the rheology and surface chemistry of kaolin clay slurries: The source of the variations, Chemical Engineering Science 64 (2009) 3817–3825

Tian 2006// B. Tian, X. Ge, G. Pan, B. Fan, Z. Luan, Adsorption and flocculation behaviors of polydiallyldimethylammonium (PDADMA) salts: Influence of counterion, Int. J. Min. Proc. 79 (2006) 209–216

Tobori 2003// N. Tobori, T. Amari, Rheological behavior of highly concentrated aqueous calcium carbonate suspensions in the presence of polyelectrolytes Colloids and Surfaces A: Physicochemical and Engineering Aspects, 215 (2003)163–171

Tombacz 1999// E. Tombacz, G. Filipcsei, M. Szekeres, Z. Gingl, Particle aggregation in complex aquatic systems, Colloids and Surfaces, A: Physicochemical and Engineering Aspects 151 (1999) 233–244.

Tombacz 2006// E. Tombácz, M. Szekeres, Surface charge heterogeneity of kaolinite in aqueous suspension in comparison with montmorillonite, Applied Clay Science 34 (2006) 105–124

Tseng 2002// W. J. Tseng, S.-Y. Li, Rheology of colloidal BaTiO3 suspension with ammonium polyacrylate as a dispersant, Materials Science and Engineering A, 333(2002)314–319

Turchiulli 2004// C. Turchiuli, C. Fargues, Influence of structural properties of alum and ferric flocs on sludge dewaterability, Chemical Engineering Journal 103 (2004) 123–131

Van Olphen 1963// H. Van Olphen. An Introduction to Clay Colloid Chemistry (2nd ed.), National Academy of Sciences, Washington (1977)

Vorobiev 2004// E. Vorobiev, Th. Mouroko-Mitoulou, Z. Soua, Precoat filtration of a deflocculated mineral suspension in the presence of a dispersant Colloids and Surfaces A: Physicochemical and Engineering Aspects, 251 (2004) 5–17

Waite, 2001// Waite, T.D., Cleaver, J.K., Beattie, J.K., 2001. Aggregation kinetics and fractal structure of γ-alumina assemblages. J. Colloid Interface Sci. 241, 333–339.

Wakeman, 1999// R. J. Wakeman, E. S. Tartleton, Filtration: equipment selection, modelling and process simulation, Elsevier, New-York (1999)

Walsh 2008// S. D. C. Walsh, M. O. Saar, Numerical models of stiffness and yield stress growth in crystal-melt suspensions, Earth and Planetary Science Letters 267 (2008) 32–44

Wan 2002// J. Wan, T. K. Tokunaga, Partitioning of Clay Colloids at Air–Water Interfaces, Journal of Colloid and Interface Science 247 (2002) 54–61

Wiekmann 1980// H. Wiekmann, K. Fincke, F. A. Wiekmann, H. Liska, German patent DE 3008682 (1980) Williams 1978// D. J. A. Williams, K. P. Williams, Electrophoresis and zeta potential of kaolinite, Journal of


114

Colloid and Interface Science 65 (1978) 79–87 Willis 1998// M. J. Willis, S. Behl, R. Young, Filter aid for clay processing, International patent

WO/1998/051623 (1998) Wu, 2002// Wu, R.M., Lee, D.J., Waite, T.D., Guan, J., 2002. Multilevel structure of sludge flocs. J. Colloid

Interface Sci. 252, 383–392. Yu 2006// J. Yu, D. Wang, X. Ge, M. Yan, M. Yang, Flocculation of kaolin particles by two typical

polyelectrolytes: A comparative study on the kinetics and floc structures, Colloids and Surfaces A: Physicochemical and Engineering Aspects 290 (2006) 288–294

Yuan 1997// J. Yuan, H. H. Murray, The importance of crystal morphology on the viscosity of concentrated suspensions of kaolins, Applied Clay Sci. 12 (1997) 209–219

Yuanling 2004// S. Yuanling, L. Xiaolin, C. Jianfeng, The maximum solid loading and viscosity estimation of ultra-fine BaTiO3 aqueous suspensions, Colloids and Surfaces A: Physicochem. Eng. Aspects 247 (2004) 27–34

Zaman 2002// A. A. Zaman, R. Tsuchiya, B. M. Moudgil, Adsorption of a low-molecular-weight polyacrylic acid on silica, alumina and kaolin, Journal of Colloid and Interface Science 256 (2002) 73–78

Źbik 2009// M. S. Źbik, R. L. Frost, Micro-structure differences in kaolinite suspensions, Journal of Colloid and Interface Science 339 (2009) 110–116

Zhang 2006// J. Zhang, M. Maeda, N. Kotobuki, M. Hirose, H. Ohgushi, D. Jiang, M. Iwasa, Aqueous processing of hydroxyapatite, Materials Chemistry and Physics, 99 (2006) 398–404

I.6.3. Literature cited on the subject of Dynamic Filtration Al-Akoum 2002// O. Al-akoum, M. Mercier-Bonin, L. Ding, C. Fonade, Ph. Aptel, M. Jaffrin, Comparison of

three different systems used for flux enhancement: application to crossflow filtration of yeast suspensions, Desalination, 147 (2002) 31–36

Al-Malack 2004// M. H. Al-Malack, A. A. Bukhari, N. S. Abuzaid, Crossflow microfiltration of electrocoagulated kaolin suspension: fouling mechanism, Journal of Membrane Science, 243 (2004) 143–153

Altmann 1997// J. Altmann, S. Ripperger, Particle deposition and layer formation at the crossflow microfiltration, J. Membr. Sci., 124 (1997) 119–128

Bacchin 1996// P. Bacchin, P. Aimar, V. Sanchez, Influence of surface interaction on transfer during colloid ultrafiltration, Journal of Membrane Science, 115 (1996) 49–63

Benkahla 1995// Y. K. Benkahla, A. Ould-Dris, M. Y. Jaffrin, D. Si-Hassen, Cake growth mechanism in cross-flow microfiltration of mineral suspensions, Journal of Membrane Science, 98 (1995) 107–117

Bott 2000// R. Bott, Th. Langeloh, E. Ehrfeld, Dynamic cross flow filtration, Chemical Engineering Journal, 80 (2000) 245–249

Bouzerar 1999// R. Bouzerar, Filtration dynamique dans un module plan à disque rotatif : application a des suspensions minerales, Ph. D. Thesis, Université de Technologie de Compiègne (2009)

Bouzerar 2000// R. Bouzerar, L. Ding, M. Y. Jaffrin, Local permeate flux–shear–pressure relationships in a rotating disk microfiltration module: implications for global performance, Journal of Membrane Science, 170 (2000) 127–141

Bouzerar 2003// R. Bouzerar, P. Paullier, M. Y. Jaffrin, Concentration of mineral suspensions and industrial effluents using a rotating disk dynamic filtration module, Desalination, 158 (2003) 79–85

Bowen 2001// W. R. Bowen, H. N. S. Yousef, J. I. Calvo, Dynamic crossflow ultrafiltration of colloids: a deposition probability cake filtration approach, Separation and Purification Technology, 24 (2001) 297–308

Buscall 1988// R. Buscall, P. D. A. Mills, J. W. Goodwin, D. W. Lawson, Scaling Behaviour of the rheology of aggregate networks formed from colloidal particles, J. Chem. Soc., Faraday Trans. I., 84 (1988) 4249–4260

Chang 1995// D.-J. Chang, F.-C. Hsu, S.-J. Hwang, Steady-state permeate flux of cross-flow microfiltration, Journal of Membrane Science, 98 (1995) 97–106

Chellam 1998// S. Chellam, M. R. Wiesner, Evaluation of crossflow filtration models based on shear-induced diffusion and particle adhesion: Complications induced by feed suspension polydispersivity, Journal of Membrane Science, 138 (1998) 83–97

Chen 2004// V. Chen, H. Li, A. G. Fane, Non-invasive observation of synthetic membrane processes – a review of methods, Journal of Membrane Science 241 (2004) 23–44

Ding 2006// L. H. Ding, M. Y. Jaffrin, M. Mellal, G. He, Investigation of performances of a multishaft disk (MSD) system with overlapping ceramic membranes in microfiltration of mineral


115

suspensions, Journal of Membrane Science, 276 (2006) 232–240 Elzo 1998// D. Elzo, I. Huisman, E. Middelink, V. Gekas, Charge effects on inorganic membrane performance in

a cross-flow microfiltration process, Colloids and Surfaces A: Physicochemical and Engineering Aspects, 138 (1998) 145–159

Foley 1995// G. Foley, D. M. Malone, F. MacLoughlin, Modelling the effects of particle polydispersity in crossflow filtration, Journal of Membrane Science, 99 (1995) 77–88

Gupta 1992// B. B. Gupta, P. Blanpain, M. Y. Jaffrin, Permeate flux enhancement by pressure and flow pulsations in microfiltration with mineral membranes, Journal of Membrane Science, 70 (1992) 257–266

Gupta 1995// B. B. Gupta, J. A. Howell, D. Wu, R. W. Field, A helical baffle for cross-flow microfiltration, Journal of Membrane Science, 102 (1995) 31–42

He 2007// G. He, L. H. Ding, P. Paullier, M. Y. Jaffrin, Experimental study of a dynamic filtration system with overlapping ceramic membranes and non-permeating disks rotating at independent speeds, Journal of Membrane Science, 300 (2007) 63–70

Horčičková 2009// J. Horčičková, P. Mikulášek, J. Dvořáková, The effect of pre-treatment on crossflow microfiltration of titanium dioxide dispersions, Desalination, 240 (2009) 257–261

Howell 1993// J. A. Howell, R. W. Field, D. Wu, Yeast cell microfiltration: Flux enhancement in baffled and pulsatile flow systems, Journal of Membrane Science, 80 (1993) 59–71

Huisman 1998// I. H. Huisman, D. Elzo, E. Middelink, A. Ch. Trägårdh, Properties of the cake layer formed during crossflow microfiltration, Colloids and Surfaces A: Physicochemical and Engineering Aspects, 138 (1998) 265–281

Husson 2003// M. Husson, C. Jacquemet, E. Vorobiev, Method for producing aqueous suspensions of mineral fillers, the thus obtained aqueous suspensions of mineral fillers and the use thereof, US Patent Application 20050249759 (2003)

Jaffrin 1994// M. Y. Jaffrin, B. B. Gupta, P. Paullier, Energy saving pulsatile mode cross flow filtration, Journal of Membrane Science, 86 (1994) 281–290

Jaffrin 2008// M. Y. Jaffrin, Dynamic shear-enhanced membrane filtration: A review of rotating disks, rotating membranes and vibrating systems, Journal of Membrane Science, 324 (2008) 7–25

Jönsson 1996// A.-S. Jönsson, C. Jönsson, M. Teppler, P. Tomani, S. Wännström, Treatment of paper coating colour effluents by membrane filtration, Desalination, 105 (1996) 263–276

Klein 1999// G.-M. Klein, J. Meier, V. Kottke, Fouling in Membrane Apparatus: The Mechanisms of Particle Deposition, Food and Bioproducts Processing, 77 (1999) 119–126

Kosmulski 2003// M. Kosmulski, E. Maczka, K. Marczewska-Boczkowska, J. B. Rosenholm, Electrokinetic potentials of mineral oxides and calcium carbonate in artificial seawater, Marine Pollution Bulletin, 46 (2003) 120–122

Krstićś 2004// D. M. Krstićś, M. N. Tekić, M. D. Carić, S. D. Milanović, Static turbulence promoter in cross-flow microfiltration of skim milk, Desalination, 163 (2004) 297–309

Li 2002// J. Li, R. D. Sanderson, E. P. Jacobs, Non-invasive visualization of the fouling of microfiltration membranes by ultrasonic time-domain reflectometry, Journal of Membrane Science, 201 (2002) 17–29

Li 2009// L. Li, L. Ding, Z. Tu, Y. Wan, D. Clausse, J.-L. Lanoisellé, Recovery of linseed oil dispersed within an oil-in-water emulsion using hydrophilic membrane by rotating disk filtration system, Journal of Membrane Science, 342 (2009) 70–79

Meier 2002// J. Meier, G.-M. Klein, V. Kottke, Crossflow filtration as a new method of wet classification of, ultrafine particles, Separation and Purification Technology 26 (2002) 43–50

Mikulášek 1998// P. Mikulášek, R. J. Wakeman, J. Q. Marchant, Crossflow microfiltration of shear-thinning aqueous titanium dioxide dispersions, Chemical Engineering Journal, 69 (1998) 53–61

Mikulášek 2004// P. Mikulášek, P. Doleček, D. Šmídová, P. Pospíšil, Crossflow microfiltration of mineral dispersions using ceramic membranes, Desalination, 163 (2004) 333–343

Mori 2008// T. Mori, T. Katsuoka, B. Ochirkhuyag, J. Tsubaki, T. Sugimoto, H. K. Choi, Development of a novel high performance continuous cake-less filtration system, Proc. 10th World Filtration Congress, Leipzig, 2008, II:340–344

Mota 2002// M. Mota, J. A. Teixeira, A. Yelshin, Influence of cell-shape on the cake resistance in dead-end and cross-flow filtrations, Separation and Purification Technology, 27 (2002) 137–144

Mouroko-Mitoulou 2002// Th.Mouroko-Mitoulou, Filtration des suspensions minérales avec formation d’un gâteau liquéfiable: cas d’une suspension de carbonate de calcium, Ph. D. Thesis, Université de Technologie de Compiègne (2002)

Nguyen 2002// M.-T. Nguyen, S. Ripperger, Investigation on the effect of flocculants on the filtration behavior in microfiltration of fine particles, Desalination, 147 (2002) 37–42

Ochirkhuyag 2008// B. Ochirkhuyag, T. Mori, T. Katsuoka, H. Satone, J. Tsubaki, H. Choi, T. Sugimoto, Development of a high-performance cake-less continuous filtration system, Chemical


116

Engineering Science 63 (2008) 5274–5282 Olivier 2007// J. Olivier, J. Vaxelaire, E. Vorobiev, Modelling of cake filtration: An overview, Separation

Science and Technology, 42 (2007) 1667–1700 Ould-Dris 2000// A. Ould-Dris, M. Y. Jaffrin, D. Si-Hassen, Y. Neggaz, Analysis of cake build-up and removal

in cross-flow microfiltration of CaCO3 suspensions under varying conditions, Journal of Membrane Science, 175 (2000) 267–283

Perdigón 2007// Ana C. Perdigón, Stuart M. Clarke, Mark Aston, Neutron diffraction study of the orientational order in filter cakes made of kaolinite under laminar and turbulent cross-flow, Journal of Membrane Science, 298 (2007) 80–91

Perdigon-Aller 2005// A. C. Perdigon-Aller, M. Aston, S. M. Clarke Preferred orientation in filtercakes of kaolinite, Journal of Colloid and Interface Science, 290 (2005) 155–165

Porter 1972// M. C. Porter, Concentration polarization with membrane ultrafiltration, Ind. Eng. Chem. Prod. Res. Develop., 11 (1972) 234–248

Raha 2005// S. Raha, K. C. Khilar, Pradip, P. C. Kapur, Pareto Profile Benchmark for Kinetics of Filtration and Extent of Dewatering of Fine and Colloidal Suspensions, Ind. Eng. Chem. Res., 44 (2005) 9364–9368

Raha 2006// S. Raha, K. C. Khilar, Pradip, P. C. Kapur, A mean Phi model for pressure filtration of fine and colloidal suspensions, Canadian Journal of Chemical Engineering, 84 (2006) 83–93

Raha 2007// S. Raha, K. C. Khilar, P. C. Kapur, Pradip, Regularities in pressure filtration of fine and colloidal suspensions, Int. J. Miner. Process. 84 (2007) 348–360

Raha 2009// S. Raha, Pradip, P. C. Kapur, K. C. Khilar, Enhancement of Colloidal Filtration: A New Combined Approach Based on Cake and Suspension Destabilization, Ind. Eng. Chem. Res., 48 (2009) 7276–7282

Ripperger 2002// S. Ripperger, J. Altmann, Crossflow microfiltration – state of the art, Separation and Purification Technology, 26 (2002) 19–31

Sethi 1997// S. Sethi, M. R. Wiesner, Modeling of transient permeate flux in cross-flow membrane filtration incorporating multiple particle transport mechanisms, Journal of Membrane Science, 136 (1997) 191–205

Šmídová 2004// D. Šmídová, P. Mikulášek, R. J. Wakeman, P. Velikovská, Influence of ionic strength and pH of dispersed systems on microfiltration, Desalination, 163 (2004) 323–332

Soua 2006// Z. Soua, O. Larue, E. Vorobiev, J.-L. Lanoiselle, Estimation of floc size in highly concentrated calcium carbonate suspension obtained by filtration with dispersant, Colloids and Surfaces A: Physicochem. Eng. Aspects 274 (2006) 1–10

Trave 2007// J. G.-C. Trave, E. Vorobiev, A. O. Dris, Production of a highly concentrated CaCO3 suspension by cross-flow microfiltration in the presence of a dispersant, Separation Science and Technology 42 (2007) 319–331

Tu 2009// Z. Tu, Filtration dynamique de suspensions de CaCO3 et de solutions de surfactants, Ph. D. Thesis, Université de Technologie de Compiègne (2009)

Vassilieff 1994// C. S. Vassilieff, I. G. Momtchilova, R. A. Krustev, Cross-flow microfiltration of kaolinite-in-water dispersions, Colloids and Surfaces A: Physicochemical and Engineering Aspects, 92 (1994) 231–247

Wakeman 2002// R. J. Wakeman, C. J. Williams, Additional techniques to improve microfiltration, Separation and Purification Technology, 26 (2002) 3–18

Wronski 1989// S. Wronski, E. Molga, L. Rudniak, Dynamic filtration in biotechnology, Bioprocess engineering, 4 (1989) 99–104

Xu-Jiang 1995// Y. Xu-Jiang, J. Dodds, D. Leclerc, Cake characteristics in crossflow and dead-end microfiltration, Filtration & Separation, 32 (1995) 795–798

Zhao 2005// Y. Zhao, W. Xing, N. Xu, F.-S. Wong, Effects of inorganic salt on ceramic membrane microfiltration of titanium dioxide suspension, Journal of Membrane Science, 254 (2005) 81–88

I.6.4. Literature cited on the subject of Filtration of Disrupted Yeast Suspension Agerkvist 1990// I. Agerkvist, L. Eriksson, S.-O. Enfors, Selective flocculation with Chitosan in Escherichia coli

disintegrates: Effects of pH and nuclease treatment, Enzyme and Microbial Technology, 12 (1990) 584–590

Aspelund 2008// M. T. Aspelund, G. Rozeboom, M. Heng, C. E. Glatz, Improving permeate flux and product transmission in the microfiltration of a bacterial cell suspension by flocculation with cationic polyelectrolytes, Journal of Membrane Science, 324 (2008) 198–208

Bailey 2000// S. M. Bailey, M. M. Meagher, Separation of soluble protein from inclusion bodies in Escherichia


117

coli lysate using crossflow microfiltration, Journal of Membrane Science, 166 (2000) 137–146

Baran 1988// A. A. Baran, Flocculation of cellular suspensions by polyelectrolytes, Colloids and Surfaces, 31 (1988) 259–264

Bowen 1995// W. R. Bowen, J. I. Calvo, A. Hernández, Steps of membrane blocking in flux decline during protein microfiltration, Journal of Membrane Science, 101 (1995) 153–165

Chellam 2006// S. Chellam, W. Xu, Blocking laws analysis of dead-end constant flux microfiltration of compressible cakes, Journal of Colloid and Interface Science, 301 (2006) 248–257

Chisti 1986// Y. Chisti, M. Moo-Young , Disruption of microbial cells for intracellular products, Enzyme Microbiology and Technology, 8 (1986), 194–204

Chupakhina 2008// S. Chupakhina, V. Kottke, Using a yeast cell layer as a secondary membrane in microfiltration, Desalination, 224 (2008) 18–22

Czekaj 2000// P. Czekaj, F. López, C. Güell, Membrane fouling during microfiltration of fermented beverages, Journal of Membrane Science, 166 (2000) 199–212

Duclos-Orsello 2006// C. Duclos-Orsello, W. Li, C.-C. Ho, A three mechanism model to describe fouling of microfiltration membranes, Journal of Membrane Science, 280 (2006) 856–866

Gan 2001// Q. Gan, J. A. Howell, R. W. Field, R. England, M. R. Bird, C. L. O’Shaughnessy, M. T. MeKechinie, Beer clarification by microfiltration — product quality control and fractionation of particles and macromolecules, Journal of Membrane Science, 194 (2001) 185–196

Ganeva 2003// V. Ganeva, B. Galutzov, J. Teissié, High yield electroextraction of proteins from yeast by a flow process, Analytical Biochemistry, 315 (2003) 77–84

Geciova 2002// J. Geciova, D. Bury, P. Jelen, Methods for disruption of microbial cells for potential use in the dairy industry—a review, International Dairy Journal, 12 (2002) 541–553

Grenier 2008// A. Grenier, M. Meireles, P. Aimar, Ph. Carvin, Analysing flux decline in dead-end filtration, Chemical Engineering Research and Design, 86 (2008) 1281–1293

Gros 2003// C. Gros, J.-L. Lanoisellé, E. Vorobiev, Towards an Alternative Extraction Process for Linseed Oil, Chemical Engineering Research and Design, 81 (2003) 1059–1065

Güell 1999// C. Güell, P. Czekaj, R. H. Davis, Microfiltration of protein mixtures and the effects of yeast on membrane fouling, Journal of Membrane Science, 155 (1999) 113–122

Hermia 1982// J. Hermia, Constant pressure blocking filtration laws: Application to power-law non-newtonian fluids, Chemical Engineering Research and Design, 60 (1982) 183–187

Ho 2000// C.-C. Ho, A. L. Zydney, A Combined Pore Blockage and Cake Filtration Model for Protein Fouling during Microfiltration, Journal of Colloid and Interface Science, 232 (2000) 389–399

Hughes 1990// J. Hughes, D. K. Ramsden, K. C. Symes, The flocculation of bacteria using cationic synthetic flocculants and chitosan, Biotechnology Techniques, 4 (1990) 55–60

Hwang 2006// K.-J. Hwang, H.-C. Hwang, The purification of protein in cross-flow microfiltration of microbe/protein mixtures , Separation and Purification Technology, 51 (2006) 416–423

Hwang 2007// K.-J. Hwang, C.-Y. Liao, K.-L. Tung, Analysis of particle fouling during microfiltration by use of blocking models, Journal of Membrane Science, 287 (2007) 287–293

Iritani 1995// E. Iritani, Y. Mukai, Y. Tanaka, T. Murase, Flux decline behavior in dead-end microfiltration of protein solutions, Journal of Membrane Science, 103 (1995) 181–191

Karim 2008// M. N. Karim, H. Graham, B. Han, A. Cibulskas, Flocculation enhanced microfiltration of Escherichia coli lysate, Biochemical Engineering Journal, 40 (2008) 512–519

Keskinler 2004// B. Keskinler, E. Yildiz, E. Erhan, M. Dogru, Y. K. Bayhan, G. Akay, Crossflow microfiltration of low concentration-nonliving yeast suspensions, Journal of Membrane Science, 233 (2004) 59–69

Kim 2001// J.-S. Kim, S. Akeprathumchai, S. R. Wickramasinghe, Flocculation to enhance microfiltration, Journal of Membrane Science, 182 (2001) 161–172

Kloosterman IV 1988// J. Kloosterman IV, P. D. van Wassenaar, N. K. H. Slater, A. van der Padt, An integrated approach to the recovery of intracellular products from yeast by bead milling and precoat filtration, Chem. Eng. J. 37 (1988), B47–B54

Kuberkar 2000// V. T. Kuberkar, R. H. Davis, Modeling of fouling reduction by secondary membranes, Journal of Membrane Science, 168 (2000) 243–258

Mahesh Kumar 2008// S. Mahesh Kumar, S. Roy, Filtration characteristics in dead-end microfiltration of living Saccharomyces cerevisiae cells by alumina membranes, Desalination, 229 (2008) 348–3611

Narong 2006a// P. Narong, A.E. James, Effect of pH on the ζ-potential and turbidity of yeast suspensions, Colloids and Surfaces A: Physicochemical and Engineering Aspects, 274 (2006) 130–137

Narong 2006b// P. Narong, A.E. James, Effect of the ζ-potential on the micro/ultra-filtration of yeast suspensions using ceramic membranes, Separation and Purification Technology, 49 (2006) 149–156

Saxena 2009// A. Saxena, B. P. Tripathi, M. Kumar, V. K. Shahi, Membrane-based techniques for the separation


118

and purification of proteins: An overview, Advances in Colloid and Interface Science, 145 (2009) 1–22

Shan 1996// J. Shan, J. Xia, Y. Guo, X. Zhang, Flocculation of cell, cell debris and soluble protein with methacryloyloxyethyl trimethylammonium chloride—acrylonitrile copolymer, Journal of Biotechnology, 49 (1996) 173–178

Shynkaryk 2009// M. V. Shynkaryk, N. I. Lebovka, J.-L. Lanoisellé, M. Nonus, C. Bedel-Clotour, E. Vorobiev, Electrically-assisted extraction of bio-products using high pressure disruption of yeast cells (Saccharomyces cerevisiae), Journal of Food Engineering, 92 (2009) 189–195

Van Reis 2001// R. van Reis, A. Zydney, Membrane separations in biotechnology, Current Opinion in Biotechnology, 12 (2001) 208–211

Wakeman 1999// R. J. Wakeman, E. S. Tartleton, Filtration: equipment selection, modelling and process simulation, Elsevier, New-York (1999)

Wickramasinghe 2002// S. R. Wickramasinghe, Y. Wu, B. Han, Enhanced microfiltration of yeast by flocculation, Desalination, 147 (2002) 25–30

Wickramasinghe 2004// S. R. Wickramasinghe, B. Han, S. Akeprathumchai, V. Chen, P. Neal, X. Qian, Improved permeate flux by flocculation of biological feeds: comparison between theory and experiment, Journal of Membrane Science, 242, (2004) 57–71

Yukseler 2007// H. Yukseler, İ. Tosun, U. Yetis, A new approach in assessing slurry filterability, Journal of Membrane Science, 303 (2007) 72–79

Zuckerman 2002// H. Zuckerman, Ya. E. Krasik, J. Felsteiner, Inactivation of microorganisms using pulsed high-current underwater discharges, Innovative Food Science & Emerging Technologies, 3 (2002) 329–336

Zydney 2002// A. L. Zydney, Chia-Chi Ho, Scale-up of microfiltration systems: fouling phenomena and Vmax analysis, Desalination, 146 (2002) 75–81


II.1. Centrifugal consolidation of calcium carbonate suspensions

II.1.1. Calcium carbonate

The aqueous suspension of calcium carbonate with solid content of 19.8 % wt (particle

volume fraction φ = 0.0827) was provided by OMYA (France). The density of CaCO3

particles s was equal to 2730 kg/m3.

II.1.2. Granulometry of CaCO3 suspensions

The volume-based function of particle size distribution SDF (%) and specific surface area

of particles in suspension S were measured using an analytical photocentrifuge LUMiSizer

610.0–135 (L.U.M. Gmbh, Germany). Rectangular plastic optical cells, supplied by the

photocentrifuge manufacturer, with the optical path length of 10 mm and cross-sectional area

of 710–5 m2, were used. The measurements required considerable dilution of the suspension

(down to 10–4 % wt). SDF and S were calculated using the original software SEPView 5.1

(L.U.M. Gmbh, Germany) for granulometric analysis. The SDF of calcium carbonate versus

particle diameter d is presented in Fig.II.1. The measured values of specific surface area S and

mean diameter of particles dm are 2.2±0.2 m2/g and 1.1±0.4 m, respectively.

0 1 2 3 40

0.5

1

1.5

d [µm]

SDF

[%]

Fig. II.1. Volume-based size distribution of CaCO3 particles in an aqueous suspension,

measured by LUMiSizer.

II.1.3. Analytical centrifugation

Twelve samples of aqueous suspension with initial mass of 1.81 g and volume fraction φ

of 0.0827 were subjected to consolidation in an analytical photocentrifuge LUMiSizer 610.0–

II.1. Centrifugal consolidation of CaCO3 suspensions 120

135 (L.U.M. Gmbh, Germany). Rectangular plastic optical cells, supplied by the

photocentrifuge manufacturer, were used. The optical path length was 10 mm and cross-

sectional area was 710–5 m2.

The schema of centrifugal experiments is presented in Fig. II.2. The radial distance of the

centrifugal cell bottom from the axis of rotation R was equal to 0.13 m. The initial height of

the sample in the cell Hi was equal to 2.2710–2 m. Centrifugation experiments were carried

out at different rotor speeds in the interval of 240–4000 rpm. The corresponding centrifugal

accelerations at the bottom of the cell were within (8.3–2320)·g, where g = 9.81 m/s2 is the

gravity acceleration.

t

HH0

H∞

320 rpm 4000 rpm

R

Hi

H∞

H0

Initial suspension

Before consolidation

After consolidation

Pre-consolidation

Consolidation

Fig. II.2. Schema of the consolidation experiment. After the stage of pre-consolidation at low

rotation speed = 320 rpm ( 14.9g), the sediment compresses at higher rotation speed

(here = 4000 rpm) and its height H decreases from the initial (H 0) to the final (H) value.

The experiments were done using pre-consolidated sediments directly prepared inside the

centrifugal cells from the initial suspensions. Pre-consolidation of the initial suspensions was

done at a sufficiently low rotation speed of 320 rpm ( 14.9g) during 60 min. It resulted in

formation of non-compressed sediment with the initial height Ho 1.610–2 m and flat vertical

interface between solids and supernatant. The rotor speed variation within 240–460 rpm

((8.3–30.1)·g) had no noticeable impact on kinetics of the following consolidation. Then

rotation speed was increased to a higher level (10004000 rpm), and consolidation

experiment was carried out at a constant value . The radial position of the sediment surface

was measured and evolution of the sediment height H (m) with time t (s) was recorded during

the consolidation experiment. Experiments were finished when the constant equilibrium

sediment height H was reached (Fig. II.2).


II.2. Fluidity of highly concentrated kaolin suspensions

II.2.1. Kaolin

The kaolin used for this study was commercially available from “Société Minière des

Kaolins du Morbihan” (Kerbrient quarry, France). The kaolin powder was used without

purification.

II.2.2. Dispersant

The dispersant used was a sodium salt of polyacrylic acid (FLOSPERSE 1000) supplied

by SNF Floerger, France.

II.2.3. Characterisation of the kaolin particles: granulometry and electron microscopy

The size distribution of the kaolin particles was measured by a laser diffraction instrument

Mastersizer X 6618 (Malvern Instruments GmbH, UK). The particles were kept in a

suspended state during the measurement with the help of a small mixer. The particle size

distribution function (SDF) was calculated using original Malvern software. The kaolin

particles have monomodal size distribution function with maximum at 4.5 μm as represented

in Fig. II.3.

d, m

SDF

, %

10 20 300

2

4

6

8

10

20 m

d, m

SDF

, %

10 20 300

2

4

6

8

10

20 m

Fig. II.3. Differential size distribution function SDF of the kerbrient kaolin versus mean

particle diameter d. The insert shows an ESEM image of the kaolin powder.

High resolution environmental scanning electron microscopy (ESEM) images of the

kaolin particles were obtained using an XL30 ESEM-FEG instrument (Phillips International,

Inc., USA), operating at voltage 15 kV and pressure 1.4-3.0 Torr, at room temperature. The


special ‘wet’ chamber mode, allowing observation of both dry powder and moist kaolin

suspensions in their natural state, was applied. As Fig. II.3 shows, the ESEM images of the

kaolin powder in a dry state confirm results of granulometric mean size measurement and

show the plate-like morphology, typical for kaolin.

II.2.4. Preparation of aqueous kaolin suspensions

The kaolin suspensions for the viscosity measurements were prepared from dry kaolin

powder. These suspensions were continuously mixed with a stirrer RW20 DZM (Ika-Werke,

Germany) at 500-1800 rpm for 24 hours. The initial solid concentration was 55% wt and

67% wt for suspensions without and with the dispersant, respectively. More diluted

suspensions were prepared by addition of an appropriate quantity of the distilled water (or

dispersant solution). Then suspensions were mixed again for 1 hour before viscosity

measurements. The dispersant concentration Cd, which was calculated on the basis of the dry

weight of solid particles in suspension, was within 0.05-1% wt dispersant/wt kaolin.

Highly concentrated (70-75% wt) kaolin suspensions were prepared from the filter-cakes.

Samples for the textural tests were obtained by dilution of the filter-cake with the distilled

water. Then suspensions were intensively mixed for 3-5 hours in soft insulated plastic

container.

Dryness of suspensions was measured after their drying in oven at 200°C until constant

weight. The volume fraction of solid particles in the kaolin suspensions was estimated as:

wkC

/)1/100(1

1

(II.1)

where w = 1.0 g/cm3 is the water density, k = 2.60 g/cm3 is the mean density of kaolin, and

C is the weight concentration (%) of kaolin in an aqueous suspension. The natural pH values

of the concentrated suspensions were within 4.5-4.7.

II.2.5. Rheological tests

Two types of the rheological tests were performed. Viscosity of the fluid-like

suspensions at different shear rates ( 10001.0 s-1) was studied using rotational coaxial

viscosimeter Haake VT 550 (Haake, Germany) equipped with SV DIN and MV1 cylindrical

sensors. The shear rate was initially raised logarithmically from 0.1 s-1 to 1000 s-1 and then

decreased to 0.1 s-1. The time of each step was 20 min. In addition, tests for the time

dependence of viscosity were done between the shear rate increasing and decreasing steps.


Viscosity measurements were limited by the maximum shear measurable stress of about

1200 Pa. The creep compliance of highly loaded and thicker kaolin suspensions was also

analyzed. The texture profile analysis was done in a Texture Analyser (model TA-XT Plus,

Stable Microsystems, England). Suspensions were loaded into plastic cells of 30 mm in

diameter and 30 mm in height and held at rest for 24 hours. The cells were sealed to avoid

water evaporation. The texturometer probe was a steel cylinder with 10 mm in diameter

(Fig.II.4).

0 200 4000

2

4

t, s

forcesensor

probe = 10 mm

cell withsample = 30 mm

l o a d i n g r e l a x a t i o n

constantspeed ofthe probe =0.05 mm/s

speed ofprobe =0 mm/s

10 mm

Fmax

F, N

0 200 4000

2

4

t, s

forcesensor

probe = 10 mm

cell withsample = 30 mm

l o a d i n g r e l a x a t i o n

constantspeed ofthe probe =0.05 mm/s

speed ofprobe =0 mm/s

10 mm

Fmax

F, N

Fig. II.4. Explanation of texture profile analysis of concentrated kaolin suspensions.

During the ‘loading’ step of texture analysis, the probe was pressed into a sample with a

constant speed of 0.05 mm/s. Then the probe was stopped at fixed penetration depth of 10 mm

and the sample was leaved for relaxation. The force F applied to the probe was registered

continuously. The maximum deforming force Fmax needed for the probe penetration was

determined as it is shown in Fig. II.2.Then the maximum shear stress τmax was estimated from

Fmax as:

τmax = Fmax / r2 (II.2)

where r is the probe radius, r = 10 mm.

Used parameters of the probe speed and maximal penetration distance allowed reaching

of satisfactory τmax sensitivity for studied intervals of kaolin and dispersant concentrations.


II.2.6. Dead-end filtration of kaolin suspensions

Figure II.5 presents a scheme of the filtration apparatus. It includes a laboratory dead-end

filter-cell (CHOQUENET, France), a feeding tank with kaolin suspension and a balance

PM 6000 (METTLER-TOLEDO, France) linked to a computer.

compressedair

suspension

filter-cake

filter cloth

feeding tank

filtration cell

filtrate

electronicbalance

t

m

data acquisition

compressedair

suspension

filter-cake

filter cloth

feeding tank

filtration cell

filtrate

electronicbalance

t

m

data acquisition

compressedair

suspension

compressedair

suspension

filter-cake

filter cloth

feeding tank

filtration cell

filtrate

electronicbalance

t

m

data acquisition

Fig. II.5. Schema of the filtration apparatus.

Suspensions were filtered at a constant pressure of 5 bars in a cylindrical polypropylene

chamber (inner diameter equals to 56 mm, width equals to 25 mm) with two grooved filter

plates made of stainless steel. Each filter plate supported a woven polypropylene filter cloth

25821AN (SEFAR FYLTIS, France) with a mean pore size of 5 μm. The total filtration area

of two filters was 50 cm2. Filter chamber was connected to a feeding tank filled with 1 liter of

liquid kaolin suspension. The initial solid concentration of suspension in the tank was 58%-

61% wt and 30% wt for suspensions with and without dispersant, respectively. In some

experiments without dispersant, the pH of suspension was adjusted before filtration by

addition of the concentrated hydrochloric acid.

Filtrate was collected in a beaker placed on electronic balance; the weight of filtrate m was

registered each 3 seconds with precision of 0.1 g by the software HPVEE v3.12 (created by

Service Electronic of UTC). The density of the filtrate was equal to 1.0 g/ml.

The software permits on-line observation of filtration curves in t/V versus V coordinates,

where t is the time of filtration, V is the volume of filtrate (Fig. II.6, left).


0 20 40 60 80

10

20

30

40t/V,s/ml

V, ml

V = V0, t = t0

0 20 40 60 80

10

20

30

40t – t0

V – V0

V + V0

K2

tan = K1

0 20 40 60 80

10

20

30

40t/V,s/ml

V, ml

V = V0, t = t0

0 20 40 60 80

10

20

30

40t – t0

V – V0

V + V0

K2

tan = K1

0 20 40 60 80

10

20

30

40t/V,s/ml

V, ml

V = V0, t = t0

0 20 40 60 80

10

20

30

40t/V,s/ml

V, ml

V = V0, t = t0

0 20 40 60 80

10

20

30

40t – t0

V – V0

V + V0

K2

tan = K1

0 20 40 60 80

10

20

30

40t – t0

V – V0

t – t0

V – V0

V + V0

K2

tan = K1

Fig. II.6. Dead-end filtration curves of a kaoline suspension (at 30% wt of solids) plotted in

Ruth-Carman’s coordinates. Experimental data (left) and calculation of K1 and K2 (right).

At the end of filtration, the filter-cake was discharged and its dryness and viscous

properties were analyzed as described above. Specific resistance of the filter α cake was

calculated using the Ruth-Carman’s equation:

2010

0 )( KVVKVV

tt

(II.3)

where t0 is the time required for pressure stabilization, V0 is the volume of filtrate processed

during t0 (values of t0 and V0 where estimated as it is shown in Fig. II.4, left). K1 and K2 are

the constants defined as

cake

lf

CC

C

pSK

/12 21

(II.4)

pS

RK lm

2 (II.5)

where α is the specific resistance, ρf and ηl are the density and viscosity of filtrate,

respectively, S is the filter surface, Δp is the filtration pressure and Rm is the hydraulic

resistance of the filter, C and Ccake are weight fractions of solid in the initial suspension and

filter cake, respectively. In our analysis, Ccake was assumed to be constant during the filtration.

For cake filtration, (t – t0)/ (V – V0) versus (V + V0) is a straight line, as shown in Fig. II.6

(right). The line slope and line intercept with the axis of ordinates are used for calculation of

the cake and filter medium resistances.

II.3. Dynamic filtration of CaCO3 suspensions 126

II.3. Dead-end dynamic filtration of highly concentrated CaCO3

suspensions in the presence of a dispersant

II.3.1. Calcium carbonate

The aqueous suspension of calcium carbonate with solid content of 20.0% wt was

provided by OMYA (France). The conductivity of suspension was equal to 250 μS/cm and pH

was equal to 7.6.

II.3.2. Dispersant

The dispersant used was a 31% wt. aqueous solution of sodium polyacrylate DV 834

produced by COATEX (France). The suspension and the dispersant were the same as those

used in the previous studies for preparation of concentrated CaCO3 suspensions*.

II.3.3. Granulometry of CaCO3 suspensions

The size distributions of aggregates and particles in CaCO3 suspension were recorded

using a laser diffraction instrument Mastersizer X 6618 equipped with the lens allowing

detection of particle sized within 0.1-80 μm. During the measurement, the particles were

suspended in equilibrium dispersant solution. In the deflocculated suspensions with addition

of a dispersant, the particles of calcium carbonate exhibited narrow monomodal size

distribution function with the maximum at 1.1±0.1 μm.

II.3.4. Filtration with rotating disk

A schema of the filtration apparatus is presented in Fig. II.7. The apparatus comprises

filtration cell with suspension, rotating disk connected to a mixer, evacuated flask for filtrate

and a vacuum pump. Filtration cell was a plastic cylinder with the total volume of 200 cm3

and internal radius equal to 27.5 mm. PA 6 (Nylon) membrane with 0.2 µm pore size

(Biodyne A, Pall Corp., USA) was fixed on the bottom of the cell and a polypropylene filter

mesh with a pore size of 300 µm was used as a filter support. Turbidity measurements showed

that the membrane was able to retain all the particles of the suspension. Filtration surface S

was equal to 2.410-3 m2. Resistance of the membranes Rm was equal to 1.5±0.2·1011 m-1; the

* E. Vorobiev, Th. Mouroko-Mitoulou, Z. Soua, Precoat filtration of a deflocculated mineral suspension in

the presence of a dispersant Colloids and Surfaces A: Physicochemical and Engineering Aspects, 251 (2004) 5–

17; J. G.-C. Trave, E. Vorobiev, A. O. Dris, Production of a highly concentrated CaCO3 suspension by cross-

flow microfiltration in the presence of a dispersant, Separation Science and Technology 42 (2007) 319–331.


membranes were washed in diluted hydrochloric acid after each filtration. Filtration was

driven by vacuum in the flask generated by the vacuum pump. The transmembrane pressure p

value was adjusted between 0.2 and 0.95 bar. Filtrate was collected in the evacuated flask

placed on the electronic balance PM 6100 (Mettler-Toledo, France), and the filtrate weight

was registered each 3 seconds with precision of 0.01 g using HP VEE software created by

Service Electronic of UTC. The flask was connected to the filtration cell and the vacuum

pump by flexible plastic tubes.

membrane

suspension filtration cell

to the stirrer

filtrate

balance

to the pump

manometer

cover

ho=2 mmrotating disk

r0=25 mm

= 5 mm

filter cake

membrane

suspension filtration cell

to the stirrer

filtrate

balance

to the pump

manometer

cover

ho=2 mmrotating disk

r0=25 mm

= 5 mm

r0=25 mm

= 5 mm

filter cake

Fig. II.7. Schema of the filtration apparatus used for CaCO3 filtration.

A stainless steel perforated disk (Fig. II.7) with radius r0 = 25 mm was placed inside the

filtration cell close to the membrane surface. Disk perforations were necessary for the

downward drainage of suspension to the membrane. They allowed intensify the shear for

better erosion of the filter cake. The disk was fixed on a metal shaft. It was connected to a

stirrer RW20 DZM (Ika-Werke, Germany) rotating with the speed adjustable up to

ω = 2000 rpm. An initial gap between the disk and the membrane surface was fixed at

h0 = 2 mm. The shear rate was dependent on the distance to the axis of rotation r and was

evaluated as = r/h, where h is a gap between the rotating disk and the cake surface and

is the angular speed (Fig.II.7). The shear rate was maximum at disk periphery at r = r0. At

h = h0 = 2 mm, the shear rate could be estimated as = 2 r0/ (60h) s-1 400 s-1 for

= 300 rpm and 2700 s-1 for = 2000 rpm.

The same initial quantity of suspension ( 190 g that is 85 mm of suspension height in

the cylinder) was taken for each experiment. Two modes of filtration were used: with initial

dispersant addition (that was designated as i-filtration) and with delayed addition of a

II.3. Dynamic filtration of CaCO3 suspensions 128

dispersant (d-filtration). In experiments with the first type of filtration, suspensions were

mixed with the dispersant 10 min before filtration at 100 rpm. In experiments with the second

type of filtration, the aggregated suspension was filtered until reaching Vd = 100 cm3 of the

filtrate, then a dispersant was added to the pre-concentrated suspension. The dispersant

concentration cd was varied between 0.1 and 2% wt dispersant/ wt dry CaCO3.

The total time of filtration experiments was within 10-40 min depending on the dispersant

concentration. Each experiment finished at the final stage of filtration, when increasing

friction between the cake and the disk was restricting rotation of the disk.

Suspension was filtered at initial ambient temperature 20°C. Owing to the friction

energy dissipation in the sheared volume between the rotating disk and the cake surface, the

temperature of suspension T was the growing function of time t. The rate of the temperature

increase at the final stage of filtration was noticeable due to increase of the shear rate in the

gap between the rotating disk and the filter cake surface. However, due to restrictions of disk

rotation, the experiments were stopped at this stage of filtration and the final temperature T of

suspension never exceeded 50°C.

For more convenience, filtration data were described by Darcy’s law:

)( mcf RR

SpdV

dt

(II.6)

where t is the filtration time, V is the filtrate volume, f is the filtrate viscosity, S is the

membrane surface, p is the transmembrane pressure, Rc and Rm are hydraulic resistances of

the filter cake and membrane, respectively. The term Rc = Rc (V) accounts for filter cake

formation on the membrane surface during filtration; Rc = α ω V/S, where α is specific cake

resistance, ω is the mass of deposited solid per volume of the filtrate. Note that for a dead-end

filtration α and ω are constants and filter-cake resistance Rc is directly proportional to the

filtrate volume V.

II.3.5. Filter cakes and concentrated suspensions

In some experiments, hydraulic resistance of the filer cake deposited on the membrane

surface Rc was directly measured. After certain volume of filtrate was processed, filtration

was terminated and suspension was poured out from the cake’s surface. Filtration cell was

accurately filled with filtrate; than it was filtered through the cake at the same pressure as the

pressure used for cake formation. As far as in these experiments the filtrate volume was

directly proportional to filtration time, resistance of the filter cake was calculated as

mfc RVtSpR /Δ (II.7)


Viscosity of the concentrated suspensions was measured using rotational coaxial

viscosimeter Haake VT 550 (Haake, Germany), equipped with cylinder SV-DIN rotor. The

shear rate was raised logarithmically from 10 s−1 to 1000 s−1. The temperature was fixed at

25°C.

The final dryness of suspension Ds and cake Dc were measured after their drying at 130ºC.

The average dryness was also estimated from material balance equation

)/(3

VmmD fsuspCaCO (II.8)

where mCaCO3 is the total mass of calcium carbonate, msusp is the mass of suspension used for

filtration and ρf is the filtrate density.

II.3.6. Characterisation of filtrate

UV absorption spectra of filtrate samples were measured in order to estimate the

dispersant losses during filtration. UV spectrophotometer Libra S32 (Biochrom, UK) and

10 mm quartz optic cells Suprasil QS (Hellma, Germany) were used. A typical UV absorption

spectrum of DV 834 dispersant solution is show in Fig. II.8.a. The spectrums were found to

be monotonous and proportional to the dispersant concentration Cd. Hence, calibration curve

was built for the wavelength of 205 ± 0.1 nm (Fig. II.8.b), and it was used for calculation of

the dispersant concentration in the filtrate. For the dispersant concentration range Cd = 0.02 –

0.08%, it equals to Cd (% wt) = 0.0449 Absorbance + 0.0025, with correlation coefficient

r2 = 0.99.

200 220 2400

0.5

1

1.5

Abs

orba

nce

wavelength, nm0 0.04 0.08

0.8

1.6

Abs

orba

nce,

λ=

205

nm

dispersant concentration, %

(a) (b)

200 220 2400

0.5

1

1.5

Abs

orba

nce

wavelength, nm200 220 2400

0.5

1

1.5

Abs

orba

nce

wavelength, nm0 0.04 0.08

0.8

1.6

Abs

orba

nce,

λ=

205

nm

dispersant concentration, %

(a) (b)

Fig. II.8. (a) typical UV absorption spectrum of DV 834 dispersant solution, dispersant

concentration Cd = 0.056% wt. (b) calibration curve for estimation of the dispersant

concentration, wavelength λ = 205 nm.

II.4. Filtration of disrupted yeast suspensions 130

II.4. Dead-end filtration of Saccharomyces cerevisiae yeast suspensions:

effects of high-pressure disruption, high-voltage electrical discharges and

flocculation

II.4.1. Yeast

Wine yeast S. cerevisiae (bayanus) cells were used throughout this study. The original

yeast was a dry granulated powder (commercial name: Vitilevure DV10, provided by Station

Oenotechnique de Champagne, Epernay, France) with a particle size approx. 0.5–1 mm

(Fig. II.9.a).

100m0.5 mm

(a) (b)

100m0.5 mm

(a) (b)

100m0.5 mm

(a) (b)

Fig. II.9. Optical microscopy images of (a) the original yeast powder Vitilevure DV10,

(b) swelled 1% wt yeast suspension

Yeast suspensions of 1% wt. were prepared by mixing the dry yeast cells and distilled

water by magnetic stirrer. The yeast cells were swelling in an aqueous medium at room

temperature. The swelling process was monitored by conductivity measurements. After,

approx., 30 min of mixing, the conductivity reached a stable value of 13010 S/cm, and the

swelling was considered to be completed (optical microscopy image of the swelled

suspension is shown in Fig. II.9.b).

II.4.2. High pressure homogenisation of the yeast suspensions (HPH disruption)

The yeast suspensions were homogenised in a two-stage high-pressure homogenizer

NS1001L–PANDA 2K (Niro Soavi S.p.A., Italy) using NHPH successive passes of the

suspension through the homogeniser at fixed homogenising pressure of 500 or 1000 bar. The

flow rate was 10.0 l/h, and 350 ml of suspension in total was processed. Only the first HPH

valve with ceramic ball (code 190015, Niro Soavi S.p.A., Italy) and stainless steal seat (code

0126311, Niro Soavi S.p.A., Italy) were used in this study (Fig. II.10).


Suspension500

Steel seat

Ceramic ballSuspension

Pump

Manometer

Pressure valve

Disruptedsuspension

Suspension500

Steel seat


Pump

Manometer

Pressure valve

Disruptedsuspension

Suspension500

Steel seat


Pump

Manometer

Pressure valve

Disruptedsuspension

Fig. II.10. Schema of high pressure homogenisation of yeast suspension.

The initial temperature of suspension was 25°C and the temperature elevation resulting

from HPH treatment was about 10°C. After each pass, suspensions were cooled to room

temperature for their further characterization or next pass through homogenizer.

II.4.3. Treatment of yeast suspensions with high voltage electric discharges (HVED

disruption)

Experimental HVED apparatus (Tomsk Polytechnic University, Russia) consisted of a

pulsed high voltage power supply and a laboratory treatment chamber with an electrode of a

needle-plate geometry (Fig.II.11). A stainless steel needle of 10 mm in diameter was used.

The grounded plate electrode was a stainless disk of 25 mm in diameter. A positive pulse

voltage was applied to the needle electrode. The high voltage pulse generator provided 40kV–

10kA discharges in a one-litre chamber. The distance between the electrodes was 10 mm, and

the peak pulse voltage was 40 kV. It corresponds to the mean electric field strength of

E = 40 kV/cm.

ProtocolHVED chamber

Vol

tage

Time

ti

tt

Plate electrode

Needle electrode

Suspension

ProtocolHVED chamber

Vol

tage

Time

ti

tt

Plate electrode

Needle electrode

Suspension

Fig. II.11. Schema of

HVED chamber and a

typical HVED protocol.


The electrical discharges were generated by electrical breakdown in an aqueous yeast

suspension. Energy was stored in a set of low-inductance capacitors, which were charged by a

high-voltage power supply. Damped oscillations with the total duration of ≈ 20 μs were thus

obtained, though the effective pulse duration corresponded to few microseconds, ti ≈ 1-2 μs

[Gros 2005]. The treatment chamber was initially filled with 350 ml of the swelled yeast

suspension (1% wt). HVED treatment lied in application of the NHVED successive pulses

(NHVED = 1–450). Electrical discharges were applied with the pulse repetition rate of 0.5 Hz

(Δtt = 2 s, Fig. II.11). Suspension characteristics were measured between successive

applications of the HVED pulses. The initial temperature was 25°C and the temperature

elevation resulting from HVED treatment was less than 5°C.

II.4.4. Flocculation

In some experiments, the aggregation of yeasts was regulated by addition of cationic

flocculant poly (diallyldimethylammonium chloride) (20% wt aqueous solution, ALDRICH,

average Mw = 400 000 – 500 000):

Appropriate amount of 0.4% wt flocculant solution was added to a beaker with 250 ml of

1% wt undisrupted or disrupted yeast suspension. The amount of added flocculant solution

depended on the desired final polymer concentration C = 0 – 0.04% wt polymer/wt dry yeast.

Then beaker with yeast suspension was 10 times turned upside-down and leaved in rest for

2 min for careful mixing of suspension and flocculant.

II.4.5. Filtration

Dead-end filtration experiments were carried out using equipment showed in Fig. II.12.

Filtration cell was a vertical stainless steel cylinder (inner diameter 5.5 cm and total volume

of 300 ml) connected with pressurized air source through pressurized air tank.


Filtration cell

Suspension

Paper filter

Filter support

Manometer

Pressurizedair tank

Filtrate

Balance

Air

Filtration cell

Suspension

Paper filter

Filter support

Manometer

Pressurizedair tank

Filtrate

Balance

Air

Fig. II.12. Schema of filtration equipment.

Filtration membrane was made from Fisherbrand qualitative filter paper (nominal pore

size was 2.5 μm) and polypropylene filter cloth 25302 AN (pore size 25 μm, SEFAR

FYLTIS, France) was used as filter support. The membrane surface area was 2.410-3 m2. All

filtrations were carried out at room temperature and at constant pressure of 1 bar. New

membrane was used for each filtration. Filtration was started immediately after filter-cell was

poured with 200 ml of freshly treated yeast suspension. Permeate was collected in a vessel

placed on an electronic balances PM 6000 (METTLER-TOLEDO, France) and permeate

weight was recorded each 3 seconds with accuracy of 0.1 g using computer software

HP VEE (Service Electronic of UTC).

II.4.6. Analysis of suspensions and filtrates

The electrical conductivity of suspensions was measured at 25°C using a conductivity

meter InoLab pH/cond Level 1 (WTW, Germany) with conductivity probe WTW Tetra

Con 325. The size distributions of aggregates in suspensions were recorded using a laser

diffraction instrument (Mastersizer X 6618, Malvern Instruments GmbH, UK). During the

measurement, the particles were kept in suspension by means of a small mixer. The optical

system allowed detection of particles sized within 1–600 μm. The particle size distribution

was calculated by the original Malvern software.

High-resolution environmental scanning electron microscopy (ESEM) images were

obtained using a XL30 ESEM-FEG instrument (Phillips International, Inc., USA) operating at

15 kV voltage and 3.6 Torr pressure, at room temperature. The special “wet” chamber mode,

allowing observation of moist suspensions in their natural state, was applied.


Turbidity and UV absorption spectra of the treated suspensions and filtrate samples where

measured in order to estimate the content of cell debris and concentration of soluble bio-

products. Following the HVED treatment, a 10 ml sample of suspension was centrifuged

10 min at 4000 g, and the supernatant was collected. Turbidity of the supernatant was

measured by Ratio/XR Turbidimeter (Hach, USA). Turbidity of filtrate samples were

measured without centrifugation. Prior to UV absorption measurements, both suspensions and

filtrate samples were separated from insoluble colloidal particles by long-continued

centrifugation (40 min at 4000 g). UV absorption spectrum of the tenfold diluted supernatant

was measured by UV-spectrophotometer Biochrom Libra S32. The wavelength range was

within 200-350 nm (with the precision of ±1 nm). The path length of the SUPRASIL quartz

optic cell was 10 mm (Hellma, Germany).

II.5. Statistical analysis of experimental data

All the experiments were replicated, at least, three times. The mean values and the

standard deviations were calculated. The error bars in figures correspond to the standard

deviations.

III.1. Fluidity of highly concentrated kaolin suspensions

135

Paper I: “Fluidity of highly concentrated kaolin suspensions: influence of

particle concentration and presence of a dispersant”

Introduction

Production of mineral powders often involves the steps resulting in formation of diluted

aqueous suspensions with solid contents below 20 % wt (e.g., sol-gel process, elutriation of

impurities, centrifugal purification). Therefore, there arises a need in removal of the excess

water from the suspensions and their concentration, so that they could respond to

requirements of their further applications in paper industry, ceramic industry, etc. Thermal

processes for evaporation of excess water are quite energy consuming. Also, production of

mineral powders usually comprises two subsequent operations: (1) concentration of diluted

suspension from 20 to 30–70 % wt1 by dead-end filtration in filter-presses and (2) evaporation

of residual water from the concentrated suspension by spray drying. The step of spraying

requires high fluidity of the concentrated suspension, while efficiency of drying increases

with increase of suspension concentration (filter-cake). Therefore, optimal dewatering of a

mineral suspension implies:

• fast filtration,

• high dryness of the filter-cake,

• high fluidity of the filter-cake.

Filtration rate, dryness and fluidity of the filter-cake depend on colloidal properties of

mineral particles. Chemical additives (called dispersants) are usually added to suspension in

order to modify its properties and to increase its dryness and fluidity. However, use of the

dispersants and decrease of solid contents in a filter-cake may decrease filterability of the

mineral suspension and reduce the total efficiency of mineral powder preparation. Therefore,

optimization of the total dewatering process requires information about colloidal properties of

the mineral particles, as well as rheological (viscosity) and barrier (filterability) properties of

the mineral suspension. It also requires information about the influence of various factors

(concentration of particles, dispersant concentration) on these properties.

Due to high aspect ratio of particles and complex distribution of the particle surface

charge, the rheological behaviour of kaolin suspensions has many peculiarities, such as low

flowability, shear-thickening and even shear-hardening at high shear-rates. Ordering of kaolin

1 final concentration of filter-cake depends on mineral properties


136

particles may decrease the filter cake permeability; this phenomenon is also related to specific

features of geometry of the kaolin particles and their colloidal properties. So, preparation of

concentrated and flowable suspensions of kaolin by dead-end filtration is more complex that

preparation of concentrated suspensions of other mineral particles.

Summary

The aims of this paper are: (1) to provide better understanding of the properties

(structural, rheological and filtration) of highly concentrated kaolin suspensions; (2) to

explain correlations between these properties; and (3) to define the limiting effects, which

prevent such suspensions from dewatering by dead-end filtration.

Rheological properties of aqueous kaolin suspensions with various concentrations of

kaolin (12–75 % wt) and dispersant (sodium polyacrylate, 0–1 % wt/wt) were studied. Two

types of rheological tests were carried out:

• using classical coaxial viscosimeter for measuring viscosity of suspensions when they

were fluid-like; and

• using texture analyzer for rheological analysis of thicker kaolin suspensions.

Structure of kaolin suspensions with different dispersant concentrations was monitored by

means of electronic microscopy.

In addition, dead-end filtration of kaolin suspensions with different concentrations of the

dispersant was carried out and specific filtration resistance and dryness of the filter-cake, as

well as texture properties of the filter-cake, were determined.

Colloids and Surfaces A: Physicochem. Eng. Aspects 325 (2008) 64–71

Contents lists available at ScienceDirect

Colloids and Surfaces A: Physicochemical andEngineering Aspects

journa l homepage: www.e lsev ier .com/ locate /co lsur fa

Fluidity of highly concentrated kaolin suspensions: Influence of particleconcentration and presence of dispersant

Maxim Loginova,b, Olivier Larueb, Nikolai Lebovkaa,b, Eugene Vorobievb,∗

a Institute of Biocolloidal Chemistry named after F.D. Ovcharenko, NAS of Ukraine, 42, blvr. Vernadskogo, Kyiv 03142, Ukraineb Departement de Genie Chimique, Universite de Technologie de Compiegne, Centre de Recherche de Royallieu, B.P. 20529-60205 Compiegne Cedex, France

ity ofersanaquef disphen its. A sthe ae fracersa

es, whelec

queoof solum d

ked caness o

a r t i c l e i n f o

Article history:Received 15 September 2007Received in revised form 15 April 2008Accepted 16 April 2008Available online 29 April 2008

Keywords:KaolinAqueous suspensionsFiltrationDispersantRheology

a b s t r a c t

This work discusses fluidin the presence of a dispcarried out on the kaolindispersant Cd (0–1 wt.% oviscosity of suspension wthicker kaolin suspensionϕc = 0.05, was observed intransition to higher volumhydrodynamic flow. A dispfaces of the kaolin particlwhich is supported by thewhich is typical for the astructure under the loadreached for a certain optimobserved for a loosely pacimproves fluidity and dry
particles, which causes a rise in
1. Introduction

The regulation of fluidity of the concentrated aqueous kaolinsuspensions is very important in many applications including thoserelated to industrial slurries, mixtures for production of ceramics,paper industry paints, pigments, cosmetics, etc. [1–3]. The kaolincontains kaolinite as a basic mineral component. Its structural for-mula is Al2O3·2SiO2·2H2O. The kaolin particles are plate-like inshape. Their edges contain tetrahedral silica and octahedral alu-mina groups and bear a positive charge at low pH. The basalsurfaces, which have exchangeable cations, are negatively chargedwithin a wide range of pH values [4].

On the one hand, the aqueous suspensions of kaolin are usuallyreferred to as the simplest clayey systems, as far as hydration ispractically absent in kaolin and its particles are stacked into strongstructural units [5]. However, the rheological behaviour of concen-trated kaolin suspensions is very complex and multivariable [6].

∗ Corresponding author. Fax: +33 3 44231980.E-mail addresses: [email protected], [email protected]

(E. Vorobiev).

0927-7757/$ – see front matter © 2008 Elsevier B.V. All rights reserved.doi:10.1016/j.colsurfa.2008.04.040

highly concentrated kaolin suspensions prepared by filtration techniquet (sodium salt of polyacrylic acid). Two types of rheological tests wereous suspensions at different concentrations of kaolin C (12–75 wt.%) andersant/wt. of solid). A classical coaxial viscosimeter was used to measurewas fluid-like. A texture analyser was used for rheological analysis of theol–gel (percolation) transition, starting from the kaolin volume fraction

bsence of a dispersant. The addition of a dispersant shifted this percolationtions. The rheological data showed that the platelet particles can align in a

nt or kaolin load suppresses the interaction forces between basal and edgeich bear different charges. As a result, a face-to-face arrangement arises,

tron microscopy images. Hence, the loosely packed card-house structure,us kaolin suspensions, undergoes a gradual conversion into an orientedid particles or dispersant. A maximum of the percolation threshold wasosage of the dispersant (Cd ≈ 0.5 wt.%). The higher filtration efficiency wasrd-house structure in dispersant-free suspensions at low pH. A dispersantf the filter cakes, however, produces an oriented face-to-face structure ofresistance to liquid flow during filtration.

© 2008 Elsevier B.V. All rights reserved.

The rheological response of concentrated suspensions depends
on the degree of shear perturbations, the flow history and timeof measurements t [7,8]. It may be characterized by effectiveviscosity , defined as a ratio of the shear stress and theshear rate . The concentrated kaolin suspensions can display anon-Newtonian thixotropic (shear thinning) or rheopectic (shearthickening) behaviour [5,9,10]. Typically, a transient time depen-dence of viscosity behaviour is observed for the kaolin suspensions.Viscosity may relax to an equilibrium state and may display period-ical changes or fluctuations with time, or other behaviour after anychange of the shear history [11–14]. Different models for descrip-tion of the (ϕ, ) dependence accounting for the shear-inducedagglomeration and deglomeration processes are intensively dis-cussed in literature [15,16]. The particles in a concentrated systemare in close contact and form continuous networks. Strong shearperturbations may provoke disaggregation of the kaolin flocs [17]and shift an equilibrium between creation and damage of the inter-particle bonds [8].
For kaolin suspensions, the flow characteristics are complexfunctions of pH [18–21]. At low pH value (pH 4.5), the positivelycharged edges of agglomerated kaolin particles and their nega-tively charged basal faces form a so-called a card-house structure

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dx.doi.org/10.1016/j.colsurfa.2008.04.040

: Physicochem. Eng. Aspects 325 (2008) 64–71 65

Haake VT 550 (Haake, Karlsruhe, Germany). The shear rate was ini-tially raised logarithmically from 0.1 s−1 (minimum) to 1000 s−1

and then decreased to 0.1 s−1. The time of each step was 20 min.In addition, tests for the time dependence of viscosity were donebetween the shear rate increasing and decreasing steps.

Viscosity measurements were limited by the maximum shearmeasurable stress of about 1200 Pa. The stiffness of highly loadedand thicker kaolin suspensions was also analyzed. The texturalmeasurements were done in a Texture Analyser (model TA-XT Plus,Stable Microsystems, England). Suspensions were loaded into plas-tic cells of 30 mm in diameter and 30 mm in height and held at restfor 24 h. The cells were sealed to avoid water evaporation. The tex-turometer probe was a steel cylinder with 10 mm in diameter. Inthe penetration test the speed of probe displacement, 0.05 mm/s,was constant, and the maximal distance of probe penetration was10 mm. The maximum stress m was determined as it is shownin Fig. 2. The said parameters allowed reaching satisfactory m

sensitivity for studied intervals of kaolin and dispersant concen-trations.

M. Loginov et al. / Colloids and Surfaces A

[22], which has enhanced viscosity [23]. However, at higher pH val-ues, when both basal and edge faces are negatively charged, theinter-particle attractions become weaker. Particles arrange face-to-face, forming electrostatically stabilized band-like structures withreduced viscosity [24]. Existence of a pronounced fluidifying effectwas reported for kaolin dispersions in the presence of multivalentanions [25]. Kaolin delamination in the swing mills may be a possi-ble way of viscosity reduction in kaolin suspensions with ultra-highconcentration (≈70 wt.%) [26].

Efficient regulation of suspension fluidity is also possiblethrough introduction of additives, such as polymers or surfactants.Adsorption of the negatively charged polymeric substances andanionic surfactants on kaolin particles allows to reach electrostaticstabilization leading to an efficient decrease of dispersion viscosity[27–32].

Different ways of preparation of the highly concentrated sus-pensions in presence of a dispersant are possible. The usualtechnique is to dilute the powder by a dispersant solution withappropriate stirring. Another possible way is to filter the dilutedsuspension containing a proper dose of the dispersant. An opti-mum dosage of the dispersant may fluidify the kaolin slurrieseven with ultra-high content of solid (≈70 wt.%) [33]. However, therheological behaviour of suspensions with ultra-high concentra-tion near the liquid–solid transition was not investigated in detailsbefore. The main issue is to find relationships between the thresh-old concentration and the width of transition zone in presence of adispersant additive.

The present work is aimed at the study of rheological propertiesof an ultra-concentrated aqueous suspension of kaolin as a functionof the content of solid particles (12–75%) and dispersant (sodiumsalt of polyacrylic acid).

2. Experimental

2.1. Materials

The kaolin used for this study was commercially available from“Societe Miniere des Kaolins du Moribihan’s” (Kerbrient quarry,France), and used without purification. The dispersant used was asodium salt of polyacrylic acid (FLOSPERSE 1000) supplied by SNFFloerger France.

2.2. Instrumentation

The size distribution of the kaolin particles was measuredby a laser diffraction instrument Mastersizer × 6618 (MalvernInstruments GmbH, Worcs., UK). The particles were kept in asuspended state during the measurement with the help of asmall magnetic mixer. The particle size distribution was calcu-lated using original Malvern software. Granulometric distributioncurves show one mode with maximum at 4.5 m as repre-sented in Fig. 1. High-resolution environmental scanning electronmicroscopy (ESEM) images were obtained using an XL30 ESEM-FEG instrument (Phillips International, Inc., WA, USA), operating atvoltage 15 kV and pressure 1.4–3.0 Torr, at room temperature. Thespecial “WET” chamber mode, allowing observation of moist kao-line suspensions in their natural state, was applied. As Fig. 1 shows,the ESEM images of the kaolin powder in a dry state confirm resultsof granulometric mean size measurement and show the plate-likemorphology, typical for kaolin. Moisture content of the sampleswas measured after their drying in oven at 200 C until constantweight.

Two types of the rheological tests were performed. Viscos-ity of the fluid-like suspensions at different shear rates ( =0.1–1000 s−1) was studied using rotational coaxial viscosimeter

Fig. 1. Differential volume F versus mean particle diameter d for the Kerbrientkaolin. The insert shows an ESEM image of the powdered kaolin.

Fig. 2. To explanation of the penetration textural test.

66 M. Loginov et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 325 (2008) 64–71

Fig. 3. Scheme of the filtration apparatus.

2.3. Preparation of aqueous kaolin suspensions

The kaolin suspensions for the viscosity measurements wereprepared from dry kaolin powder. These suspensions were contin-uously mixed with a stirrer RW20 DZM (Ika-Werke, Germany) at500–1800 rpm for 24 h. The initial solid concentration was 55 and67 wt.% for suspensions without and with the dispersant, respec-tively. The diluted suspensions were prepared by addition of anappropriate quantity of the distilled water (or dispersant solution).Then suspensions were mixed again for 1 h before viscosity mea-surements. The dispersant concentration Cd, which was calculatedon the basis of the dry weight of solid particles in suspension, waswithin 0.05–1%. The volume fraction of solid particles in a kaolinsuspension can be estimated as:

ϕ =(

1 + (100/C − 1)k

w

)−1

(1)

where w = 1000 kg/m3 is the water density, k = 2600 kg/m3 is themean density of kaolin [34], and C is the weight concentration (%)of kaolin in an aqueous suspension. The natural pH values of theconcentrated suspensions were within of 4.5–4.7.

The kaolin concentrations used for texture measurements were
larger than for viscosity measurements. Thus, filter cakes with70–75 wt.% were obtained from diluted suspensions with and with-out a dispersant. Fig. 3 presents a scheme of the filtration apparatus.It includes a laboratory filter-press cell (CHOQUENET, France), atank with suspension and a balance PM 6000 (METTLER-TOLEDO,France) linked to a computer. Suspensions were pressure filtrated(at 5 bar) in a cylindrical chamber with two filter plates compris-ing liquid collectors and an outlet pipe. The total filtration areaof the filter plates was 50 cm2. Each filter plate was equippedwith a polypropylene filter cloth 25821AN (SEFAR FYLTIS, France).In some experiments, the pH of suspensions without dispersantwas adjusted before filtration by addition of the concentratedhydrochloric acid. Each experiment was repeated three times inaverage to calculate the mean value of the experimental data. Thetemperature in all the experiments was fixed at 25 C. The initialsolid concentration in suspension tank was 30 and 58–61 wt.%,respectively, for suspensions with and without a dispersant. Sam-ples for the textural tests were obtained by dilution of the filter cakeby the distilled water. Then suspensions were intensively mixed for3–5 h in soft insulated container.
Fig. 4. Viscosity of the kaolin suspension versus its shear rate at different solidcontent C. The insert shows the time dependence of at shear rate of 200 s−1 andsolid content C of 54.4 wt.%.

3. Results and discussion

3.1. Shear thinning–shear thickening behaviour

Viscosity of the kaolin suspensions is greatly influenced bythe shear rate and the content of solid particles C. Viscosityof the dispersant-free kaolin suspension displays an evidentshear thinning behaviour in the wide interval of concentrationsC ≈ 12–55 wt.% (Fig. 4). The concentration of 55 wt.% was the highestthat could be loaded into viscosimetric cup without any dispersant[30]. A small hysteretic loop was observed between the regimesof increasing and decreasing shear rate . A time-dependentbehaviour was also noticed at constant shear rate. The insert inFig. 4 shows typical time dependencies for C ≈ 40–55 wt.% at theshear rate of 200 s−1. The time-dependent behaviour evidences thatthe structural transformation in suspensions is caused by the shearperturbations. For kaolin, such transformation can be noticeablyimportant because of the loose packing, which is typical for thecard-house structures. The hydrodynamic perturbations can dam-
age and reconfigure the card-house structures, which results in theobserved behaviour.The viscosity curves within the concentrationrange of C = 20–55% (without dispersant) well represented by theclassical shear thinning power law (Ostwald de Waele model) [35]
∝ −n (2)

with n = 0.8 ± 0.1 for least square fitting of the experimental datawithin = 20–1000 s−1.

Origination of evident non-Newtonian flow in wide interval ofshear rates ( = 20–1000 s−1) was observed for high concentrationof kaolin (>20 wt.% in Fig. 4), and these data are in correspondencewith data of other authors [5,9,10].

Fig. 5 shows the typical shear stress versus shear rate depen-dencies at different solid content C. Bingham yield stress B andplastic viscosity * were calculated as explained in Fig. 5. BothBingham yield stress B and plastic viscosity * display the sharptransition from Newtonian (B ≈ 0) to non-Newtonian (B > 0) flowbehaviour in a close vicinity of 12 wt.% (see insert in Fig. 5). Theobserved behaviour may evidence proximity to the percolationthreshold at Cc ≈ 12 wt.% (ϕc ≈ 0.05) of kaolin. The percolation-

M. Loginov et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 325 (2008) 64–71 67

Fig. 5. Shear stress versus shear rate at different solid content C. Here, yieldstress (or Bingham stress) B is determined by extrapolating of () relationship tozero shear rate and the plastic viscosity * is determined by the slope of the ()curve at high shear rate. The insert shows the concentration dependence of yieldstress B and plastic viscosity * .

like behaviour should imply the presence of viscosity jump in thevicinity of percolation volume fraction ϕ ≈ ϕc and rather moderatechanges in viscosity in both below (ϕ < ϕc) and above (ϕ > ϕc) thisvolume fraction. Increase of the volume fraction of solid ϕ actu-ally results in transition from a fluid-like (sol) to a solid-like (gel)behaviour at some threshold point ϕc. Above this threshold con-centration ϕc, construction of a continuous percolative 3D networktakes place owing to the strong interactions between particles andclusters.

In principle, the estimated value of ϕc is close to the value, pre-dicted by the percolation theory for randomly distributed structuralelements of spherical shape, ϕc ≈ 0.15–0.2 [36]. The experimentallyestimated value was somewhat smaller than it was theoreticallypredicted. However, precise estimation of the percolation transitionis a rather complex task. The value of ϕc can depend on the parti-cle aspect ratio r (r (>1) is diameter-to-width ratio for a plate-like
kaolin particle), details of the local microstructure, inter-particleinteractions and presence of a card-house structure in the kaolinsuspensions. The theory predicts decrease of the percolation con-centration with increase of the particle aspect ratio [37,38] andwith decrease of the alignment of particles [39–41]. Moreover, thethreshold concentration, corresponding to the network connectiv-ity, can be smaller than that corresponding to the network rigidity[42]. For example, this value estimation for platelet clay particlesgives [39]
ϕc ≈ 2.15r(2S + 1)

(3)

where S is the order parameter, which is equal to S = −1/2 for aperfect alignment of the platelet particles and S = 0 for their randomspatial distribution.

The estimated from ESEM images aspect ratios r of kaolinparticles falling within 10–20. With these values of r, Eq. (3)gives ϕc ≈ 0.1–0.2 subject to random spatial distribution, whichreasonably approximates the experimental value for the kaolin sus-pensions, ϕc = 0.05. For better correspondence it is necessary toaccount for the distribution of particle sizes, aspect ratios, etc.

Fig. 6. Shear thinning–shear thickening for 62.2 wt.% suspension of kaolin in thepresence of 0.5 wt.% of dispersant. Arrows show directions of the shear rate evolu-tion. Insert shows the time dependence of at the shear rate of 200 s−1.

The transition between the non-Newtonian and Newtonianflows can be characterised by the hydrodynamic Peclet number,which is defined as the ratio of hydrodynamic and Brownian ener-gies [43]:

Peh = d3s

kT(4)

where d is the particle diameter, s is the solvent viscosity and kT isthe thermal energy. At room temperature (T = 298 K), this equationgives Peh ≈ 1 at = 0.03 s−1 for the kaolin particles (d ≈ 5.0 m)in water ( = 10−3 Pa s). The hydrodynamic Peclet number is ratherlarge in available range of the shear rates ( = 0.1–1000 s−1), so,Newtonian behaviour prevails, as a rule, for diluted kaolin systems(C < Cc).

At high concentrations of particles C (C > 20 wt.%) the moreevident non-Newtonian shear thinning behaviour prevails, whichreflects the presence of direct contacts between the particles. Insuch a case, the rheological behaviour can be characterized by theratio of the hydrodynamic energy to the energy of inter-particle
interaction E [43]:
Pee ≈ d3

E=

c(5)

where is the shear stress and c = E/d3. So, in highly concentratedsuspensions, the shear thinning behaviour is directly related to theenergy of inter-particle interaction E.

Shear shinning behaviour can also reflect the effects of particlesorganization related with their binding in a secondary potentialminimum, or progressive alignment in shear flows.

The addition of a dispersant promotes fluidity of the systemand affects noticeably its rheological behaviour. The kaolin sus-pensions with ultra-high concentration (C ≈ 55–75%, in presenceof dispersant) displays a typical shear thinning at moderate shearrates ( < 10–20 s−1) and shear thickening at higher hydrodynamicperturbation (Fig. 6). Note that very similar transition from theshear thinning to the shear thickening was already observed indispersant-free kaolin suspensions [44] but at larger shear rate (≈10000 s−1). Typical time dependencies of viscosity were alsoobserved at constant shear rate (insert in Fig. 6). The shear thinningpossibly reflects the structure weakening the resulting from hydro-

68 M. Loginov et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 325 (2008) 64–71

Fig. 7. Viscosity of the kaolin suspension versus solid content C (wt.%) at differentconcentrations of the dispersant Cd. The shear rate was fixed at 100 s−1. The insertshows scaling of viscosity near the percolation threshold, which corresponds to Eq.(7). Here Cc ≈ 12% is the percolation concentration.

dynamic perturbations. The shear thickening may be associated toenhancement of interaction between the differently charged edgesand basal surfaces in the highly perturbed suspensions.

3.2. Effects of kaolin and dispersant concentrations

In order to characterise and to compare the rheologicalbehaviour of suspensions with and without a dispersant at differ-ent solid content, we have analyzed viscosity at the same shearrate = 100 s−1. In this case, the shear thinning or shear thicken-ing behaviour was always present in the studied suspensions, andtheir viscosity was rather sensitive to changes in the solid contentC and dispersant concentration Cd.

Viscosity was a growing function of the solid content C. Viscos-ity of the dispersant-free suspensions increased approximately bytwo orders of magnitude with increase of C within the studied range

−1
of solid content (20–55 wt.%) at the shear rate of 100 s (Fig. 7).The increase of with concentration of suspension in a wide rangeof concentrations from 0.11 (25 wt.%.) to 0.33 (55 wt.%.), was fairlyapproximated by the following exponential equation:
= o exp ˛C (6)

where o = (2.3 ± 0.3) × 10−3 Pa s and ˛ = 0.140 ± 0.003.The sol–gel transition was rather sharp and close to the percola-

tion threshold ϕc ≈ 0.05 (Cc ≈ 12%), so, the viscosity is expected tofollow a power law [36].

∝ (C − Cc) (7)

where depends on dimensionality of the system.Insert in Fig. 7 clearly demonstrates good applicability of Eq.

(7) to description of viscosity data in the vicinity of the percola-tion threshold, and the straight line obtained by the least squarefitting corresponds to the slope of = 1.3 ± 0.2. A noticeable vis-cosity growth of the dispersant-free kaolin suspensions above thepercolation threshold ϕ > ϕc ≈ 0.05, possibly reflects continuousstructure changes and transition from a loosely packed card-housestructure at low concentrations to more compacted ordered struc-

Fig. 8. Maximum stress m versus solid content C (wt.%) at different concentrationsof the dispersant Cd.

tures at high concentrations. An ordering at high volume fraction ofthe plate-like particles may have an entropic nature [45–47]. Thetheory predicts nematic ordering with strong orientation for thedisk-like particles at [48]:

ϕ = ϕn ≈ 3r

. (8)

For kaolin particles with the aspect ratios r lying within 10–20,this equation gives ϕn = 0.15–0.3. So, it may be concluded, that ori-entation effects of entropic origin can noticeably influence viscositybehaviour in the concentration range C = 31–53 wt.% (ϕ = 0.15–0.3).

The textural measurement of the dispersant-free kaolin suspen-sions with concentration C between 59 and 69 wt.% (ϕ ≈ 0.37–0.47)displays continuous increase of suspension stiffness up to concen-tration corresponding to the filter cake, C ≈ 70 wt.% (Fig. 8). So, itis highly probable, that a smooth transition of viscosity behaviourfor the dispersant-free suspensions may be also extended up to thefilter-cake concentration, C ≈ 70 wt.% (dashed line in Fig. 7).

Introduction of a dispersant dramatically affects the observedviscosity (Fig. 7) and stiffness (Fig. 8) behaviours. In presence of
a dispersant, the fluidity transition follows to a classical perco-lation behaviour with a sharp change in viscosity at ϕ > ϕc. Thethreshold concentration ϕc as determined from origination ofthe non-Newtonian flow, was shifted to the high concentrationsand was observed from ϕc,d ≈ 0.33–0.38 (55–60 wt.%) (Fig. 7). Thethreshold range ϕ, corresponding to the high rate of viscositygrowth, was rather narrow, ϕ ≈ 0.05. Therefore, the concentra-tion dependences of viscosity and stiffness of the dispersant-loadedsuspensions supports the percolation nature of fluidity transi-tions in the studied systems. A difference between percolationthresholds for dispersant-free (ϕc ≈ 0.05) and dispersant-loaded(ϕc,d ≈ 0.33–0.38) suspensions can be explained by the presence oforientational ordering in a dispersant-loaded suspension. Assum-ing the random spatial distribution of aligned platelet particles in adispersant-free suspension (S = 0), the orientation order parameterS in suspension with dispersant can be approximately estimatedfrom Eq. (3) as S ≈ (ϕc/ϕc,d − 1)/2 ≈ −(0.42–0.43).
The difference between structures of the dispersant-free anddispersant-loaded suspensions is evidently demonstrated by theESEM images (Fig. 9). In the absence of a dispersant, the ESEMimage reveals a card-house structure with loose-packed arrange-

M. Loginov et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 325 (2008) 64–71 69

Fig. 10. Viscosity of the kaolin suspension versus dispersant concentration Cd atC = 62 wt.% and = 100 s−1. The insert shows the representative rheological curvesof viscosity versus the shear rate at different concentrations of dispersant.

particles. The excess dispersant concentration in a kaolin sus-pension is not desirable and may exert a negative effect, causingdestabilization and flocculation of the system [30].

3.4. Filtration behaviour

The porous structure of a filter cake may partially reflect thepacking of the particles in the highly concentrated suspensions.The filtration efficiency was analyzed in filtration–pressure exper-iments using the Ruth–Carman expression [49]:

t − to

V − Vo= ak1(V + Vo) + k2 (9)

where t and V are the time of filtration and filtrate volume, to andVo the initial filtration time and initial volume of filtrate requiredto reach the stabilised regime of filtration at constant pressure; ais the specific cake resistance; and k1, k2 are filtration parameters.

Fig. 9. ESEM images of the aqueous kaolin suspensions, C = 30 wt.%, without (a) andwith a dispersant, Cd = 0.5% (b).

ment of particles and the absence of their orientation. However,orientational ordering is evidently present in the dispersant-loadedsuspensions with the same solid content (30 wt.%), where particleshave face-to-face orientation.

3.3. Presence of optimality in dispersant concentration

The maximum percolation threshold was observed at a certainoptimum concentration of the dispersant (Cd ≈ 0.5%). The presenceof an optimal value of the dispersant concentration can be easilydemonstrated from dependence of viscosity versus dispersant con-centration (Fig. 10). The viscosity was noticeably reduced at optimalconcentration of the dispersant. Moreover, the dispersant concen-tration influenced the shape of the rheological curves of viscosityversus the shear rate (insert in Fig. 10). The optimal concentrationof the dispersant (Cd ≈ 0.5%) reflects the weakest shear thickeningflow, though the dispersant overloading at Cd ≈ 1.0% initiated boththe shear thinning and shear thickening flows.

The observed complexity of fluidity response to the shear rateinduced perturbation evidently reflects the complex structure ofa highly concentrated suspension, packing characteristics of theparticles with a plate-like geometry, different charges of the edgeand basal planes, inter-particle interactions and many other fac-tors.

It is expected that the optimum dose of the dispersant cor-responds to the limit adsorption capacity of the edges of kaolin

Fig. 11. Presentation of filtration data in Ruth–Carman coordinates for differentdispersant concentrations Cd, and for Cd = 0% and different pH.

70 M. Loginov et al. / Colloids and Surfaces A: Phys

ous kaolin suspensions, can gradually transfer into an oriented stateunder the load of solid particles or dispersant (Fig. 13). However,

Fig. 12. Specific cake resistance a (a) and dryness of the filter cake Cm (b) versusdispersant concentration of Cd or pH.

The filtration efficiency decreases with increase of the specific cakeresistance a.

Fig. 11 demonstrates a good applicability of Eq. (9) for descrip-tion of experimental data for both dispersant free and dispersantloaded kaolin suspensions. Introduction of a dispersant resulted innoticeable increase of a and filtration efficiency decrease (Fig. 12a).This corresponds to the previous results on filtration of calciumcarbonate suspensions in presence of dispersant [50,51].

There exists a correlation between specific cake resistance a(Fig. 12a) and the cake dryness after filtration Cm (Fig. 12b). Appar-ently, the cake dryness reflects compactness of the packing of thekaolin particles. In the absence of a dispersant, the kaolin particlesarrange in loosely packed structure, which is less resistant to theliquid flow during filtration. With a dispersant, the kaolin particlesget orientated, as it is demonstrated by Fig. 9. Such orientation andsubsequent change of the structural packing increases resistanceto the liquid flow inside the cake structure, but also increases thecake dryness.

Fig. 13. Schematical presentation of fluidity model for highly co

icochem. Eng. Aspects 325 (2008) 64–71

If we want to prepare the highly concentrated suspensionsby filtration, it is obvious that initial addition of a dispersant isundesirable. Filtration may become considerably longer in thiscase due to increase of the specific resistance of the cake. Theother filtration technique for drastic decrease of specific cake resis-tance in presence of a dispersant was recently proposed [50,51].A dispersant-free suspension was first filtered to form a precoat.At the second step of filtration, the precoat served to trap the dis-persant from the dispersant loaded-suspension. Such a techniqueallows to filter suspensions loaded with a dispersant with the samespeed as for dispersant-free suspensions.

The pH change in absence of a dispersant is also related tomodification of the cake built-up. The decrease of pH causes a mea-surable increase of filtration velocity and decrease of Cm, whichis accounted for reinforcement of the loosely packed card-housestructure at low pH (Fig. 12).

4. Summary and conclusions

This study shows that fluidity of the kaolin suspensions is a com-plex function of concentrations of the dispersant and solid particles.Fluidity depends on arrangement of the particles, their orientationand hydrodynamic perturbations in the rheological measurements.A loosely packed card-house structure, which is typical for aque-

in both cases, the nature of this orientation may be quite different.This orientation may reflect entropic effects, caused by increase ofthe content of kaolin platelets, or effects of electrostatic stabiliza-tion, related to neutralization of the edge charges in presence ofa dispersant. The presence of the ordered structure correspondingto regions of aligned kaolin plates in very concentrated suspen-sions was recently shown by cryomicroscopy and it was used forexplanation of nonlinear behaviour in shear flows [52].

The shear thinning–shear thickening transformation at a cer-tain threshold shear rate c is typical for the kaolin suspension andreflects the flow-stimulated orientational ordering at < c andenhancement of the face-edge interactions, related to turbulentdistortions at > c (Fig. 12). The value of c ≈ 104 s−1, character-istic to a dispersant-free suspension [44], dramatically decreasedto c ≈ 101–102 s−1 in suspensions with a dispersant. The perco-lation transition was evidently present in viscosity behaviour forthe kaolin dispersions. The introduction of a dispersant shifted thepercolation transition to higher volume fractions. The increase ofthe percolation threshold is desirable for production of the flow-

ncentrated kaolin suspensions. See the text for the details.

: Phys

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[taining 3D randomly distributed graphite nanoplatelets, Compos. Sci. Technol.

M. Loginov et al. / Colloids and Surfaces A

ing suspensions an their maximum loading by the solid particles.The shift in percolation was explained by enhancement of ori-entation alignment of the platelet particles in the presence of adispersant. The results demonstrate existence of a maximum forthe percolation threshold, which was observed at a certain opti-mum dosage of the dispersant. Filtration efficiency data, obtainedfrom filtration–compression tests, allow to suggest an enhancedcompactness of the packing of kaolin particles in presence of adispersant.

Acknowledgments

The authors would like to acknowledge the ADEME (Agence del’Environnement et de la Maıtrise de l’Energie) for its financial sup-port (project ADEME no. 03-74-0163). The authors thank Dr. N.S.Pivovarova for her help with the manuscript preparation.

References

[1] W.B. Jepson, Kaolins: their properties and uses, Philos. Trans. R. Soc. Lond., Ser.A 311 (1984) 411–432.

[2] W.M. Carty, The colloidal nature of kaolinite, Ceram. Eng. Sci. Proc. 22 (2001)31.

[3] H.H. Murray, J.E. Kogel, Engineered clay products for the paper industry, Appl.Clay Sci. 29 (2005) 199–206.

[4] S.B. Johnson, G.V. Franks, P.J. Scales, D.V. Boger, T.W. Healy, Surfacechemistry–rheology relationships in concentrated mineral suspensions, Int. J.Miner. Process. 58 (2000) 267–304.

[5] A. Pantet, P. Monnet, Liquid–solid transition of kaolinite suspensions, Mech.Mater. 39 (2007) 819–833.

[6] R. Lapasin, Rheology of clay/kaoline aqueous suspensions and ceramic slips,Sci. Ceram. 11 (1981) 91–98.

[7] Th.F. Tadros, Use of viscoelastic measurements in studying interactions in con-centrated dispersions? Langmuir 6 (1990) 28–35.

[8] H.A. Barnes, The yield stress—a review or ‘ ’—everything flows? J.Non-Newtonian Fluid Mech. 81 (1999) 133–178.

[9] D. Komatina, M. Jovanovic, Experimental study of steady and unsteady freesurface flows with water–clay mixtures, J. Hydraulic Res. 35 (1997) 579–590.

10] C.G. Litzenberger, R.J. Sumner, Flow behaviour of kaolin clay slurries, in: Pro-ceedings of the 16th International Conference on Hydrotransport, Santiago,Chile, 2004, pp. 77–91.

[11] F. Bagusat, O. Seidel, H.-J. Mogel, Time periodic changes of viscosity in kaolinsuspensions as an example for modelling concentrated suspensions, Prog. Col-loid Polym. Sci. 111 (1998) 82–84.

12] F. Bagusat, P. Schiller, O. Seidel, T. Zehl, H.-J. Mogel, Optical detection of shearinduced structure changes in concentrated suspensions, Colloids Surf. A 215(2003) 131–136.

13] O. Seidel, F. Bagusat, H.-J. Mogel, Time periodic viscosity of concentrated kaolinsuspensions at constant shear rates, Rheol. Acta 38 (1999) 305–310.

14] F. Tatsuoka, M. Ishihara, H. Di Benedetto, R. Kuwano, Time-dependent sheardeformation characteristics of geomaterials and their simulation, Soils Found.42 (2002) 103–129.

15] H.V. Atkinson, Modelling the semisolid processing of metallic alloys, Prog.Mater. Sci. 50 (2005) 341–412.

16] A. Mujumdar, A.N. Beris, A.B. Metzner, Transient phenomena in thixotropicsystems, J. Non-Newtonian Fluid Mech. 102 (2002) 157–178.

[17] L.A. Glasgow, R.H. Luecke, Mechanisms of deaggregation for clay–polymer flocsin turbulent systems, Ind. Eng. Chem. Fundam. 19 (1980) 148–156.

18] F. Cravero, I. Gonzalez, E. Galan, E. Dominguez, Geology, mineralogy, origin andpossible applications of some Argentinian kaolins in the Neuquen basin, Appl.Clay Sci. 12 (1997) 27–42.

19] K. Tone, Y. Shibasaki, O. Yamamoto, Surface ion-exchange of Georgia kaolin andrheological properties, J. Ceram. Soc. Jpn. 105 (1997) 228–232.

20] C.A. Paredes, R.A. Haber, Effect of soluble ions on the rheological stability ofclay slurries, Ceram. Eng. Sci. Proc. 22 (2001) 89–96.

21] S. Thongphrom, R. Watanesk, K. Keowkamnerd, S. Watanesk, O. Arquero, R.Beckett, Influence of pH on dispersion stability of a ceramic glaze and its com-ponents, Ceram. Forum Int. 80 (2003) E39–E43.

[

[

[

[

[

[

[

[

[

[

[

icochem. Eng. Aspects 325 (2008) 64–71 71

22] H. Van Olphen, An Introduction to Clay Colloid Chemistry, Wiley, New York,1977.

23] M.L. Taylor, G.E. Morris, P.G. Self, R.St.C. Smart, Kinetics of adsorption of highmolecular weight anionic polyacrylamide onto kaolinite: the flocculation pro-cess, J. Colloid Interface Sci. 250 (2002) 28–36.

24] F.P. Luckham, S. Rossi, The colloidal and rheological properties of bentonitesuspensions, Adv. Colloid Interface Sci. 82 (1999) 43–92.

25] D. Penner, G. Lagaly, Influence of anions on the rheological properties of claymineral dispersions, Appl. Clay Sci. 19 (2001) 131–142.

26] H.-G. Bothe, H.-J. Kroeck, G. Struebel, Investigations on Rheological Propertiesof Kaolin from Hirschau, Bavaria, Sprechsaal 116 (1983) 968–972.

27] J. Koetz, S. Kosmella, Interactions between polyanion–polycation systems andkaolin, J. Colloid Interface Sci. 168 (1994) 505–513.

28] M. Sjoberg, L. Bergstrom, A. Larsson, E. Sjostrom, The effect of polymer and sur-factant adsorption on the colloidal stability and rheology of kaolin dispersions,Colloids Surf. A 159 (1999) 197–208.

29] A. Zaman, R. Tsuchiya, B.M. Moudgil, Adsorption of a low-molecular-weightpolyacrylic acid on silica, alumina, and kaolin, J. Colloid Interface Sci. 256 (2002)73–78.

30] A. Papo, L. Piani, R. Ricceri, Sodium tripolyphosphate and polyphosphate asdispersing agents for kaolin suspensions: rheological characterization, ColloidsSurf. A 201 (2002) 219–230.

31] M. Brumbach, W.M. Carty, Dispersant demand curves: effect of PAA on theviscosity of several clays, Ceram. Eng. Sci. Proc. 24 (2003) 183.

32] F. Zibouche, H. Kerdjoudj, Rheological properties of the Tamazert’s Kaolin, Eur.J. Sci. Res. 13 (2006) 22–30.

33] X.-H. Wang, X.-C. Lu, Y.-C. Li, Viscosity of kaolin slurry from coal seam and theinfluencing factors, Chin. J. Process. Eng. 4 (2004) 295–299.

34] S. Chandrasekhar, S. Ramaswamy, Influence of mineral impurities on the prop-erties of kaoline and its thermally treated products, Appl. Clay Sci. 21 (2002)133–142.

35] R.B. Bird, W.E. Steward, E.W. Lightfoot, Transport Phenomena, Wiley, New York,1960.

36] D. Stauffer, A. Aharony, Introduction to Percolation Theory, Taylor & Francis,London, 1992.

37] S. Lohmander, Aspect ratios of pigment particles determined by different meth-ods, Nordic Pulp Pap. Res. J. 15 (2000) 221–230.

38] A. Celzard, E. McRae, C. Deleuze, M. Dufort, G. Furdin, J.F. Mareche, Criticalconcentration in percolating systems containing a high aspect-ratio filler, Phys.Rev. B 53 (1996) 6209–6214.

39] C. Lu, Y.W. Mai, Influence of aspect ratio on barrier properties of polymer–claynanocomposites, Phys. Rev. Lett. 95 (2005) 088303.

40] F. Du, J.E. Fischer, K.I. Winey, Effect of nanotube alignment on percolationconductivity in carbon nanotube/polymer composites, Phys. Rev. B 72 (2005)121404.

41] J. Li, J.-K. Kim, Percolation threshold of conducting polymer composites con-

67 (2007) 2114–2120.42] M. Sahimi, Non-linear and non-local transport processes in heterogeneous

media: from long-range correlated percolation to fracture and materials break-down, Phys. Rep. 306 (1998) 213–395.

43] C. Baravian, D. Vantelon, F. Thomas, Rheological determination of interactionpotential energy for aqueous clay suspensions, Langmuir 19 (2003) 8109–8114.

44] V.T. O’Brien, M.E. Mackay, Shear and elongation flow properties of kaolin sus-pensions, J. Rheol. 46 (2002) 557–572.

45] L. Onsager, Shear and elongation flow properties of kaolin suspensions, Ann. N.Y. Acad. Sci. 51 (1949) 627–659.

46] F.M. van der Kooij, H.N.W. Lekkerkerker, Formation of nematic liquid crystals insuspensions of hard colloidal platelets, J. Phys. Chem. B 102 (1998) 7829–7832.

47] P. Davidson, J.-C.P. Gabriel, Mineral liquid crystals, Curr. Opin. Colloid InterfaceSci. 9 (2005) 377–383.

48] J.A.C. Veerman, D. Frenkel, Phase behavior of disklike hard-core mesogens, Phys.Rev. A 45 (1992) 5632–5648.

49] R.J. Wakeman, E.S. Tarleton, Filtration: Equipment Selection, Modelling andProcess Simulation, Elsevier, Oxford, 1998.

50] Z. Soua, O. Larue, E. Vorobiev, J.-L. Lanoiselle, Estimation of floc size in highlyconcentrated calcium carbonate suspension obtained by filtration with disper-sant, Colloids Surf. A 274 (2006) 1–10.

51] M. Husson, C. Jacquemet, E. Vorobiev, Demande de brevet francais, nBR012 du17 juillet 2002.

52] M. Moan, T. Aubry, F. Bossard, Nonlinear behavior of very concentrated sus-pensions of plate-like kaolin particles in shear flow, J. Rheol. 47 (6) (2003)1493–1504.


145

Conclusions

The percolation transition was observed both in the dispersant-free and dispersant-loaded

suspensions. Percolation (or structure formation) was accompanied by abrupt jump of

suspension viscosity. In the absence of a dispersant, the percolation started at kaolin

concentrations above 12 % wt. It resulted in formation of a “card house” structure that was

observed by means of electronic microscopy. Such a low concentration for transition in the

structured state was explained in the framework of percolation theory for plate-like particles.

Addition of a dispersant suppressed the interaction forces between basal and edge faces of

the kaolin particles. As a result, “card house” structure was disappearing and “face-to-face”

arrangement of particles was arising after addition of a dispersant, which was supported by

the electron microscopy images. The addition of a dispersant shifted percolation to higher

particles concentration (55–60 % wt). According to the percolation theory, high value of the

percolation concentration was explained by “face-to-face” arrangement of particles.

Maximum of the percolation concentration (and lowest suspension viscosity) was reached

for certain optimum dosage of the dispersant (≈ 0.5 % wt/wt).

Hence, the loosely packed “card-house” structure, which is typical for the aqueous kaolin

suspensions, undergoes gradual conversion into an oriented structure under the load of solid

particles or under addition of dispersant. Higher filtration efficiency was observed for loosely

packed “card-house” structure in dispersant-free suspensions. Dispersant improves fluidity

and dryness of the filter-cakes, however, produces an oriented “face-to-face” structure of

particles, which causes a rise in resistance to liquid flow during filtration.

III.2. Dead-end dynamic filtration of CaCO3 suspensions

146

Paper II: “Dead-end dynamic filtration of highly concentrated CaCO3

suspensions in the presence of a dispersant”

Introduction

It was shown in Paper I that preparation of a concentrated and flowable mineral

suspension by means of dead-end filtration technique is limited by formation of the filter-cake

with high specific resistance. Several variants of this technique were proposed in order to

decrease the filter-cake resistance and enhance filtration: filtration of naturally flocculated

suspension with mixing of the filter-cake with appropriate amount of a dispersant

(Wiekmann, 1980; Bleakley, 1997; Willis, 1998), combined treatment of feed suspension by

mixture of a dispersant and a flocculant (Parker, 1997), use of two-stage dead-end filtration

(Soua, 2004; Vorobiev, 2004; Mouroko-Mitoulou, 2002; Husson, 2003). However, these

techniques have two disadvantages:

• their implementation results in formation of a filter-cake that reduces filtration rate;

• filter-cake fluidization (crushing or homogenization) is required for obtaining of a liquid

suspension with high fluidity;

• batch dead-end filtration techniques do not allow continuous production of the

suspension.

Use of dynamic filtration technique may be proposed in order to avoid these

disadvantages. Dynamic filtration together with cross-flow microfiltration became a usual

technique for processing of diluted suspensions and purification of liquids. However, only

several studies were devoted to dynamic filtration of concentrated mineral suspensions

(Mikulášek, 1998; Bouzerar, 2000, 2003; Ding, 2006; He, 2007) or preparation of highly

concentrated mineral suspensions (Trave, 2007; Ochirkhuyag, 2008). Despite of negative

conclusions of Mikulášek (1998) and Bouzerar (2000) regarding low filtration rate of

concentrated suspensions, Trave (2007) and Ochirkhuyag (2008) have demonstrated the

possibility of preparation of a highly concentrated mineral suspension by cross-flow and

dynamic filtration. In these studies diluted mineral suspensions were mixed with a dispersant

prior to filtration. It is known that addition of a dispersant weakens interaction between

particles in the filter-cake and should the enhance cake erosion during dynamic filtration.

However, dispersant also decreases permeability of the filter-cake and results in chemical

contamination of the filtrate.


147

In dead-end filtration, contamination of the filtrate and formation of low permeable filter-

cake may be avoided by using of two-stage filtration technique (Soua, 2004; Vorobiev, 2004;

Mouroko-Mitoulou, 2002; Husson, 2003). According to this technique, the dead-end filtration

is divided in two stages and dispersant is added to suspension only at the second stage of

filtration:

• the first stage of the process is an ordinary filtration of suspension without dispersant,

with formation of “precoat layer” of the filter-cake;

• at the second stage, the excess quantity of the dispersant is added to the suspension; then

deflocculated suspension is filtered on the precoat. The filtrate from deflocculated suspension

(enriched by the dispersant) displaces the dispersant-free interstitial liquid remaining in the

pores of precoat. Precoat absorbs and retains the dispersant molecules coming from the

deflocculated suspension and, thus, prevents the filtrate from contamination.

In dynamic filtration, the moment of dispersant addition must also play an important role.

However, the influence of this factor on the kinetics of dynamic filtration and quality of the

filtrate and final suspension was not studied before.

Summary

The aims of this paper are:

(1) to study a possibility of preparation of a concentrated and flowable calcium carbonate

suspension by means of dynamic filtration technique;

(2) to analyze the influence of operational parameters (transmembrane pressure, disk

rotation speed, concentration of dispersant and time of dispersant addition to

suspension) on efficiency of filtration and quality of final products (dryness and

viscosity of final suspension and dispersant losses in the filtrate);

(3) to compare efficiency of novel dynamic filtration technique with those of dead-end

and cross-flow filtrations.

Diluted (20 % wt) suspensions of calcium carbonate were filtered in a specially designed

dead-end filtration cell equipped by rotating disk. Kinetics of filtration was measured at

various transmembrane pressures (0.2–0.95 bar) and disk rotation speeds (0–2000 rpm). The

dispersant (sodium polyacrylate) concentration varied from 0 to 2 % wt/wt.

Two types of filtration were carried out: with initial and with delayed addition of a

dispersant. In experiments with initial dispersant addition, the suspension and dispersant were

mixed before dewatering. In experiments with delayed dispersant addition, the dispersant-free


148

suspension was filtered until reaching ~ 55 % of total filtrate quantity, then a dispersant was

added to the pre-concentrated suspension in the course of filtration.

Dryness and rheological properties of final concentrated suspensions were measured. In

addition, the dispersant concentration was measured and adsorption of dispersant molecules

on calcium carbonate was determined.

Research Article

Dead-End Dynamic Filtration of HighlyConcentrated CaCO3 Suspensions in thePresence of a Dispersant

This work discusses dewatering of CaCO3 suspensions in the presence of a disper-sant (sodium polyacrylate). Suspensions were dewatered using the rotating disk-aided dead-end dynamic filtration technique. Dewatering efficiency was studiedas a function of the dispersant content and operational parameters (disk rotationspeed, filtration pressure). Two dewatering modes, with initial (i-dewatering) anddelayed (d-dewatering) dispersant addition, were tested. For concentrated sus-pensions, the d-dewatering allowed higher final dryness and better fluidity thani-dewatering with minimum dispersant losses in the filtrate.

Keywords: Calcium carbonate, Concentrated suspension, Dewatering, Dispersant, Dynamicfiltration, Fluidity

Received: February 24, 2010; revised: March 22, 2010; accepted: March 23, 2010

DOI: 10.1002/ceat.201000073

1 Introduction

Mineral suspensions with a high concentration of particles andlow viscosity are required for many practical applications, suchas ceramic processing and preparation of paints, or paper coat-ings [1, 2]. However, viscosity is generally high with concen-trated mineral suspensions due to their aggregation and for-mation of spatial networks [3, 4]. One effective way of fluidityregulation is based on the addition of suitable dispersants [5].

The highly concentrated (72–75 wt %) and low-viscositysuspensions of calcium carbonate (CaCO3) are required forimprovement of paper whiteness, gloss, and printability. Thesodium and ammonium salts of polyacrylic acid were found tobe effective dispersants for CaCO3 suspensions [6, 7].

Different methods for preparation of highly loaded CaCO3

suspensions, based on powder rehydration in the presence of adispersant [8], excess water evaporation by spray drying [9],dead-end filtration [10–14], and precoat dead-end filtration[15] were recently proposed. The latter technique allowedpreparation of CaCO3 suspensions with low viscosity, g1) ≈0.3 Pa s, for low shear rates about 20 s–1, containing up to74 wt % CaCO3 in the presence of 0.5 wt % sodium polyacry-late [16, 17]. However, a supplementary stage of mechanical

cake homogenization is required for cake fluidization and highdryness can be achieved after CaCO3 cake compression at10–15 bars. The dead-end filtration technique always results ingrowth of the filter cake in low filtration efficiency and it re-quires supplementary mechanical agitation for filter cake flui-dization. To avoid these limitations, different continuousmicrofiltration techniques with shear flow were tested [18, 19,20–24].

The filtration flux in a rotating disk system is governed bydifferent operational parameters, such as filtration pressure,rotation speed, concentration of feed suspension, as well as thedesign of the filtration module. The moment of dispersant ad-dition in the course of filtration may also be an important fac-tor influencing the dryness and fluidity of the final suspensionand filtrate contamination by the dispersant. Then, it requiresfurther investigation.

This work is devoted to the study of dewatering of CaCO3

suspensions using a lab-scale dynamic filtration module. Thecylindrical filter cell comprised a rotating disk with adjustablespeed and filtration was carried out on a fixed microfiltrationmembrane. The time of dispersant (sodium polyacrylate) ad-dition and operational parameters (disk rotation speed, filtra-tion pressure) were analyzed.

2 Materials and Methods

2.1 Materials

The aqueous suspension of calcium carbonate with an initialsolid content of 20.0 wt % was provided by OMYA (France).The average particle diameter was 1.1 ± 0.1 lm. The dispersant

www.cet-journal.com © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim Chem. Eng. Technol. 2010, 33, No. 8, 1260–1268

Maksym Loginov1,2

Nikolai I. Lebovka1,2

Olivier Larue1

Lu Hui Ding1

Eugene Vorobiev1

1 TIMR, University ofTechnology of Compiegne,Research Centre of Royallieu,Compiegne, France.

2 F. D. Ovcharenko Institute ofBiocolloidal Chemistry, NAS ofUkraine, Kyiv, Ukraine.

–Correspondence: Prof. N. I. Lebovka ([email protected]), F. D.Ovcharenko Institute of Biocolloidal Chemistry, NAS of Ukraine, 42,blvr. Vernadskogo, Kyiv 03142, Ukraine.

–1) List of symbols at the end of the paper.

1260

used was a 31-wt % solution of sodium polyacrylate DV 834,produced by COATEX (France).

2.2 Dewatering

A schematic of the dewatering apparatus is presented in Fig. 1.The apparatus comprises a filtration cell with suspension, a ro-tating disk connected to a mixer, an evacuated flask for the fil-trate, and a vacuum pump. The filtration cell is a plastic cylin-der with a total volume of 200 cm3 and an internal radius of27.5 mm. PA 6 (Nylone) membrane with a pore size of 0.2 lm(Biodyne A, Pall Co.) was fixed at the bottom of the cell.

Turbidity measurements showed that the membrane wasable to retain all the particles of the suspension. The mem-brane filtration area, S, was equal to 2.4 · 10–3 m2. Membraneswith the resistance of Rm = 1.5 ± 0.2 · 1011 m–1 were used in eachexperiment. Filtration was driven by the negative pressure gen-erated by the vacuum pump. The transmembrane pressure val-ue, p, was adjusted between 0.2 and 0.95 bar.

Filtrate was collected in the evacuated flask placed on theelectronic balance and the filtrate mass was registered. Theflask was connected to the filtration cell and the vacuum pumpby flexible plastic tubes. A stainless steel perforated disk (Fig. 1)with 25 mm in radius r0 was placed inside the filtration cell. Itwas fixed on a metal shaft and was connected to a mixer rotat-ing with adjustable speed, x, up to 2000 rpm.

An initial gap between the disk and the membrane surfacewas ho = 2 mm. The shear rate, c

, was dependent on the dis-

tance to the axis of rotation, r, and was evaluated as c

= h r/h,where h is the gap between the rotating disk and the cake sur-face, and h is the angular speed (Fig. 1). The maximum shearrate was at the disk periphery at r = r0. At h = ho = 2 mm, theshear rate can be estimated as c

= 2p x r0/(60h) s–1 ≈ 400 s–1 for

x = 300 rpm and c ≈ 2700 s–1 for x = 2000 rpm.

The same initial quantity of suspension (≈ 190 g; ∼ 85 mm insuspension height in the cylinder) was taken in each experi-ment. Two modes of dewatering were applied: with initial dis-

persant addition (i-dewatering) and with delayed addition of adispersant (d-dewatering). In experiments with the first typeof dewatering, the suspension and dispersant were mixed for10 min at 100 rpm before dewatering. In experiments with thesecond type of dewatering, the aggregated suspension was fil-tered until reaching Vd = 100 cm3 of filtrate, then a dispersantwas added to the pre-concentrated suspension in the course offiltration. The dispersant concentration, cd, was varied between0.1 and 2 wt % dispersant/wt CaCO3. The total time of the ex-periment was within 10–40 min depending on the dispersantconcentration. Suspensions were filtered at initial ambienttemperature ≈ 20 °C. Owing to the frictional energy dissipationin the sheared volume between the rotating disk and the cakesurface, the temperature of the suspension, T, was a growingfunction of time, t. The rate of frictional energy dissipation perunit volume is s c

g

c

2 x2 [26], where s is the shearstress. So, the rate of temperature increase, dT/dt, can theoreti-cally be calculated as:

dTdt 2ph

r0

0

g c

2rdrCm (1)

where C is the specific thermal capacity and m is the mass ofsuspension.

For estimation purposes, we let g ≈ 1 Pa·s and C = 4.18 J/(g K).At m = 190 g and h = 2 mm, this equation gives dTdt p r4

0gx22hCm ≈ 4 · 10–4 K/s for x = 300 rpm and dTdt ≈ 0.02 K/sfor x = 2000 rpm. Hence, the rate of temperature increase wasinessential at the initial stage of dewatering. However, it couldbecome noticeable at the final stage of dewatering. Lettingh = 0.1 mm and m = 50 g, we get dTdt ≈ 0.03 K/s forx = 300 rpm and dTdt ≈ 1.2 K/s for x = 2000 rpm. Still, due tothe disk rotation restrictions, the experiments were stopped atthis stage of dewatering and the final temperature, T, never ex-ceeded 50 °C. The sharp increase of temperature, T (> 3 °C),was observed only at the final stages of filtration when the vol-ume of filtrate exceeded 130–135 cm3. This temperature in-crease reflected reaching of the state when the cake fills the totalspace between filter medium and rotation disk. After that, fil-tration was immediately stopped. Note that filtrate viscosity, gf,increased with an increase in T (e.g., gf ≈ 1.0 mPa s at 20 °C andgf ≈ 0.55 mPa s at 50 °C). However, at the final stages of filtra-tion, the decrease of filtration rate with T increase was alwaysobserved. So, the effect of temperature viscosity change on fil-tration rate was less significant.

According to [27, 28], filtration is typical for diluted suspen-sions, while consolidation takes place in a concentrated sus-pension. The solidosity (maximal particle concentration of un-compressed filter cake) of the naturally-aggregated CaCO3

suspensions is equal to u = 0.2–0.3 (45–55 wt %) and highersolidosity (u > 0.3) requires supplementary compression [29].In our study, much more concentrated suspensions were pre-pared by means of the dynamic filtration technique. It suggeststhat consolidation of the cake occurred during the dynamic fil-tration.

Ruth-Carman’s filtration equation [30] fails to explain theexperimental curves in the case of cake consolidation, espe-cially in the late stage of dewatering. Application of the filtra-tion-consolidation equation (for example, [27]) is more ap-

Chem. Eng. Technol. 2010, 33, No. 8, 1260–1268 © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.cet-journal.com

Figure 1. Scheme of the filtration apparatus.

Dynamic filtration 1261

propriate for the description of the consolidation period of de-watering. Another known approach is solution of the filtra-tion-consolidation equation with a moving boundary condi-tion due to deposition of the particles and increase in the cakethickness. This approach is more complicated and implies aknown relation between the cake volume and the volume offiltrate [31].

Unfortunately, the material balance seems to be more com-plicated in our experiments. The concentration of feed suspen-sion is not constant during dewatering with a rotating disk[21]. The total weight of solid particles in the cake is not con-stant during the consolidation period [32]. Additionally, thevalue of the shear stress on the cake surface and viscosity ofsuspension varies in the direction from the axis of rotation tothe external edge of the rotating disk [33]. Accounting forthese difficulties, a simplified approach based on Darcy’s law[30]:

dtdV gf Rc RmSp (2)

was used in the present work for dewatering data presentationand fitting.

Here, t is the dewatering time, V is the filtrate volume, gf isthe filtrate viscosity, S is the membrane filtration area, p is thetransmembrane pressure, and Rc and Rm are resistances of thefilter-cake and membrane, respectively.

Note that for dead-end filtration:

Rc = awV/S (3)

where a is the specific cake resistance and w is the mass of de-posited solid per filtrate volume. In the dead-end filtration, aand w are generally constants and the filter cake resis-tance, Rc, is directly proportional to the filtrate vol-ume, V.

The value of the specific cake resistance, a, is moreconventionally used but, in this study, erosion of thecake means that the mass of solids deposited, w, canvary with time. So, the value of Rc was estimated fromEq. (2) using S = 2.4 · 10–3 m2, Rm = 1.5 ± 0.2 · 1011 m–1,and gf = 1.0 mPa s at ambient temperature ≈ 20 °C.

2.3 Analysis Instruments

The size distribution function (SDF) of aggregates insidesuspensions was recorded using a laser diffraction in-strument (Mastersizer X 6618, Malvern InstrumentsGmbH, UK). This function corresponds the volumefraction of particles with a certain size (in %). For allsamples, the measurements were made in diluted CaCO3

suspensions with concentration, c ≈ 5 · 10–5 wt %.UV absorption spectra of filtrate samples were mea-

sured using the UV spectrophotometer Biochrom Li-bra S32 for estimation of the dispersant losses in thefiltrate. Viscosity at 25 °C was measured using the rota-tional coaxial viscosimeter, Haake VT 550 (Haake,Karlsruhe, Germany).

The final dryness of suspension, Ds, and cake, Dc, was mea-sured after their drying at 130 °C. The average dryness was esti-mated from the material balance equation:

D mCaCO3msusp qf V (4)

where mCaCO3 is the total mass of calcium carbonate, msusp isthe mass of suspension used for dewatering, and qf is the den-sity of filtrate.

All the experiments were repeated at least three times. Themean values and standard deviations were calculated.

3 Results and Discussion

3.1 Dewatering Behavior

3.1.1 Influence of Rotation Speed and Pressure

Fig. 2 presents dewatering data in terms of dt/dV vs. V coordi-nates at different (a) disk rotation speeds, x, and (b) pressuredrops, p. Here, dispersant was added before dewatering (i-de-watering) and its concentration, cd, was fixed at 0.5 wt %. De-watering at x = 0 rpm and p = 0.95 bar (Fig. 2a)) does not yielda straight line in dt/dV vs. V as it should normally be expectedfor the dead-end filtration. The presence of the disk accountsfor the deviation from a straight line. When the disk was re-moved (not presented here), a straight line was observed in thedt/dV vs. V coordinates for x = 0 rpm.

For more convenience, dynamic dewatering results (withx > 0) are also presented in Fig. 2. According to Eq. (2), thecurve in Fig. 2b) reflects evolution of the filter-cake resistance,


Figure 2. Dynamic dewatering behavior of CaCO3 suspension: (a) rotationspeed, x, variation at constant pressure, p = 0.95 bar; (b) filtration pressure,p, variation at constant rotation speed, x = 300 rpm. Initial concentration ofthe dispersant, cd, was 0.5 wt %.

1262 M. Loginov et al.

Rc, at the given pressure. A linear curve with the constant slopevalue > 0 would indicate that the term a·w is constant. In sucha case, the filtrate flux should decrease proportionally to thefiltrate volume. The steeper slope in dt/dV vs. V indicates anincrease in the a·w term and a decrease of the filtrate flux.

The first parts of the curves in the dt/dV vs. V coordinatesare nearly linear at different disk rotation speeds (Fig. 2a)) andat different values of the pressure (Fig. 2b)). Therefore, a·w re-mains constant for the given conditions of dynamic dewater-ing (x and p). It means that at the initial stage of dynamicdewatering of the studied suspension (V < 60 cm3), the filtercake grows despite of the disk rotation. However, such cakegrowth is slower than for dewatering without disk rotation(x = 0 rpm), which explains the lower slope of dt/dV vs. Vcurves (Fig. 2a)) for x > 0.

At the late stages of dynamic dewatering, the dV/dt vs.curves deviate from linear behavior. That means that a·w isnot constant at those stages. Suspension behavior in the gapbetween the cake and rotating disk surface is not elucidatedenough. It is reasonable to suppose that both a and w can bevariable. Based on the mass balance analysis, w can be pre-sented as:

w 1

1c 1qse qs(5)

where c is the mass concentration of CaCO3 in suspension, e isthe cake porosity, and qs is the density of CaCO3.

The concentration of suspension, c, increases during dewa-tering with disk rotation. At the final stage of dynamic dewa-tering, the velocity of disk rotation may be insufficient formaintaining the layer of suspended particles over the cake. Itcan accelerate deposition of the CaCO3 particles and growingof the cake may become accelerated. On the other hand, specif-ic cake resistance, a, may also increase due to disk rotation[34].

Fig. 3 presents photos of the filter cake for dynamic dewater-ing at V ≈ 100 cm3 after removal of the retentate at differentdisk rotation speeds. The dispersant concentration wascd = 0.5 wt %. Visually, the structure and compactness ofthe cake are different at x = 300 rpm (Fig. 3a)) and atx = 2000 rpm (Fig. 3b)). According to [33], a particle at thecake surface is subjected to two main forces: the shear stress(depending on the shear rate applied to the particle) and the

drag force. When the shear force exceeds the drag force, theparticle losses contact with the cake.

At the beginning of dynamic dewatering, we observed fastgrowth of the filter cake. For instance, at chosen operation pa-rameters (x = 300 rpm, p = 0.95 bar) and different dispersantconcentrations (cd = 0–2 wt %), the filter cake nearly filled thegap between the filter membrane and the disk after only20 cm3 of filtrate recovered. With narrowing of the gap be-tween the cake surface and the disk, the shear rate was increas-ing since c

= hr/h and particles could no longer deposit on the

cake surface. If the velocity of the disk motion is high, the in-tense shear rate at the periphery erodes the filter cake (Fig. 3).

Fig. 4a) shows a drop in the filter-cake resistance with fasterrotation of the disk. More intense cake erosion (Fig. 3) may ex-plain such a drop in the cake resistance. However, surprisingly,a rotation speed of 300 rpm gives higher final cake dryness


Figure 3. Filter cake photos obtained at V ≈ 100 cm3 and differentdisk rotation speeds, (a) x = 300 rpm and (b) x = 2000 rpm. Thefiltration pressure, p, was 0.95 bar; the dispersant concentration,cd, was 0.5 wt %.

Figure 4. Resistance of the filter-cake, Rc, calculated using Eq.(2) for V = 50 cm3, versus (a) rotation speed, x, and (b) filtrationpressure, p. The dispersant concentration, cd, was 0.5 wt %. Errorbars correspond to the mean standard deviations.


(that is a larger volume of filtrate extracted) compared to2000 rpm. More compact internal structure of the cake (thus,higher a) at higher rotation speeds may account for this behav-ior. Note that resistance, Rc (= awV/S), can decrease even withan increase in a at higher rotation speed if the decrease in w athigher rotation speed is more significant. The total water re-moved from 0 to 2000 rpm (Fig. 2a)) allows one to suggest thatthe peak of suspension dryness at a given pressure may be ob-tained for a certain optimal rotating speed (x = 300 rpm).

The effect of pressure at any disk speed is shown in Fig. 4b),presenting Rc versus p, where Rc is calculated from the linearportions of curves in Fig. 2b) for V = 50 cm3. Fig. 4b) showsthat higher-pressure results in an increase in resistance, Rc, forall the disk rotation speeds tested. The higher pressure in-creases the drag force and facilitates the particle deposition.The pressure increase also results in faster draining of the filtercake and pressure variation (from 0.2 to 0.95 bar) does not in-fluence water extraction (Fig. 2b)). In order to ensure fast de-watering and high final dryness of the suspension, 300-rpm ro-tation speed (x) and 0.95 bar of pressure (p) were used infurther experiments.

3.1.2 Influence of Dispersant on the Cake Resistance

The experimentally-measured cake resistance, Rc, is plotted inFig. 5 against filtrate volume, V, for different dispersant con-centrations. It is worth noting that profiles of dt/dV vs V andRc vs V curves were similar (Fig. 2 and Fig. 5). The cake resis-tance, Rc, was increasing quickly during the first 20 cm3 of fil-trate extraction. As far as the a·w term in Eqs. (2) and (3) isapproximately constant, the dynamic dewatering was progres-sing with cake resistance proportional to V.

The cake resistance increased with the concentration of theinitially added dispersant, cd (Fig. 5). Dispersant introductioninto CaCO3 suspension may result in deflocculation of theloose flocks followed by stabilization and formation of a morecompact structure with higher resistance to flow [16, 20].

Existence of deflocculation support the size distributionfunctions (SDF) of the CaCO3 particles (Fig. 6). The disper-sant-free suspensions displayed rather broad SDF with themean diameter of a particle, dm, of 5.3 ± 0.5 lm. Addition ofthe dispersant resulted in a noticeable deflocculation, narrow-ing of SDF, and a decrease in dm (= 1.1 ± 0.1 lm). Fig. 6 showsthat the SDF of the filter cake is nearly the same as for reten-tate. At 0.5 wt % of the dispersant, a supplementary narrowingof SDF and decrease in dm in the concentrated retentate ascompared with initial suspension was observed. It may reflectthe intense additional disaggregation of CaCO3 particles in dy-namic dewatering.

3.1.3 Time of Dispersant Addition

Dewatering curves for suspensions with different concentra-tion of the dispersant, cd (0–2 wt %), are presented in Fig. 7.The arrows show the time of dispersant addition for i-dewater-ing and d-dewatering modes. At cd = 0.1 wt %, polyacrylate actsrather as a flocculant accelerating the dynamic dewatering.However, a higher content of the dispersant results in lower fil-terability at i-dewatering. The initial section of the d-dewater-ing curve in Fig. 7 at V < Vd corresponds to dewatering of thedispersant-free suspension. For cd > 0.1 wt % and delayed dis-persant addition (that is, for V > Vd; dashed lines in Fig. 7), anabrupt drop in the dewatering rate is observed. The insert inFig. 7 shows an abrupt change in the dt/dV derivative upon


Figure 5. Cake resistance, Rc, versus filtrate volume, V, at differ-ent dispersant concentrations, cd, for i-dewatering, andx = 300 rpm and p = 0.95 bar. Symbols are experimental points,solid lines are obtained from Eq. (2) using dt/dV data at filtrationarea, S = 2.4 · 10–3 m2, membrane resistance, Rm = 1.5 ±0.2 · 1011 m–1, and filtrate viscosity, gf = 1.0 mPa s, at ambienttemperature ≈ 20 °C.

Figure 6. Influence of the dispersant on particle size distributionfunction (SDF) in the initial suspension, in the filter cake, and inthe concentrated retentate. Here, d is the particle diameter. Theconcentrated suspensions and cakes were prepared by i-dewa-tering; x = 300 rpm, p = 0.95 bar, and cd = 0.5 wt %. Error barscorrespond to the mean standard deviations.


dispersant addition for d-filtration. This drop depends on thequantity of introduced dispersant. In this case, dynamic dewa-tering is similar to re-dispersion of the deposited filter cake.

3.2 Properties of Suspension, Filter Cake,and Filtrate

3.2.1 Dryness

Fig. 8 presents the dryness of (a) the final suspension, Ds,and (b) the cake, Dc, versus dispersant concentration, cd.It is worth noting that at dispersant concentrations,cd ≥ 0.5 wt %, the measured suspension dryness, Ds, was1–2 wt % higher than the average dryness, D, calculatedfrom the material balance equation, Eq. (4).

This difference in dryness may be explained by waterevaporation from the filter cell during the last step of de-watering, when the temperature is increasing from the am-bient to ∼ 50 °C. However, the measured dryness of thecake, Dc, is close to D. The dryness of the suspension, Ds,and the cake, Dc, were noticeably increasing with the in-crease of dispersant concentration, cd, from 0 to 0.5 wt %.The upper dryness limit was reached at cd = 0.5 wt %.Further dispersant additions above this limit did not im-prove the dryness (Fig. 8). The optimal doses of the disper-sant were also found earlier for the dead-end and cross-flow filtrations of the same CaCO3 suspension [16, 20].Note that d-dewatering resulted in higher values of Ds andDc than i-dewatering. Moreover, the maximum drynessvalues reached at d-dewatering were Ds = 79.6 ± 1.0 wt %and Dc = 77.1 ± 0.7 wt %. These final dryness values arehigher than previously reported in [20] for the cross-flowfiltration (Ds = 70 %) and dead-end filtration (Ds = 74 %)of the same CaCO3 suspension with the same dispersant.

3.2.2 Dispersant Losses

The residual dispersant concentration in the retentate, cd, canbe significantly lower than its initial concentration, cd, imme-diately after dispersant addition [20]. Such dispersant losses inthe filtrate may be explained by incomplete adsorption of thedispersant molecules on the surface of CaCO3 and possibledrainage of the unabsorbed dispersant with the filtrate outsidethe filter cake [35]. The remaining residual dispersant concen-tration in suspension, cd, can be estimated from the dispersantconcentration in the filtrate, cf:

cd cd1 cf mfmd (6)

where md is the mass of the dispersant added to the suspensionand mf is the mass of the filtrate.

Dependencies of cd versus cd for the i-dewatering and d-de-watering modes are presented in Fig. 9a). At low dispersantconcentrations, cd (below 0.1 wt %), the cd and cd values ap-proximately coincide, which evidences complete dispersantbinding with CaCO3 particles. At higher dispersant concentra-tions, the value of cd is lower than cd. This difference betweenthe values of cd and cd reflects dispersant losses in the filtrate,which were much lower for d-dewatering as compared to i-de-watering experiments (Fig. 9a)).

In d-dewatering experiments, the dispersant was added to amore concentrated suspension (≈ 40 wt % of CaCO3) contain-ing less water than the initial one. In this case, adsorption ofpolyacrylate molecules on the surface, A, of CaCO3 particlescan be estimated as:

A cd cf mmCaCO3 1 (7)


Figure 7. Influence of the dispersant concentration on calciumcarbonate suspension dewatering for i-dewatering (solid lines)and d-dewatering (dashed lines) modes; x = 300 rpm,p = 0.95 bar. Insert shows an abrupt change in the dt/dV deriva-tive upon dispersant addition for d-filtration.

Figure 8. Dryness of the final suspension Ds (a) and cake Dc (b) versusdispersant concentration cd for i-dewatering and d-dewatering. The filtra-tion pressure p was 0.95 bar; rotation speed x was 300 rpm. Error barscorrespond to the mean standard deviations.


For i-dewatering, the dispersant adsorption value, A,reached a maximum at cd = 0.3 wt % and then remained practi-cally constant (Fig. 9b)). For d-dewatering, dispersant additionto concentrated dispersions resulted in a higher adsorptionvalue, A. The differences in adsorption behavior observed ini-dewatering and d-dewatering experiments possibly reflect theeffect of suspension concentration on the mechanism of ad-sorption of the macromolecules on CaCO3 surface [35] andextra retention of the dispersant molecules by the filter cake ind-dewatering experiments [17].

3.2.3 Viscosity of the Final Suspensions

Fig. 10 presents viscosity, g, versus shear rate, c, for suspen-

sions obtained in i-dewatering and d-dewatering experiments(cd = 0.5 wt %), respectively. Such shear-thinning dependencieswere typical to those previously observed for concentratedCaCO3 suspensions in the presence of a dispersant [36]. An in-teresting fact is that d-dewatering allows preparation of a moreconcentrated suspension with a smaller viscosity (Insert inFig. 10). This behavior can be explained by higher residual dis-persant concentration, cd, in suspensions obtained in d-dewa-tering experiments (Fig. 9a)). In the d-dewatering experi-ments, the viscosity of the suspension passed through aminimum at the dispersant concentration, cd = 0.5 wt % (Insertin Fig. 10) even if suspension dryness was higher at the pointof minimum.

Tab. 1 compares viscosity and dryness of the final sus-pension and efficiency of dewatering for dynamic filtration(this work), crossflow filtration [20], and dead-end filtra-tion [16] techniques using CaCO3 of the same quality andthe same dispersant. According to [20], the process effi-ciency was estimated as the final mass of the concentratedsuspension obtained from the unit membrane surface dur-ing the unit time of dehydration (kg m–2s–1):

E = m/(S·t) (8)

For all the mentioned filtration techniques, the retentateviscosity was below 1 Pa s for the low shear rate of 20 s–1,which is required in industrial applications [1, 2]. How-ever, the proposed method of dynamic dewatering resultsin the highest dryness of suspension, Ds ≈ 79.6 wt %. Notethat for the highly concentrated suspensions, obtainedin d-dewatering experiments, the dispersant level ofcd ≈ 0.5 wt % can be accepted as optimal for purposes ofhigh dryness (Fig. 8a)) and small viscosity (Insert inFig. 10) at moderate dispersant losses in the filtrate(Fig. 9a)).

4 Conclusions

The technique of rotation disk dynamic filtration was usedfor dewatering and preparation of the highly concentrated(> 75 wt %) CaCO3 suspensions in the presence of a dis-persant (sodium polyacrylate). The time of dispersant

addition was an important factor influencing efficiency ofdewatering, final dryness, and fluidity of the suspensions. De-


Figure 9. (a) Residual dispersant concentration in suspension, cd, and(b) the value of dispersant adsorption on calcium carbonate, A, versusinitial dispersant concentration, cd, for the i-dewatering and d-dewateringmodes. The filtration pressure, p, was 0.95 bar; rotation speed, x, was300 rpm. Error bars correspond to the mean standard deviations.

Figure 10. Viscosity, g, versus shear rate, c, for a final suspen-

sion obtained in i-dewatering (Ds = 77.1 %) and d-dewatering(Ds = 79.6 %) experiments (cd = 0.5 wt %). Insert shows the effectof the dispersant concentration, cd, on viscosity, g, of a CaCO3

suspension in d-dewatering experiments. The dryness of the sus-pension is shown near the symbols. The filtration pressure, p,was 0.95 bar; rotation speed, x, was 300 rpm, and temperature,T, was 20 °C. Error bars correspond to the mean standard devia-tions.


watering with delayed dispersant addition (d-dewatering) gavebetter results than dewatering with initial dispersant addition(i-dewatering). The d-dewatering resulted in a higher finaldryness and smaller fluidity of suspension. The largest drynessvalues, obtained for d-dewatering, were Ds = 79.6 ± 1.0 wt %and Dc = 77.1 ± 0.7 wt %. The optimal dispersant concentra-tion, allowing attainment of the high dispersion dryness andfluidity levels at moderate dispersant losses in the filtrate, wasestimated as cd ≈ 0.5 wt %.

Acknowledgements

The authors would like to acknowledge OMYA and COATEXfor providing raw materials for this study.

Symbols use

A [wt % dispersant/wt CaCO3] adsorption ofpolyacrylate molecules onto thesurface of CaCO3 particles

C [J g–1 K–1] specific thermal capacityc [wt %] mass concentration of CaCO3 in

suspensioncd [wt % dispersant/ wt CaCO3] dispersant

concentrationcd [wt % dispersant/ wt CaCO3] residual

dispersant concentration in theretentate

cf [g g–1] dispersant concentration in thefiltrate

d [lm] particle diameterdm [lm] mean diameter of a particlesD [wt %] average dryness corresponding

to the dryness of the suspensionand cake

Dc [wt %] maximal dryness of the finalcake

Ds [wt %] maximal dryness of the finalsuspension

E [kg m–2s–1] efficiency of dewateringh [mm] gap between the disk and the

membrane surfaceho [mm] initial gap between the disk and

the membrane surface

hc [mm] thickness of the cake, ho – hm [g] mass of suspensionmd [g] mass of dispersant added to

suspensionmCaCO3 [g] total mass of calcium carbonate

in the suspensionmf [g] mass of filtratemsusp [g] mass of suspension used for

dewateringp [bar] filtration pressurer [mm] distance to the axis of rotationr0 [mm] radius of the rotating diskRc [m–1] resistance of the deposited cake

layerRm [m–1] resistance of the membraneS [m2] membrane filtration areaT [K] temperature of the suspensiont [s] time of dewateringVd [m3] volume of filtrate processed in

d-dewatering before addition ofthe dispersant

V [m3] volume of filtratew [kg m–3] mass of deposited solid per

volume of filtrate

Greek letters

a [m kg–1] specific cake resistancec

[s–1] shear ratee [–] porosity of filter cakegf [Pa s] viscosity of filtrateg [Pa s] viscosity of suspensionqf [g cm–3] density of filtrateqs [g cm–3] density of CaCO3

h [s–1] angular speeds [Pa] shear stressx [rpm] rotation speed of the disk

Abbreviations

i-dewatering dewatering with initial addition of thedispersant

d-dewatering dewatering with delayed addition of thedispersant

SDF particle size distribution function


Table 1. Viscosity and dryness of the final suspension, and filtration efficiency at dynamic fil-tration (this work), crossflow filtration [20], and dead end filtration [16].

Type of filtration Viscosity of suspension, g[Pa s–1], at c

= 20 s–1

Dryness of suspension, Ds

[wt %]Efficiency of filtration, E[kg m–2s–1]

Dynamic < 0.8 79.6 11.0 · 10–3 (p = 0.95 bar)

Crossflow [20] < 0.8 70 5.83 · 10–3 (p = 1 bar)

Dead-end [16] < 0.3 74 13.3 · 10–3 (p = 5 bar)


References

[1] J. C. Roberts, Paper Chemistry, Chapman & Hall, Glasgow1996.

[2] J. S. Reed, Principles of Ceramics Processing, John Wiley andSons, New York 1994.

[3] H. A. Barnes, J. E. Hutton, K. Walters, An introduction torheology, Elsevier, Amsterdam 1993.

[4] J. W. Goodwin, R. W. Hughes, Rheology for Chemists: An In-troduction, The Royal Society of Chemistry, Cambridge 2000.

[5] H. N. Stein, The Preparations of Dispersions in Liquids, Mar-cel Dekker, New York 1995.

[6] S. I. Conceição, S. Olhero, J. L. Velho, J. M. F. Ferreira, Cer-am. Int. 2003, 29 (4), 365.

[7] C. Geffroy et al., Revue de L’Institut Francais du Pétrole 1997,52, 183.

[8] G. Tari, J. M. F. Ferreira, Ceram. Int. 1998, 24 (7), 527.[9] T. A. Ring, Fundamentals of Ceramic Powder Processing and

Synthesis, Academic Press, New York 1996.[10] I. S. Bleakley, P. M. McGenity, C. Nutbeem, C. R. L. Golley,

EP Patent 0768344, 1997.[11] J. A. Purday, GB Patent 1463974, 1977.[12] C. W. Hansen, International Patent WO 00/39029, 1998.[13] R. J. Chamberlahm, US Patent 4026991, 1977.[14] P. M. Story, International Patent WO 90/13606, 1990.[15] M. Husson, C. Jacquemet, E. Vorobiev, French Patent FR

0209015, 2002.[16] Z. Soua, T. Mouroko-Mitoulou, E. Vorobiev, Chem. Eng. Res.

Des. 2004, 82 (1), 105.[17] E. Vorobiev, T. Mouroko-Mitoulou, Z. Soua, Colloids Surf. A:

Physicochem. Eng. Aspects 2004, 251 (1–3), 5.[18] L. H. Ding, M. Y. Jaffrin, M. Mellal, G. He, J. Membr. Sci.

2006, 276 (1–2), 232.

[19] R. Bouzerar, P. Paullier, M. Y. Jaffrin, Desalination 2003, 158(1–3), 79.

[20] J. G.-C. Trave, E. Vorobiev, A. Ould Dris, Sep. Sci. Technol.2007, 42 (1), 319.

[21] B. Ochirkhuyag et al., Chem. Eng. Sci. 2008, 63 (21), 5274.[22] M. Y. Jaffrin, J. Membr. Sci. 2008, 324 (1–2), 7.[23] R. J. Wakeman, C. J. Williams, Sep. Purif. Technol. 2002,

26 (1), 3.[24] G. He, L. H. Ding, P. Paullier, M. Y. Jaffrin, J. Membr. Sci.

2007, 300 (1–2), 63.[25] R. Bott, T. Langeloh, E. Ehrfeld, Chem. Eng. J. 2000, 80 (1–3),

245.[26] H. Rouse, Elementary Mechanics of Fluids, Dover Publica-

tions, New York 1979.[27] M. Shirato, T. Murase, M. Negawa, T. Senda, J. Chem. Eng.

Japan 1970, 3 (1), 105.[28] C. Tien, Introduction to Cake Filtration: Analyses, Experi-

ments, and Applications, Elsevier, Oxford 2006.[29] S. K. Teoh, R. B. H. Tan, D. He, C. Tien, Trans. Filt. Soc.

2001, 1 (1), 81.[30] R. J. Wakeman, E. S. Tarleton, Filtration: equipment selection,

modelling and process simulation, Elsevier, Oxford 1998.[31] K. Stamatakis, C. Tien, Chem. Eng. Sci. 1991, 46 (8), 1917.[32] A. Ould-Dris, M. Y. Jaffrin, D. Si-Hassen, Y. Neggaz,

J. Membr. Sci. 2000, 175 (2), 267.[33] R. Bouzerar, L. Ding, M. Y. Jaffrin, J. Membr. Sci. 2000,

170 (1), 127.[34] S. Ripperger, J. Altmann, Sep. Purif. Technol. 2002, 26 (1), 19.[35] R. Eriksson, J. Merta, J. B. Rosenholm, J. Coll. Interf. Sci.

2007, 313 (1), 184.[36] Z. Soua, O. Larue, E. Vorobiev, J.-L. Lanoisellé, Colloids Surf.

A: Physicochem. Eng. Aspects 2006, 274 (1–3), 1.




158

Conclusions

It was shown that highly concentrated (> 75 % wt) and flowable suspension of calcium

carbonate may be prepared by means of dynamic filtration with addition of sodium

polyacrylate. The time of dispersant addition was an important factor influencing efficiency

of filtration, final dryness, and fluidity of the suspension. Filtration with delayed addition of a

dispersant gave better results than filtration with initial dispersant addition: it resulted in

higher final dryness and better fluidity of suspension. The highest dryness of suspension,

obtained by dynamic filtration with delayed addition of dispersant, was 79.6±1.0 % wt, while

viscosity of such suspension was below 0.8 Pas (at shear rate 20 s–1). The maximal dryness

of suspension obtained by filtration with initial addition of a dispersant was 77.1 % wt. The

values of suspension dryness obtained in dynamic filtration were higher by 5–9 % than for

cross-flow filtration (70 % wt) and dead-end filtration (74 % wt) of the same calcium

carbonate suspension.

The optimal dispersant concentration in suspension, allowing attainment of the high

dryness and fluidity levels at moderate dispersant losses in the filtrate, was estimated as

≈ 0.5 % wt/wt.

III.3. Filtration of disrupted yeast suspensions

159

Paper III: “Effect of high voltage electrical discharges on filtration

properties of Saccharomyces cerevisiae yeast suspensions”

and

Paper IV: “Dead-end filtration of Saccharomyces cerevisiae yeast

suspensions: effects of high-pressure disruption, high-voltage electrical

discharges and flocculation”

Introduction

Separation of soluble proteins from bio-suspensions is an important technological

problem. Many valuable proteins are intracellular constituents of yeast cells and bacteria.

Therefore, extraction of these proteins requires damaging of the membrane and cell wall of

the host cell. The damage of cells involves physical or chemical treatment of cell suspension.

Efficiency of extraction depends on intensity of treatment of the cell suspension. Vigorous

treatment results in disruption of cell walls and complete liberation (extraction) of the target

proteins. However, vigorous treatment of cell suspension may also generate colloidal

impurities (cell debris). Since difference in the density of cell debris and solution of extracted

proteins is low and the size of the cell debris is below one micron, purification of the

extracted soluble proteins from the cell debris by conventional method of centrifugation may

be quite difficult. In this case, filtration of the disrupted cell suspension may be more efficient

tool for the purification.

However, filtration of biological suspensions may be limited by membrane fouling.

During filtration, cell debris may interact with the membrane surface, plug the pores and thus

decrease filtration rate and cause rejection of the target proteins. These processes must depend

on the colloidal properties of cell debris and its concentration in the treated suspension.

Consequently, it is necessary to find an adequate technique for disruption of cells, which will

yield minimum of cell debris and maximum of extracted proteins.

Numerous techniques have been proposed for yeast cell disruption. The mechanical

method of high-pressure homogenisation is most appropriate for industrial-scale disruption.

Application of this method results in considerable breakage of yeast cells and high recovery

of intracellular proteins. However, it generates a large quantity of cell debris, which

complicates the downstream purification. Other classical methods of cell disruption are either

less effective, or expensive, or can not be realized in an industrial scale. This encourages

seeking for new methods of yeast cell disruption that will result in lower concentration of cell


160

debris and better filtration of the disrupted suspension. The method of high voltage electric

discharges seems to be a promising solution of this problem.

Summary

The aims of the Paper III are:

(1) to study the influence of high voltage electric discharge (HVED) treatment of

Saccharomyces cerevisiae yeast suspension on disruption of yeast cells and extraction

of intracellular components;

(2) to study the influence of the intensity of HVED treatment on filtration of disrupted

suspensions and separation of cell debris;

(3) to find the mechanism of filtration (type of the membrane fouling) of the disrupted

suspensions; and

(4) to study the possibility of acceleration of the filtration of extracted bio-products by

means of flocculation of the disrupted suspension.

The aim of the Paper IV is to compare the efficiency of HVED with classical method of

cell disruption (high pressure homogenization, HPH).

With this aim, the diluted (1 % wt/wt) aqueous suspension of yeast cells was treated by

HVED with mean electric field strength of 40 kV/cm. Various number (N = 1 – 450) of

successive discharges was applied to the suspension in order to vary the intensity of the

treatment. Homogenisation was carried out at the pressure of 1000 bar with different number

of successive passes of suspension through the homogenizer (up to 20). The efficiency of the

treatment and cell disruption was characterised using conductivity disintegration index Z

(Z increases from 0 to 1 during the treatment).

Efficiency of the cell disruption and extraction of bio-products was characterised by

measurements of turbidity of disrupted suspensions, UV-spectroscopy of supernatants,

electronic microscopy and granulometry analysis; the results obtained for HPH and HVED

treated suspensions were compared.

Dead-end filtration of HPH and HVED-disrupted suspensions was carried out and the

influence of disintegration degree Z and disruption method on filtration kinetics was analysed.

Since the disrupted yeast particles bear the negative charge, flocculation of the disrupted

suspension was carried out using cationic polymer poly(diallyldimethylammonium chloride)

as a flocculating agent and the influence of flocculant concentration on filtration rate and

filtrate quality was analysed.

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Journal of Membrane Science 346 (2010) 288–295


Journal of Membrane Science

journa l homepage: www.e lsev ier .com/ locate /memsci

ffect of high voltage electrical discharges on filtration properties ofaccharomyces cerevisiae yeast suspensions

. Loginova,b, N. Lebovkaa,b,∗, O. Laruea, M. Shynkaryka,b, M. Nonusa,.-L. Lanoiselléa, E. Vorobieva

Unité Transformations Intégrées de la Matière Renouvelable, Université de Technologie de Compiègne, Centre de Recherche de Royallieu,.P. 20529-60205 Compiègne Cedex, FranceInstitute of Biocolloidal Chemistry named after F. D. Ovcharenko, NAS of Ukraine, 42, blvr. Vernadskogo, Kyiv 03142, Ukraine

r t i c l e i n f o

rticle history:eceived 5 March 2009eceived in revised form 2 August 2009ccepted 23 September 2009vailable online 1 October 2009

eywords:accharomyces cerevisiae yeast suspension

a b s t r a c t

In the present work the dead-end filtration of Saccharomyces cerevisiae yeast suspensions disrupted byhigh voltage electrical discharges (HVED treatment) was investigated. The efficiency of disruption wasevaluated using conductivity disintegration index of suspension Z (Z = 0–1) and absorbance spectra ofsupernatant solutions. The electronic microscopy study, particle sizing and measuring of -potential andturbidity were used to characterize variation of the colloidal properties of a yeast suspension duringdisruption. The HVED treatment was found to cause an effective disruption of yeast cells and extractionof intracellular proteins and other bio-products. The study of filtration revealed suspension filterability

isruptionigh voltage electrical dischargesio-products recoveryead-end filtrationlocculation

deterioration after disruption. It was shown that filtration behaviour of the HVED-processed suspen-sions was governed by cake formation, the filtrate volume decreased and the cake resistance increasedwith increase of Z. For high levels of disruption (Z > 0.99), filtration was governed by membrane foul-ing. The optimal dosage of polycationic flocculant promoted the formation of flocks and acceleratedfiltration. However, selected flocculant (poly(diallyldimethylammonium chloride)) provoked binding ofbio-product and was inappropriate for using as an agent enhancing extraction from disrupted yeast cells.

. Introduction

The interior of the yeast cells (Saccharomyces cerevisiae) isrich source of bio-products (proteins, cytoplasmic enzymes,

olysaccharides, etc.), which are valuable for different applicationsn biotechnology, brewing and food industry. Extraction of bio-roducts from cells usually involves disruption of the cell wallsliberation of bio-products) and separation of extract from theells, cell debris and from other insoluble colloidal particles. Effec-iveness of disruption technique depends on the yield of desiredio-products in the disrupted yeast suspension and possibility ofurther extract purification from the solid phase.

Numerous techniques have been proposed for cell disruption
1,2]. The mechanical method of high-pressure homogenisations most appropriate for industrial-scale disruption. This methods non-specific and results in considerable breakage of cells andigh recovery of bio-products. However, its final product contains
∗ Corresponding author at: Institute of Biocolloidal Chemistry named after F. D.vcharenko, NAS of Ukraine, 42, blvr. Vernadskogo, Kyiv 03142, Ukraine.el.: +380 44 424 0378; fax: +380 44 424 8078.

E-mail addresses: [email protected], [email protected] (N. Lebovka).

376-7388/$ – see front matter © 2009 Elsevier B.V. All rights reserved.oi:10.1016/j.memsci.2009.09.048

© 2009 Elsevier B.V. All rights reserved.

large quantity of cell debris, which complicates the downstreamprocesses of purification.

Treatment of a yeast suspension with high-intensity pulsedelectric field was proposed as promising for the extraction ofproteins [3]. The high electric fields of microsecond duration(typically, 5–10 kV/cm) can cause electroporation of membranes,which seems to enhance release of the intracellular bio-products.Electroporation has some advantages as compared with thehomogenisation: it does not require formation of fine cell debrisand any significant temperature elevation. Nevertheless, effective-ness of pulsed electric field method for the extraction of proteins isstill under discussion [4,5].

Alterative electrical method allowing to enhance extraction ofbio-products from cells is based on the utilization of high voltageelectrical discharges (HVED). Underwater HVED of microsecondduration was shown to create shock waves (pulsed high pressure)and powerful light radiation [6]. These phenomena may result inconsiderable disruption and homogenisation of colloidal particles
in water suspensions [7]. HVED treatment has found applicationfor inactivation of microorganisms [8] and extraction of solublematerials from the cellular tissues [9–11]. HVED seems to have noeffect on the quality of proteins extracted by this method [10,12].It was shown recently [6] that HVED treatment of ˇ-lactoglobulin
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dx.doi.org/10.1016/j.memsci.2009.09.048

mbrane Science 346 (2010) 288–295 289

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M. Loginov et al. / Journal of Me

olutions provokes secondary and tertiary changes of the proteintructure, however, protein aggregation was not observed. Thus,VED treatment of an aqueous bio-suspension at 40–50 kV/cm canrovoke a noticeable mechanical damage of cells, disintegrationf cell walls and membrane rupture; it can induce homogeni-ation of cells or, on the contrary, their aggregation. Recently,pplication of the combined HVED-mechanical homogenisation forisruption of yeast suspension was reported [5]. It was shown thatven small disintegration initially induced by HVED pre-treatmentesults in a noticeable acceleration of homogenisation disruptioninetics and high yield of extracted proteins, and HVED applica-ion seems to have no undesirable effect on the quality of proteinxtracts.

The extract can be purified by filtration, which is widely used inood industry and biotechnology. For instance, the dead-end filtra-ion is implemented for beer and wine clarification by removal ofeast cells and colloid particles. Cross-flow microfiltration, filtra-ion with rotating disks, rotating and vibrating membranes, wereroposed for bio-separation processes and in dairy industry forurification of fermented beverages [13–19]. Application of filtra-ion for the treatment of bio-suspensions is hindered by membraneouling and formation of a cake layer with high compressibility16,18,20–22]. Usually, it is assumed that the fine-sized colloidalraction of filtered suspension is responsible for membrane foulingf bio-suspensions (e.g., cell debris or lysates of dead cells, pro-ein aggregates, polyphenoles). Colloidal particles get entrappednto the membrane pore volume and plug the pores, thus increas-ng hydraulic resistance of the membrane. Fouling substantiallyecreases filtration flux rate and transmission of bio-moleculeshrough the membrane. Various mechanisms of filtration, includingake formation and models of standard, complete and intermedi-te pore blocking, were proposed for description of the membraneouling [23,24].

Conventional way to enhance filtration and to reduce the mem-rane fouling is to increase the average particle size by flocculation.ationic polymers had been proposed as flocculants for undis-upted yeast suspensions [25–28]. It was shown that flocculation ofeast cells prior to microfiltration leads to increase in the permeateux, and the fouling rate declines with increase of the average flocsize [26]. Flocculation of the yeast cells by aluminium salts insteadf cationic polymers was found to increase the flux rate duringhe cross-flow filtration through zirconia and alumina membranes29]. Important role of electrostatic interactions between parti-les and filtration membranes and importance of the membraneaterial choice were demonstrated in this work. Karim et al. [30]

howed that polymeric flocculants could also enhance microfiltra-ion of disrupted cells (homogenised lysate of Escherichia coli). Glatznd co-workers [31] recently showed that cationic polyelectrolytesmprove permeate flux and protein transmission in a cross-flownd dead-end microfiltration of an industrial suspension of Bacillusubtilis cells.

Though numerous works were published in the field of bio-eparation, most of them describe filtration of suspensions of theashed yeast cells or filtration of model two-component suspen-

ions (undisrupted yeast cells in a protein solution) [32–34]. Onlyew authors have paid their attention to filtration of complex bio-ogical suspensions containing yeast cells, cell debris, salts andio-molecules extracted from the cell interior [30,31,35].

In present work the effect of HVED disruption on the dead-nd filtration of S. cerevisiae yeast suspensions was investigated.he HVED-treated suspensions contain disrupted and undisrupted
ells, cell debris, salts and extracted bio-molecules. Influence ofhe disruption index of yeasts Z on extraction of proteins, colloidalroperties and filterability of the yeast cell suspension was inves-igated. A polycationic flocculant (poly(diallyldimethylammoniumhloride)) was used for flocculation of disrupted yeast suspensions,
Fig. 1. Scheme of the HVED treatment of yeast suspension.

and possibility of using flocculation for facilitation of recovery of theproteins was discussed.

2. Materials and methods

2.1. Yeast suspension

Wine yeast S. cerevisiae (bayanus) cells (Vitilevure DV10, Sta-tion Oenotechnique de Champagne, Epernay, France) were usedthroughout this study. Suspensions of 1% (w/w) were prepared bymixing the dry yeast cells and distilled water by magnetic stir-rer. The yeast cells were swelling in an aqueous medium at roomtemperature. The swelling process was monitored by means ofconductivity measurement. After, approx., 30 min of mixing theconductivity reached a stable value of 130 ± 10 S/cm, and theswelling was considered to be completed. Suspensions were gentlymixed before HVED treatment.

2.2. HVED treatment

Experimental HVED apparatus (Tomsk Polytechnic University,Tomsk, Russia) consisted of a pulsed high voltage power supply anda laboratory treatment chamber with an electrode of a needle-plategeometry (Fig. 1). A stainless steel needle of 10 mm in diameterwas used. The grounded plate electrode was a stainless disk of25 mm in diameter. A positive pulse voltage was applied to theneedle electrode. The high voltage pulse generator provided 40 kVto 10 kA discharges in a one-liter chamber. The distance betweenthe electrodes was 10 mm, and the peak pulse voltage was 40 kV. Itcorresponds to the mean electric field strength of 40 kV/cm. Theelectrical discharges were generated by electrical breakdown inan aqueous yeast suspension. Energy was stored in a set of low-inductance capacitors, which were charged by a high voltage powersupply. Damped oscillations with the total duration of ≈20 s werethus obtained, though the effective pulse duration correspondedto few microseconds, ti ≈ 1–2 s [12]. The treatment chamberwas initially filled with 350 ml of yeast suspension (1%, w/w).HVED treatment lied in application of the NHVED successive pulses(NHVED = 1–450). Electrical discharges were applied with the pulserepetition rate of 0.5 Hz (tt = 2 s, Fig. 1). Suspension characteris-tics were measured between successive applications of the HVEDpulses. The initial temperature was 25 C and the temperature ele-vation resulting from the HVED treatment was less than 5 C.

2.3. Flocculation

In some experiments, the aggregation of yeasts was regulated bythe addition of cationic flocculant poly(diallyldimethylammoniumchloride) (ALDRICH, typical Mw = 400 000–500 000).

2 mbrane Science 346 (2010) 288–295

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sntfi2Swtyt2afiw

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90 M. Loginov et al. / Journal of Me

Appropriate amount of 0.4% (w/w) flocculant solution wasdded to a beaker with 250 ml of 1% (w/w) undisrupted orVED-treated yeast suspension. The amount of added flocculant

olution depended on the desired final polymer concentration= 0–0.04 wt.% polymer/wt.% yeast. Then beaker with yeast sus-ension was 10 times turned upside-down and leaved in rest formin for careful mixing of suspension and flocculant.

.4. Filtration

The unstirred dead-end filtration cell was a vertical stainlessteel cylinder (inner diameter 5.5 cm and total volume 300 ml) con-ected with the pressurized air source by means of pressurized airank. Filtration membrane was made from Fisherbrand qualitativelter paper (which is a depth filter with a particle retention level.5 m) and polypropylene filter cloth 25302 AN (pore size 25 m,EFAR FYLTIS, France) was used as a filter support. Though filtersith smaller pore size are typically used for purification of proteins,

he pore size of material used in this study was small enough foreast cell suspension and could be utilized, e.g., at the first step ofhe membrane separation process [36]. The membrane surface was.4 × 10−3 m2. All filtrations were carried out at room temperaturend at constant pressure 1 bar. A new membrane was used for eachltration. Filtration was started immediately after the filter-cellas poured with 200 ml of freshly treated yeast suspension.

The permeate was collected in a vessel placed on electronicalances and the permeate weight m was recorded every 1 s byomputer software. The permeate weight m was recalculated intoermeate (filtrate) volume V as V = m/, where is the filtrate den-ity. The filtrate flux J was calculated by means of mathematicaloftware Table Curve 2D (Jandel Scientific) as follows

= dV

dt · S(1)

here t is the filtration time, V is the filtrate volume, S is the mem-rane surface area.

.5. Analysis instruments

The electrical conductivity of suspensions was measured at5 C using a conductivity meter InoLab pH/cond Level 1 (WTW,eilheim, Germany) with conductivity probe WTW Tetra Con

25. The size distributions of aggregates in suspensions wereecorded using a laser diffraction instrument (Mastersizer X 6618,alvern Instruments GmbH, UK). During the measurement, the

articles were kept in suspension by means of a small mixer.he optical system allowed the detection of particles sized within–600 m. The particle size distribution was calculated by the orig-

nal Malvern software. High-resolution environmental scanninglectron microscopy (ESEM) images were obtained using a XL30SEM-FEG instrument (Phillips International, Inc., WA, USA) oper-ting at 15 kV voltage and 3.6 Torr pressure, at room temperature.he special “WET” chamber mode, allowing observation of moistuspensions in their natural state, was applied.

Turbidity and UV absorption spectra of the treated suspensionsnd filtrate samples where measured in order to estimate contentf cell debris and concentration of soluble bio-products. Followinghe HVED treatment, a 10 ml sample of suspension was centrifuged0 min at 4000 g, and the supernatant was collected. Turbidityf the supernatant was measured by Ratio/XR TurbidimeterHach, Loveland, USA). Filtrate samples were taken each 100 s of
ltration. Turbidity of filtrate samples f were measured withoutentrifugation. Prior to UV absorption measurements both suspen-ions and filtrate samples were separated from insoluble colloidalarticles by means of long-continued centrifugation (40 min at000 g). UV absorption spectrum of the tenfold diluted supernatant
Fig. 2. Conductivity disintegration index of yeasts Z versus number of HVED pulsesat E = 40 kV/cm.

was measured by UV-spectrophotometer Biochrom Libra S32. Thewavelength range was within 200–350 nm (with the precision of±1 nm). The path length of the SUPRASIL quartz cuvette was 10 mm(Hellma, Müllheim, Germany).

All the experiments were repeated, at least, three times. Themean values and standard deviations were calculated.


3.1. Disruption of yeasts by HVED treatment

In order to estimate efficiency of cell disruption, electricalconductivity of suspension was measured, and the conductivity dis-integration index of yeasts Z was determined from the followingexpression [37,38]:

Z = − i

max − i(2)

where is the electrical conductivity of suspension after treatment,i is the initial electrical conductivity of suspension before treat-ment and max is the electrical conductivity of suspension withmaximum of disrupted cells. The value of max was estimated bymeans of extrapolation as a value of conductivity for suspensionafter 450–500 successive pulses. Eq. (2) gives Z = 0 for an intactsystem and Z = 1 for a maximally disintegrated suspension.

Evolution of Z during the HVED treatment of a yeast suspensionis presented in Fig. 2.

Increase of Z during the treatment is related to release of ionicintracellular components from the damaged cells. It is proportionalto degree of disruption [38]. For HVED method of treatment, Zincreases gradually with the number of pulses and attains maximallevel after 400–450 pulses (Fig. 2). As in case of yeast homogeni-sation [1], continuous HVED treatment is required for completedisintegration of cells and extraction of their content. However, theincremental disintegration by additional passes may be economi-cally unreasonable.

Various experiments were carried out to characterize alterationof yeasts during disruption of their cells. Evolution of particle size
distribution is shown in Fig. 3. The particle size distribution functionof the untreated yeast suspension has one broad peak with maxi-mum at 4.3 ± 0.2 m. The content of fine particles with d < 2.5 mis less than 10%. Disruption of cells in a yeast suspension results indecrease of the average particle size (up to 3.7 ± 0.2 m for Z = 0.99);

M. Loginov et al. / Journal of Membrane Science 346 (2010) 288–295 291

Fcd

tiidaaf(5

asfi

usdttndTn

cad

3

fii0fitt

arouses a largest interest. Unlike the other suspensions, its filtrationcurve cannot be fitted by equation of cake formation (3). For thissuspension, fast initial decrease of the filtrate flux is followed by theregion of a relatively stationary filtration (Fig. 6a). Such dependenceis typical when filtration is complicated by membrane fouling. It

ig. 3. Particle size distribution function and ESEM images of untreated (Z = 0) andompletely disrupted (Z = 0.99) yeast suspensions. Error bars correspond to standardeviations.

his evidences disaggregation and damage of cells. Triple increasen the content of fine particles (∼28% of particles with d < 2.5 m)s associated with formation of cell debris. Broadening of the sizeistribution function after HVED suggests that aggregation, as wells homogenisation, of particles occurs during the treatment. HVEDlso results in a noticeable broadening of -potential distributionunction, though an average value of -potential remains constant:= −18 ± 1 mV for untreated (Z = 0) and −18 ± 4 mV for disrupted

Z = 0.99) yeast. The pH of suspensions changes from 4.9 ± 0.1 to.4 ± 0.2 during the disruption.

Insert in Fig. 3 shows the ESEM images of yeast cells beforend after the treatment. Prior to disruption the yeast cells arepheroids with a smooth surface. HVED strongly damage their sur-ace; disrupted cells are covered with a demi-translucent layer ofntracellular components.

In order to estimate efficiency of extraction of the high molec-lar weight compounds, absorbance spectra of the supernatantolutions of treated yeast suspensions were measured. In accor-ance with the literature data, the peak observed at the wavelengthmax, 1 ≈ 210–220 nm corresponds to absorption by bonds of pep-ides and proteins, which are the main intracellular constituents ofhe S. cerevisiae, and peak at max, 2 ≈ 260–270 nm corresponds toucleic acids [39] (Fig. 4). Absorbance gradually increased with Zuring the HVED treatment. It reflected extraction of bio-products.he absorbance level maximum was observed in suspension super-atants with Z = 0.99.

Increase in turbidity of supernatant solution with Z (Fig. 5)onfirms both gradual formation of fine-sized nonsetting cell debrisnd release of high molecular weight proteins during the HVEDisruption of yeast cells in suspensions.

.2. Filtration of disrupted yeast suspensions

Filtrate flux was calculated by means of Eq. (1). Evolution of theltration during the HVED treatment of yeast suspensions is shown

n Fig. 6. Filtrate flux gradually decreases with increase of Z from
to 0.99. In Fig. 6b, filtration data are presented in conventional
ltration coordinates t/V versus V [40]. This coordinates allow to fithe experimental filtration curves for suspensions with low disin-egration indexes and initial segment of the curve for suspension

Fig. 4. UV absorbance of supernatant solutions A as a function of Z. On insert: typicalabsorbance spectrum of extracted bio-products (supernatant for suspension withZ = 0.99). Error bars correspond to standard deviations.

with Z = 0.7 by linear equation

t

V= k1V + k2 (3)

where k1 and k2 are the slope and intercept, respectively. Accordingto Ruth–Carman’s classical cake formation model, k1 is directly pro-portional to specific cake resistance [40]. Hence, gradual increaseof the slope with Z is related to increase of specific cake resistanceafter treatment. Increase of the cake’s resistance is associated withaforementioned disaggregation and damage of cells and formationof cell debris. It results in more dense cake structure with narrowpores and high compressibility.

Since disrupted yeast suspension with Z = 0.99 contains max-imum of extracted bio-products (Fig. 4), its filtration behaviour

Fig. 5. Turbidity of supernatant solution as a function of Z. Error bars correspondto standard deviations.

292 M. Loginov et al. / Journal of Membrane Science 346 (2010) 288–295

FfuE

idsfsoc

wtiotrHsficZmfrn

filtof centrifugated filtrate and feed suspension, respectively. It is seenfrom Fig. 8 that turbidity of filtrate f steeply decreased duringthe filtration for any disintegration index of suspension. Therefore,regardless of the reason (either internal fouling or cake forma-

ig. 6. Experimental filtration curves of the HVED-treated yeast suspensions as aunction of Z: (a) filtrate flux J versus time; (b) ratio of filtration time and filtrate vol-me t/V versus filtrate volume V. Concentration of yeast suspension was 1% (w/w).rror bars correspond to standard deviations.

s generally accepted that the mechanism of filtration depends oniameter of particles and size of membrane pores. Filtration of auspension consisting of only large particles is governed by cakeormation. Appearance of relatively small particles in the suspen-ion may switch its filtration mechanism to the fouling. Appearancef fouling can be evidenced by analysis of initial regions of filtrationurves using equation [23,24,40]

d2t

dV2= k

(dt

dV

)n

(4)

here k and n are constants. The exponent n characterizes fil-ration mechanism: n = 0 for cake formation, n = 1, 1.5 and 2 forntermediate, standard and complete pore blocking mechanismsf fouling, respectively. As suggested by Eq. (4), plotting of a fil-ration curve as log(d2t/dV2) versus log(dt/dV) must yield a linearelationship with a slope equal to n. Re-plotted filtration curves ofVED-disrupted yeast suspensions are presented in Fig. 7. One can

ee that plots are linear at small dt/dV, which correspond to shortltration times. For suspensions with low disintegration indexes,alculated values of the slope are close to zero: n = 0.07 ± 0.01 for
= 0, n = 0.17 ± 0.01 for Z = 0.2 and n = 0.03 ± 0.01 for Z = 0.7. It onceore suggests cake formation as the main filtration mechanism
or the moderately treated yeast suspensions. For completely dis-upted suspension with Z = 0.99, linear fitting gives a larger value= 0.71 ± 0.01. This value does not refer exactly to one of the classic

Fig. 7. Filtrate flux analysis for suspensions with different disintegration indices Z.

models of fouling [24]. However, this result is consistent with theprevious studies [41,42], which indicates inequality of the experi-mentally observed values of n to 1, 1.5 or 2. Usually, combinationof models is required for adequate description of filtration curvesfor a complex suspension and a membrane with non-ideal poregeometry [43]. As it is shown in [44], the membrane pore geometry(circular pores, slotted pores) may be an important factor influenc-ing the yeast cell fouling and the value of the exponent n duringmicrofiltration. For the yeast suspension with Z = 0.99, increasein content of the cell debris and decrease in the average particlediameter after HVED disruption results in complication of filtrationbehaviour. This behaviour corresponds to transition between cakeformation (n = 0) and internal fouling (n = 1) mechanisms. Uncom-mon value for the exponent (n = 0.71 ± 0.01) may be related withcomplex pore geometry of the fibre filter used in this work.

To examine effect of fouling on separation performance turbid-ity f and bio-products transmission T in filtrate were measured(Fig. 8). Transmission of extracted bio-products in filtrate was cal-culated by equation

T (%) = Afilt

A× 100 (5)

where A and A are UV absorbance (at the wavelength = 210 nm)

Fig. 8. Variation of bio-products transmission T and filtrate turbidity f with timeof filtration.

mbrane Science 346 (2010) 288–295 293

tdlw

tdtod

3s

osycufotwlytofiecotbcaph[Tcar

pp[ppttfrmodfi

fTtd(t

a

Fig. 9. Particle size distribution function versus flocculant concentration C in HVED-disrupted yeast suspensions (Z = 0.99). Error bars correspond to standard deviations.


ion) membrane fouling enhanced purification of extract from cellebris. However, fouled membranes rejected only insoluble col-

oidal impurities, transmission of soluble bio-products in filtrateas close to 100%.

It is important that HVED treatment appreciably impairs filtra-ion of yeast suspensions. It is seen from Fig. 6a that completeisruption of yeast cells 15 times decreases the filtrate flux (for= 600 s when flux is relatively stationary). Therefore, objective ofur further study deals with improvement of filterability of theisrupted suspensions.

.3. Influence of flocculation on filtration of disrupted yeastuspensions

It was found that decrease of the particle size and appearancef a fine-sized cell debris during disruption of a yeast suspen-ion negatively affects its filtration. So, experiments with disruptedeast suspensions flocculated prior to filtration were carried out. Aationic polymer (poly(diallyldimethylammonium chloride)) wassed for flocculation of HVED-treated suspensions, since it wasound to be effective for flocculation of cell debris and purificationf bio-products [30,31]. Influence of the polymer concentration onhe content of colloidal fraction in a flocculated yeast suspensionas assessed by measuring of supernatant turbidity after floccu-

ation. The chosen polymer was an effective flocculant for disruptedeasts and addition of this polymer resulted in a tenfold decrease ofurbidity . The positively charged polymer molecules easily adsorbn the negatively charged cells and cell debris and aggregation ofne particles into flocks due to polymer bridging is observed. Therexists an optimal dose of polymer, which minimizes turbidity afterentrifugation Copt = 0.012 wt.% polymer/wt.% yeast. It implies anptimal coverage of the cell surface with polymer, high concen-ration of polymer tails and maximum probability of interparticleridging. The surface coverage decreases with increase of the spe-ific surface and the number of particles (content of cell debris)t a given adsorbate concentration. Therefore, the optimal dose ofolymer observed in this study for suspensions with Z = 0.99 wasigher than Copt = 0.003–0.004%, which was previously reported in25,27] for cationic polymers and undisrupted yeast suspension.he supernatant turbidity increases when the level of added floc-ulant exceeds the optimal dose. In this case, the yeast particlesdsorb an excess of polymer and become re-stabilized due to chargeeversing or steric effect.

The optimal filtration of a flocculated or disrupted yeast sus-ension requires low content of the fine particles, high averagearticle size and narrow particle size distribution function (SDF)45,46]. The shapes of SDF for disrupted yeast suspensions in theresence of flocculant additions are presented in Fig. 9. Addition ofolymer increases the average particle size and decreases the con-ent of cell debris with d < 2.5 m. The optimal polymer dose leadso formation of flocks with maximum average diameter of 57 mor HVED-disrupted suspensions. The SDF in a flocculated dis-upted yeast suspension containing the optimal polymer dose areuch broader than in suspensions before flocculation. Flocculant

ver-dosage results in considerable broadening of the particle sizeistribution function and increase of the fraction of re-stabilizedne particles.

Filtrate flux dependence on the time and dose of polymer usedor flocculation of disrupted yeast suspension is presented in Fig. 10.he enhanced flocculation resulted in increase of the yeasts filtra-ion efficiency. The flux rate was maximal at the optimal polymer
ose C = 0.012%, while over-dosage of polymer impaired the fluxFig. 10a). This accentuates important role of the particle size dis-ribution in filterabilty of a yeast suspension.
Filtration curves re-plotted in the Ruth–Carman’s coordinatesre presented in Fig. 10b. Deviation of the curves from linearity

Fig. 10. Influence of flocculation on filtration curves of HVED-disrupted yeast sus-pensions (Z = 0.99): (a) filtrate flux J versus time; (b) ratio of filtration time and filtratevolume t/V versus filtrate volume V. Experimental curves. Error bars correspond tostandard deviations.

294 M. Loginov et al. / Journal of Membran

Ftc

rfc

tf(opHesirIp(oap

e

Fsb

ig. 11. Variation of filtrate flux Js (at 600 s of filtration) with flocculant concen-ration C in disrupted yeast suspensions (Z = 0.99). Experimental curves. Error barsorrespond to standard deviations.

eflects settling of the flocculated particles on the membrane sur-ace. Linear sections of curves correspond to filtration governed byake formation.

Comparison of filtrate fluxes at different polymer concentra-ions shows that optimal flocculation accelerates extract separationrom HVED-treated cells and cell debris, approximately, by 15 timesFig. 11). This result is consistent with the recently reported datan filtration of microbial suspensions flocculated with cationicolymers [30,31]. However, it was found that flocculation of aVED-disrupted yeast suspension also reduced the quality ofxtract. Fig. 12 presents the absorbance spectra of supernatantolutions for disrupted yeast suspensions (Z = 0.99) without, andn the presence of, flocculant. The optimal polymer dose additionesults in substantial decrease of absorbance of the extract solution.t reflects decrease in concentration of proteins and other bio-roducts. It can be assumed that selected polycationic flocculantpoly(diallyldimethylammonium chloride)) enhances flocculation
f bio-molecules or provokes their bridging to the surface of cellsnd cell debris. It is an undesirable phenomenon, because bio-roducts remained bound in a sediment or in a filter-cake.
Since cationic polymer addition can decrease concentration ofxtracted bio-products, addition of undisrupted yeast cells could

ig. 12. Influence of optimal flocculant dose on absorbance spectra of supernatantolution for HVED-disrupted yeast suspensions (Z = 0.99). Experimental curves. Errorars correspond to standard deviations.

[

[

e Science 346 (2010) 288–295

be suggested for separation of the extract from cell debris. In[22,32–34], utilization of undisrupted yeast cells instead of poly-meric flocculant was proposed in order to reduce the membranefouling during filtration of protein solutions. Formation of a yeastcake on the membrane surface either during, or before, the proteinfiltration resulted in significant reduction of microfiltration mem-brane fouling by proteins. The protein transmission was nearly100% and the filtrate flux rate was significantly higher in the pres-ence of the yeast cells. In order to maximise the permeate flux, theamount of undisrupted cells in the prefilter is to be optimised. Acalculation accounting for the presence of large (yeast cells) andsmall (protein aggregates) particles in suspension may be used forthis optimisation [33].

4. Conclusions

The HVED treatment of S. cerevisiae yeast suspensions wasfound to cause an effective disruption of yeast cells and extrac-tion of intracellular proteins and other bio-products. Disruptionprocess was accompanied by disintegration of cells and forma-tion of a fine-sized cell debris, which causes membrane foulingand impairs filterability of disrupted suspensions. Flocculation ofa disrupted suspension with optimal dose of cationic polymer(poly(diallyldimethylammonium chloride)) promoted formation offlocks and accelerated filtration, but reduced concentration of bio-products in the filtrate.

In this case, utilization of undisrupted yeast cells can be effec-tive for enhancement of the protein solution filtration [33]. Furtherwork is required in future for selection of suitable flocculants withsmall binding and high filtration efficiency, and appropriate com-position of the bio-suspension and degree of its destruction Z.

Acknowledgements

The authors would like to acknowledge the Sofrolab (StationOenotechnique de Champagne, Epernay, France) for its financialand material support and the society GEA Niro Soavi France forthe kind supply of high-pressure homogenizer NS1001L-PANDA2K. The authors thank Dr. N.S. Pivovarova for her help with themanuscript preparation.

References

[1] J. Geciova, D. Bury, P. Jelen, Methods for disruption of microbial cells for poten-tial use in the dairy industry—a review, Int. Dairy J. 12 (2002) 541–553.

[2] Y. Chisiti, M. Moo-Young, Disruption of microbial cells for intracellular prod-ucts, Enzyme Microb. Technol. 8 (1986) 194–204.

[3] V. Ganeva, B. Galutzov, Electropulsation as an alternative method for proteinextraction of from yeast, FEMS Lett. 174 (1999) 279–284.

[4] V. Ganeva, B. Galutzov, J. Teissi, High yield electroextraction of proteins fromyeast by a flow process, Anal. Biochem. 315 (2003) 77–84.

[5] M.V. Shynkaryk, N.I. Lebovka, J.-L. Lanoisellé, M. Nonus, C. Bedel-Clotour, E.Vorobiev, Electrically-assisted extraction of bio-products using high pressuredisruption of yeast cells (Saccharomyces cerevisiae), J. Food Eng. 92 (2009)189–195.

[6] M. Kimeldorf, S. Gleizer, Ya.E. Krasik, J. Felsteiner, V. Brumfeld, H. Zuck-erman, Effect of underwater high-current discharge on the properties oflow-concentration -lactoglobulin solutions, Innovative Food Sci. Emerg. Tech-nol. 4 (2003) 151–159.

[7] M. Mikula, J. Panak, V. Dvonka, The destruction effect of a pulse discharge inwater suspensions, Plasma Sources Sci. Technol. 6 (1997) 179–184.

[8] H. Zuckerman, Ya.E. Krasik, J. Felsteiner, Inactivation of microorganisms usingpulsed high-current underwater discharges, Innovative Food Sci. Emerg. Tech-nol. 3 (2002) 329–339.

[9] C. Gros, J.-L. Lanoisellé, E. Vorobiev, Towards an alternative extraction processfor linseed oil, Trans. Inst. Chem. Eng. 81 (2003) 1059–1065.

10] L.I. Vishkvaztzev, B.I. Kuretz, G.L. Lobanova, G.P. Filatov, A.V. Barskaya, Use
of electrical discharges for the treatment of soya beans (in Russian), VestnikRossiyskoy Akademii Selskohozyaistvennih Nauk (in Russian) 6 (1998) 71–72.
11] A.V. Barskaya, B.I. Kuretz, G.L. Lobanova, Extraction of water soluble mattersfrom vegetative raw material by electrical pulsed discharges, in: Proceedingsof the 1st International Congress on Radiation Physics, High Current Electronicsand Modification of Materials, Tomsk, Russia, 2000, pp. 533–535.

mbran

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[


12] C. Gros, Extraction aqueuse et athermique de l’huile de lin assistee pardecharges electriques de haute tension, in: These presentee pour l’obtentiondu grade de Docteur de l’UTC, 2005.

13] L. Fillaudeau, B. Boissier, A. Moreau, P. Blanpain-avet, S. Ermolaev, N. Jitariouk,A. Gourdon, Investigation of rotating and vibrating filtration for clarification ofrough beer, J. Food Eng. 80 (2007) 206–217.

14] M.Y. Jaffrin, Dynamic shear-enhanced membrane filtration: a review of rotatingdisks, rotating membranes and vibrating systems, J. Membr. Sci. 324 (2008)7–25.

15] Q. Gan, J.A. Howell, R.W. Field, R. England, M.R. Bird, C.L. O’Shaughnessy,M.T. MeKechinie, Beer clarification by microfiltration-product quality controland fractionation of particles and macromolecules, J. Membr. Sci. 194 (2001)185–196.

16] E. Darnon, L. Lafitte, M.P. Belleville, G.M. Rios, A global approach of ultrafiltra-tion of complex biological solutions, Sep. Purif. Technol. 26 (2002) 283–293.

17] P. Czekaj, F. López, C. Güell, Membrane fouling during microfiltration of fer-mented beverages, J. Membr. Sci. 166 (2000) 199–212.

18] S.P. Beier, G. Jonsson, Separation of enzymes and yeast cells with a vibratinghollow fiber membrane module, Sep. Purif. Technol. 53 (2007) 111–118.

19] D.L. Grzenia, J.O. Carlson, S.R. Wickramasinghe, Tangential flow filtration forvirus purification, J. Membr. Sci. 321 (2008) 373–380.

20] J.S. Knutsen, R.H. Davis, Deposition of foulant particles during tangential flowfiltration, J. Membr. Sci. 271 (2006) 101–113.

21] G. Belfort, R.H. Davis, A.L. Zydney, The behaviour of suspensions and macro-molecular solutions in crossflow microfiltration, J. Membr. Sci. 96 (1994) 1–58.

22] C. Güell, P. Czekaj, R.H. Davis, Microfiltration of protein mixtures and the effectsof yeast on membrane fouling, J. Membr. Sci. 155 (1999) 113–122.

23] S.M. Kumar, S. Roy, Filtration characteristics in dead-end microfiltration of liv-ing Saccharomyces cerevisiae cells by alumina membranes, Desalination 229(2008) 348–361.

24] J. Hermia, Constant pressure blocking filtration laws—application to power-lawnon-Newtonian fluids, Trans. Inst. Chem. Eng. 60 (1982) 183–187.

25] S.R. Wickramasinghe, Y. Wu, B. Han, Enhanced microfiltration of yeast by floc-culation, Desalination 147 (2002) 25–30.

26] J.-S. Kim, S. Akeprathumchai, S.R. Wickramasinghe, Flocculation to enhance
microfiltration, J. Membr. Sci. 182 (2001) 161–172.
27] S.R. Wickramasinghe, B. Han, S. Akeprathumchai, V. Chen, P. Neal, X. Qian,Improved permeate flux by flocculation of biological feeds: comparisonbetween theory and experiment, J. Membr. Sci. 242 (2004) 57–71.

28] S.R. Wickramasinghe, B. Han, S. Akeprathumchai, A. Jaganjaca, X. Qian, Model-ing flocculation of biological cells, Powder Technol. 156 (2005) 146–153.

[

[[

e Science 346 (2010) 288–295 295

29] P. Narong, A.E. James, Effect of the -potential on the micro/ultra-filtration ofyeast suspensions using ceramic membranes, Sep. Purif. Technol. 49 (2006)149–156.

30] M.N. Karim, H. Graham, B. Han, A. Cibulskas, Flocculation enhanced microfil-tration of Escherichia coli lysate, Biochem. Eng. J. 40 (2008) 512–519.

31] M.T. Aspelund, G. Rozeboom, M. Heng, C.E. Glatz, Improving permeate flux andproduct transmission in the microfiltration of a bacterial cell suspension byflocculation with cationic polyelectrolytes, J. Membr. Sci. 324 (2008) 198–208.

32] D. Hughes, R.W. Field, Crossflow filtration of washed and unwashed yeast sus-pensions at constant shear under nominally sub-critical conditions, J. Membr.Sci. 280 (2006) 89–98.

33] V.T. Kuberkar, R.H. Davis, Modeling of fouling reduction by secondary mem-branes, J. Membr. Sci. 168 (2000) 243–258.

34] V.T. Kuberkar, R.H. Davis, Microfiltration of protein-cell mixtures with cross-flushing or backflushing, J. Membr. Sci. 183 (2001) 1–14.

35] J. Kloosterman IV, P.D. van Wassenaar, N.K.H. Slater, A. van der Padt, An inte-grated approach to the recovery of intracellular products from yeast by beadmilling and precoat filtration, Chem. Eng. J. 37 (1988) B47–B54.

36] M. Dixit, Membranes and filtration: membrane filtration in the biopharmindustry, Filtrat. Sep. 45 (2008) 18–21.

37] N.I. Lebovka, M.I. Bazhal, E. Vorobiev, Estimation of characteristic damage timeof food materials in pulsed-electric fields, J. Food Eng. 54 (2002) 337–346.

38] E. Vorobiev, N.I. Lebovka, in: J. Raso, V. Heinz (Eds.), Extraction of Intercellu-lar Components by Pulsed Electric Fields; Pulsed Electric Field Technology forthe Food Industry: Fundamentals and Applications, Springer, Berlin, 2006, pp.153–194.

39] Y. Iida, T. Tuziuti, K. Yasui, T. Kozuka, A. Towata, Protein release from yeastcells as an evaluation method of physical effects in ultrasonic field, Ultrason.Sonochem. 15 (2008) 995–1000.

40] R.J. Wakeman, E.S. Tarleton, Filtration: Equipment Selection, Modelling andProcess Simulation, Elsevier, Oxford, 1998.

41] K.-J. Hwang, C.-Y. Liao, K.-L. Tung, Analysis of particle fouling during microfil-tration by use of blocking models, J. Membr. Sci. 287 (2007) 287–293.

42] E. Iritani, Y. Mukai, Y. Tanaka, T. Murase, Flux decline behavior in dead-endmicrofiltration of protein solutions, J. Membr. Sci. 103 (1995) 181–191.

43] E. Iritani, N. Katagiri, Y. Sugiyama, K. Yagishita, Analysis of flux decline behaviors
in filtration of very dilute suspensions, AIChE J. 53 (2007) 2275–2283.
44] M. Chandler, A. Zydney, Effects of membrane pore geometry on fouling behaviorduring yeast cell microfiltration, J. Membr. Sci. 285 (2006) 334–342.

45] R. Hogg, Flocculation and dewatering, Int. J. Miner. Process 58 (2000) 223–236.46] A. Yelshin, J.A. Texeira, W.R. Bowen, M. Mota, Role of fractional cake composi-

tion in cake resistance, Trans. Filt. Soc. 2 (2002) 45–48.

GPE-EPIC 2nd International Congress on Green Process Engineering 2nd European Process Intensification Conference 14-17 June 2009 - Venice (Italy)

DEAD-END FILTRATION OF SACCHAROMYCES CEREVISIAE YEAST SUSPENSIONS: EFFECTS OF HIGH-PRESSURE DISRUPTION,

HIGH-VOLTAGE ELECTRICAL DISCHARGES AND FLOCCULATION

M. LOGINOV (1, 2), O. LARUE (1), N. LEBOVKA (2), M. NONUS (1), J.-L. LANOISELLÉ (1), M. SHYNKARYK (1) , E. VOROBIEV (1)

♦ (1) Unité Transformations Intégrées de la Matière Renouvelable, Université de Technologie de Compiègne, Centre de Recherche de Royallieu, B.P. 20529-60205 Compiègne Cedex, FRANCE e-mail : [email protected] (E. Vorobiev)

♦ (2) Institute of Biocolloidal Chemistry named after F.D. Ovcharenko,

NAS of Ukraine, 42, blvr. Vernadskogo, Kyiv 03142, UKRAINE e-mail : [email protected] (N. Lebovka)

Abstract. Filtration is commonly used for purification of extracted intracellular bio-products from cells and cell debris after disruption. Disruption enhances recovery of bio-products but provokes cells reorganisation and generates cell debris which impedes the filtration. Thus it needs to be investigated in order to reduce the time of filtration and to control the quality of filtrate. This paper compares two techniques for disruption of Saccharomyces cerevisiae yeast suspensions, a classical one: the High Pressure Homogenization (HPH), and an alternative way: the High Voltage Electrical Discharges (HVED). The disruption was evaluated by means of conductivity disintegration index Z (0 ≤ Z ≤ 1) and absorbance spectra of supernatant solutions. Optical and electronic microscopy, particle sizing, ζ-potential and turbidity measures were performed to characterize colloidal properties of disrupted yeast suspension. Filtration was analysed through the Hermans-Bredée equation. The filtration behaviour changes with Z: from filter cake filtration for low Z values to standard pore blocking for high Z values. For a same value of Z, HPH allows a higher extraction of proteins and other bio-products and better filtration than after HVED. Best extraction performances were observed for intense breakage (Z = 0.99). Flocculation of disrupted cells was also tested with cationic polymer. The aggregation of particles with the flocculant promotes the filtration rate as expected but entraps bio-products in filter cake, hindering the recovery of bio-products in extract. Key-words. yeast, disruption, high-pressure homogenization, high voltage electrical discharges, bio-products recovery, filtration.

The interior of the yeast cells (Saccharomyces cerevisiae) is a rich source of bio-products

(proteins, enzymes, polysaccharides etc.) used for many applications in biotechnology, brewing and food industry. Extraction of bio-products from cells usually involves release of cell interior by disruption of cell walls and separation of extract from cells, cell debris and other insoluble particles. The effectiveness of solid-liquid separation greatly depends on the peculiarities of chosen disruption technique.

Among various techniques proposed in the literature the mechanical method of High Pressure Homogenization (HPH) is most appropriate for industrial-scale disruption. HPH results in considerable breakage of cells and high recovery of bio-products. However, the final product contains large quantity of cell debris, which complicates the downstream separation. Other restrictions of HPH method are undesirable temperature elevation and necessity of multiple passes or application of higher pressure for complete proteins recovery.

Recently, treatment of yeast suspension with high voltage electrical discharges (HVED) was proposed as an alternative way for production of proteins1. HVED of an aqueous bio-suspension of 40 kV provokes a noticeable mechanical damage of cells and rupture of cell walls. Shock waves and electrical charge redistribution generated by HVED may induce the homogenisation of yeasts cells in suspension or, on the contrary, their aggregation.

The separation step can be performed by filtration which is widely used in food industry and bio-technology. For instance, the dead-end filtration is implemented for beer and wine clarification from

dead yeast cells and other colloids. However these fine particles quickly foul the filter membrane, increase its hydraulic resistance and decrease the filtration flux. Dead-end filtration can be substituted by crossflow filtration or filtration with rotating and vibrating membranes2. However, such techniques cannot entirely prevent the membrane fouling which inevitably occurs. The apparition of fouling can be evidenced by analysing the filtration rate through Hermans-Bredée’s equation3.

Survey of the literature shows that numerous works have described the filtration of washed yeasts suspensions or model suspensions with two components (undisrupted cells and proteins solution). However, only few authors have paid their attention to filtration of complex microbial suspensions containing disrupted cells, cell debris, salts and bio-molecules extracted from the cell interior4, 5.

In this work the dead-end filtration of disrupted S. cerevisiae yeast suspensions was investigated. Two methods were used for yeast cells disruption and bio-molecules recovery: HPH and HVED. These methods enable to obtain complex suspensions with different content of disrupted and undisrupted cells, cell debris, salts and extracted bio-molecules. Influence of the disruption index of yeast Z on proteins extraction, colloidal properties and filterability of the yeast cell suspension was investigated. A polycationic flocculant (poly(diallyldimethylammonium chloride)) was used for flocculation of disrupted yeast suspensions and possibility of using flocculation for facilitation of recovery of the proteins was discussed.

DISRUPTION OF YEAST SUSPENSION

Suspensions of 1% w/w were prepared from dry yeast cells and distilled water. The yeasts were

swelled in an aqueous suspension at room temperature and gently mixed for 30 min before HPH or HVED. The swelling process was monitored by means of conductivity measurement.

HPH was performed in a two-stage high-pressure homogenizer NS1001L-PANDA 2K kindly supplied by GEA Niro Soavi France. NHPH successive passes at fixed homogenizing pressure P = 500 or 1000 bar were used. The initial temperature of suspension was 25°C and the temperature elevation resulting from HPH was about 10°C. After each pass suspension was cooled to room temperature for its further characterization or next pass through homogenizer.

HVED apparatus (Tomsk Polytechnic University, Tomsk, Russia) with a batch-treatment chamber and stainless steel electrodes with neelde-plate geometry was used. The distance between the electrodes was 10 mm, the 40 kV peak pulse voltage was used, which resulted in the mean electric field strength of 40 kV/cm. Effective pulse duration was 1-2 microseconds. HVED lay in application of the NHVED successive pulses with the repetition rate of 0.5 Hz. Suspension characteristics were measured between successive applications of HVED pulses. The temperature elevation resulting from HVED was less than 5°C.

Efficiency of HPH and HVED methods was estimated by means of conductivity disintegration index of yeasts Z, which was determined from the following expression1:

Z = (σ – σi)/( σmax – σi) (1) were σ is the electrical conductivity of suspension after treatment, σi is the initial electrical conductivity of suspension before treatment and σmax is the conductivity of suspension with maximum of disrupted cells. Eq. (1) gives Z = 0 for an intact system and Z = 1 for a maximally disintegrated suspension.

Evolutions of Z during both HPH and HVED treatments of suspension are presented in Fig. 1. Increase of Z during the treatment is related to extraction of ionic intracellular components from damaged cells and it is proportional to the degree of disruption. Z increases gradually with the number of treatment cycles both for HPH and HVED methods. Disintegration and extraction attain maximal level after long-term treatment. But incomplete disintegration is typically performed because the long time treatment may be economically unreasonable. Using the data of Fig. 1 required parameters of disruption (P, NHPH or NHVED) can be chosen.

0 100 200 300 400 500

0.2

0.4

0.6

0.8

1

Z

a)

NHVED

0 100 200 300 400 500

0.2

0.4

0.6

0.8

1

Z

a)

NHVED

0 5 10 15 20

0.2

0.4

0.6

0.8

1

Z

P = 1000 bar

500 bar

NHPH

b)

0 5 10 15 20

0.2

0.4

0.6

0.8

1

Z

P = 1000 bar

500 bar

NHPH

b)

Fig. 1. Conductivity disintegration index of yeasts Z vs. number of HVED pulses at E = 40 kV (a), Z vs. number of successive HPH passes at pressure values 500 and 1000 bar (b).

COLLOIDAL PROPERTIES OF DISRUPTED YEAST SUSPENSIONS

Though both HPH and HVED treatments result in considerable cells disruption, their mechanisms are not similar. Hence, condition of yeast cells and colloidal properties of yeast suspensions after HPH and HVED treatments can be quite different even at the same value of disintegration index Z. Various experiments were carried out to verify this assumption and characterize alteration of yeasts during the treatment.

Evolution of size distribution function (SDF) after HPH and HVED is shown in Fig. 2. SDF of the untreated yeast suspension has one broad peak with maximum at 4.3±0.2 µm. The content of fine particles with d < 2 µm is rather low. Disruption of a yeast suspension results in decrease of the average particle size to 3.7±0.2 µm (both for HPH and HVED). Increased content of fine particles (d < 2 µm) is associated with formation of cell debris. Narrowing of SDF peak after HPH evidences that probability of HPH-disruption is directly proportional to initial particles diameter. While broadening of SDF after HVED suggests that both homogenisation and aggregation occur during the treatment. Last assumption is confirmed with ζ-potential values of disrupted particles. The ζ-potential for yeast particles is equal to -18±1mV (Z = 0), -18±5 mV (Z = 0.99, HVED) and -10±5 mV (Z = 0.99, HPH). In all this cases the modules of ζ are lower than 30 mV, which is the lower limit for stable non-aggregating particles.

The optical microscopy reveals the presence of both aggregates and fine particles in all the studied yeast suspensions. In an untreated suspension, aggregates are formed as a result of incomplete disaggregation of yeast cells agglutinated during suspension preparation. The HPH destructs these aggregates; instead, ramified aggregates of 50-100 µm average size appear. Dense opaque flocks are presented in a HVED treated suspension together with individual fine particles.

Electronic microscopy of yeast suspensions clearly reveals cells damage during the treatment. Prior to disruption the yeast cells are spheroids with a smooth surface. HPH and HVED strongly damage the surface of cells; disrupted cells are covered with a translucent layer of released intracellular components.

Absorbance spectra of supernatant solutions were measured for HPH and HVED treated suspensions in order to estimate extraction efficiency during treatment. In accordance with literature data, the peak observed at the wavelength λmax, 1 ≈ 210-220 nm corresponds to absorption by bonds of peptides and proteins, which are the main intracellular constituents of the S. cerevisiae, and peak at λmax, 2 ≈ 260-270 nm corresponds to nucleic acids6. Absorbance gradually increased with increase of Z during HPH or HVED. Data show that absorbance of supernatant is much higher for suspensions after HPH-treatment than for HVED-treated suspensions at the same disintegration level Z (Fig. 3a). Hence, disruption of yeast cells by HPH method seems to be more effective than HVED-treatment and results in higher release of proteins. This conclusion agrees with data on turbidity of supernatants of the treated suspensions (Fig. 3b).

Increase of turbidity with Z increase reflects release of proteins and fine cell debris during the treatment. However, turbidity is much higher after homogenization of a yeast suspension than after its HVED treatment at the same level of Z.

200 220 240 260 280 30010-2

10-1

100

Abs

orba

nce

λ, nm

HPH, Z = 0.99

HVED, Z = 0.99

(a)

200 220 240 260 280 30010-2

10-1

100

Abs

orba

nce

λ, nm

HPH, Z = 0.99

HVED, Z = 0.99

(a)

0 0.2 0.4 0.6 0.8 1

101

102

103

Turb

idity

, NTU

Z

HPH

HVED

(b)

0 0.2 0.4 0.6 0.8 1

101

102

103

Turb

idity

, NTU

Z

HPH

HVED

(b)

Fig. 3. (a) Absorbance spectra of supernatant solutions for HPH and HVED disrupted yeast suspensions; (b) turbidity of supernatant vs. Z for yeast suspensions after HPH or HVED treatment.

5 100

5

10

15

20

SDF

,%

d, μm

Z = 0

Z = 0.99 HVED

Z = 0.99 HPH

5 100

5

10

15

20

SDF

,%

d, μm

Z = 0

Z = 0.99 HVED

Z = 0.99 HPH

Fig. 2. Size distribution function of intact (Z = 0)

and disrupted (Z = 0.99) yeast suspensions.

FILTRATION BEHAVIOUR OF DISRUPTED YEAST SUSPENSIONS

The dead-end filtration experiments were carried out at constant pressure of 1 bar. Filtration membrane was made from Fisherbrand qualitative filter paper (nominal pore size was 2.5 μm). Though filters with smaller pore size are typically used for purification of proteins, the pore size of material used in this study was small enough for yeast cell suspension and could be utilized, e.g., at the first step of the membrane separation process. Filtration was started immediately after the filter-cell was poured with 200 ml of freshly treated yeast suspension. The dimensionless filtrate volume was calculated V* = V/Vsusp (here V is the volume of filtrate, ml, Vsusp is the volume of suspension before filtration (Vsusp = 200 ml)).

Evolution of the filtration curves after HVED treatments of yeast suspensions is shown in Fig. 4a. During HVED the filtrate flux gradually decreases with increase of Z from 0 to 0.99. Filtration data for HVED-treated suspensions are presented in Fig. 4b in conventional filtration coordinates t/V* versus V*. This coordinates allow to fit experimental filtration curves for suspensions with low disintegration indexes and initial segments of curves for suspensions with Z ≤ 0.7 by linear equation3:

t/V* = k1V* + k2 (2) where k1 and k2 are the slope and intercept, respectively. According to Ruth–Carman’s classical cake filtration model, k1 is directly proportional to specific cake resistance3. Hence, gradual increase of the slope is related to increase of specific cake resistance after treatment. Increase of the cake’s resistance is associated with disaggregation and damage of cells and formation of cell debris. It results in more dense cake structure with narrow pores and high compressibility.

0 500 100010-6

10-5

10-4

10-3

J, m

/s

(a)Z = 0

t, s

Z = 0.99

Z = 0.7

Z = 0.2

0 500 100010-6

10-5

10-4

10-3

J, m

/s

(a)Z = 0

t, s

Z = 0.99

Z = 0.7

Z = 0.2

0 0.2 0.4 0.6 0.8 10

2000

4000

V*

t/V

* , s

Z = 0

Z = 0.99

Z = 0.2

Z = 0.7(b)

0 0.2 0.4 0.6 0.8 10

2000

4000

V*

t/V

* , s

Z = 0

Z = 0.99

Z = 0.2

Z = 0.7(b)

Fig. 4. Filtration curves of HVED-treated yeast suspensions as a function of Z: (a) filtrate flux J vs. time; (b) filtration curves in coordinates of Ruth-Carman’s cake formation model.

In HPH-treated suspensions, increase of Z from Z = 0 to 0.7 also results in decrease of the flux,

same as for those treated by HVED. However, at Z = 0.9 or higher, filtration behaviour becomes different than for HVED-treated suspensions. Fast initial decrease of the filtrate flux (initial stage of filtration) in Fig. 5a is followed by the region of a relatively stationary flux (final stage of filtration). At the initial stage of filtration, the flux is maximal for completely disrupted suspension (Z = 0.99). At the final stage of filtration, the flux decreases with increase of Z and is minimal for Z = 0.99. Nevertheless, at Z = 0.99 more than half of suspension volume gets filtered quickly during the initial stage of filtration.

Observed non-monotonous dependence of filterability on Z for HPH-treated suspensions can be explained if we assume that various mechanisms of filtration dominate in suspensions with different disintegration degree. The pore blocking mechanism is expected in the case of filtration of a relatively small particles that get entrapped inside the pores and cause internal fouling of a membrane. In the case of the pore blocking model, filtration curves are described by linear Hermans-Bredée’s equation:

t/V* = kb t + k3, (3) where kb and k3 are constants3.

Fig. 5b presents filtration curves of homogenized yeast suspensions in coordinates of Eqs. (2) and (3).

0 500 100010-6

10-5

10-4

10-3

J, m

/s

(a)

Z = 0

t, s

Z = 0.99

Z = 0.7Z = 0.2

Z = 0.9

0 500 100010-6

10-5

10-4

10-3

J, m

/s

(a)

Z = 0

t, s

Z = 0.99

Z = 0.7Z = 0.2

Z = 0.9

0 500 1000 1500

0.2 0.4 0.6 0.8 1

2000

4000

t, s

t/V

* , s

Z = 0.99Z = 0.2

Z = 0.9Z = 0.7

V*

Z = 0

(b)

0 500 1000 1500

0.2 0.4 0.6 0.8 1

2000

4000

t, s

t/V

* , s

Z = 0.99Z = 0.2

Z = 0.9Z = 0.7

V*

Z = 0

(b)

Fig. 5. Filtration curves of HPH-treated yeast suspensions: (a) filtrate flux J vs. time; (b) ratio of filtration time and normalized filtrate volume t/V* vs. V* (dashed lines) and t/V* vs. t (solid lines).

It is obvious that initial segments of filtration curves for HPH suspensions with Z ≤ 0.7 are linear when presented in coordinates t/V* versus V* (dashed lines). Accordingly to Eq. 2, it evidences that the cake formation prevails when disintegration index of suspension is low. Slopes of the segments increase with increase of Z. Hence disaggregated and disrupted particles build up a cake with higher specific resistance (Eq. 2). Increase of specific cake resistance may be explained by both decrease of the particle diameter and over-clogging effect lying in fouling of the deposited cake layer with fine-sized cell debris.

Unlike the moderately homogenized suspensions, filtration curves of HPH-treated suspensions with Z ≥ 0.9, which are described by Eq. (3), are linear in coordinates t/V* versus t (solid lines on Fig. 5b). The filtration process in such suspension is governed by internal membrane fouling. It may be characterized by the pore blocking constant kb (slopes of the solid lines). The pore blocking constant is lower for suspension with Z = 0.99. Filterability of this suspension is better and shorter time of filtration is required to process higher filtrate volumes. However, fouling of a membrane significantly increases its resistance during filtration and filtration flux declines rapidly to a very low value (Fig. 5a).

Hence, long-term homogenization of yeast suspensions changes filtration mechanism from cake filtration to pore blocking. The filtrate volume passes through minimum with Z increase from 0 to 0.99. These data may be explained on the basis of filtration model developed by Davis and Kuberkar7. These authors have analysed filtration of bidisperse suspensions with various concentrations of small and large particles. It was shown that internal fouling of a membrane dominates at high concentrations of small particles and filtration was faster when disperse particles are small. The filtrate volume rapidly approaches certain maximal value and filtrate flux becomes zero. In a system with large dispersed particles the volume of filtrate continuously grows.

Fig. 6 compares the filtrate flux Js at 600 s of filtration for HPH and HVED treated yeast suspensions at different values of disintegration index Z. Both HVED and HPH disruptions of yeast decrease filtrate flux in 15-20 times for Z = 0.99. Therefore objective of our farther study was an improvement of filterability of the disrupted suspensions.

INFLUENCE OF FLOCCULATION ON FILTRATION OF DISRUPTED YEAST

SUSPENSIONS

It was found that decrease of particle size and appearance of a fine-sized cell debris during HPH and HVED disruption negatively affects filtration. A conventional way to enhance the filtration and to reduce the membrane fouling is the particles flocculation. Recently, cationic polymers had been proposed as flocculants for undisrupted yeast suspensions8 and homogenised microbial lysate4, 5.

So, experiments with disrupted yeast suspensions flocculated prior to filtration were carried out. The flocculant used was cationic polymer poly(diallyldimethylammonium chloride) (Mw = 400.000-500.000). The concentration of flocculant was varied within the range C = 0-0.04% wt.polymer/wt.yeast. Influence of the polymer concentration on the content of colloidal fraction in a flocculated yeast suspension was assessed by measuring turbidity of a supernatant after flocculation.

The chosen polymer was an effective flocculant for disrupted yeasts and addition of this polymer results in a tenfold decrease of turbidity. The positively charged polymer molecules easily adsorb on the negatively charged cells and cell debris and aggregation of fine particles into flocks due to polymer bridging was observed. There exists an optimal dose of polymer, which minimizes turbidity after centrifugation (Copt = 0.012 % for HVED and 0.02 % for HPH disrupted suspensions). It implies an optimal coverage of the cell surface with polymer, high concentration of polymer tails and maximum probability of interparticle bridging. The surface coverage decreases with increase of the specific surface and number of particles (content of cell debris) at a given adsorbate concentration. The higher dose of polymer is required for flocculation of a more turbid HPH-disrupted suspension.

The optimal filtration of a flocculated or disrupted yeast suspension requires low content of the fine particles, high average particle size and narrow particle size distribution function. It was found that addition of polymer increases the average particle size and decreases the content of cell debris with d < 2.5 µm. The optimal polymer dose leads to formation of flocks with maximum average diameter of 27 µm and 57 µm for HPH and HVED disrupted suspensions, respectively. The SDF in a flocculated disrupted yeast suspension containing the optimal polymer dose are broader than in suspensions before flocculation. Flocculant over-dosage results in considerable broadening of the particle size distribution function and increase of the content of re-stabilized fine particles.

0 0.2 0.4 0.6 0.8 1

1

2

3

4

5J s

×10

5 , m

/s

Z

HPH

HVED

0 0.2 0.4 0.6 0.8 1

1

2

3

4

5J s

×10

5 , m

/s

Z

HPH

HVED

Fig. 6. Variation of the filtrate flux at 600 s of filtration Js with Z for HPH and HVED treated

suspensions.

Flux dependence on time and dose of polymer used for flocculation of disrupted yeast suspensions were studied. The enhanced flocculation resulted in increasing of yeasts filtration. Fluxes were maximal at the optimal polymer doses Copt = 0.012 % for HPH-disrupted and 0.02 % for HVED-disrupted suspensions, respectively. However, the effect of flocculation was dependent on the mode of yeast disruption and the most pronounced increase of the filtrate flux Js was observed for HVED treated suspensions (Fig. 8). Presumably it reflects the different flock structures and filtration mechanisms in HPH and HVED treated suspension.

Fig. 9 presents the absorbance spectra of

supernatant solutions for HPH and HVED disrupted yeast suspensions (Z = 0.9) without and in presence of flocculant. The polymer dosage was optimal and equal to 0.02% and 0.012% for HPH and HVED treated suspensions, respectively. The addition of polymer results in decreases of absorbance of extract solution. It reflects decreasing of proteins and other bio-products concentration. It can be assumed that selected polycationic flocculant (poly-(diallyldimethylammonium chloride)) enhances the flocculation of bio-molecules or provokes their bridging to the surface of cells and cell debris. It is undesirable phenomenon because the bio-products are bounded in sediment or in a filter-cake.

CONCLUSIONS

HPH-treatment was found to be more effective disruption method than HVED, since it results in higher extraction of proteins and other bio-products at the same value of disintegration index of yeast Z. Filtration behaviour of HVED-processed suspensions and homogenized suspensions with Z ≤ 0.7 was governed by cake formation. For HPH-treated suspensions high level of damage (Z > 0.9) filtration was governed by membrane fouling. Addition of optimal dose of polycationic flocculant promoted flocks formation and accelerated filtration but reduced the concentration of bio-products in filtrate.

ACKNOWLEDGEMENTS

The authors would like to acknowledge the Sofrolab (Station Oenotechnique de Champagne, Epernay, France) for its financial and material support and the society GEA Niro Soavi France for the kind supply of high-pressure homogenizer NS1001L-PANDA 2K. The authors thank Dr. N. S. Pivovarova for her help with the manuscript preparation.

LITERATURE CITED

1. Shynkaryk M. V., Lebovka N. I., Lanoisellé J.-L., Nonus M., Bedel-Clotour C., Vorobiev E. (2009) J. Food Eng., 92, 189-195.

2. Jaffrin M. Y. (2008) J. Membr. Sci. 324, p. 7. 3. Ho C.-C., Zydney A. (2000) J. Colloid Interface Sci., 232, p. 389. 4. Karim M. N., Graham H., Han B., Cibulskas A. (2008) Biochem. Eng. J., 40, p. 512. 5. Aspelund M. T., Rozeboom G., Heng M., Glatz C. E. (2008) J. Membr. Sci., 324, p. 198. 6. Iida Y., Tuziuti T., Yasui K., Kozuka T., Towata A. (2005) Ultrason. Sonochem. 15, p. 995. 7. Kuberkar V. T., Davis R. H. (2000) J. Membr. Sci., 168, p. 243. 8. Wickramasinghe S. R., Han B., Akeprathumchai S., Jaganjaca A., Qian X.(2005), Powder Technol.,

156, p. 146.

0 0.01 0.02 0.03 0.04

2

4

6

J s×

105 ,

m/s

C, %

HPH

HVED

0 0.01 0.02 0.03 0.04

2

4

6

J s×

105 ,

m/s

C, %

HPH

HVED

Fig. 8. Variation of the filtrate flux at 600 s of filtration Js with flocculant concentration C in HPH and HVED disrupted yeast suspensions

(Z = 0.9).

200 220 240 260 280 300

10-2

10-1

100

Abs

orba

nce

λ, nm

HPH, C = 0%

HVED, C = 0%HPH, C = 0.02%

HVED, C = 0.012%

200 220 240 260 280 300

10-2

10-1

100

Abs

orba

nce

λ, nm

HPH, C = 0%

HVED, C = 0%HPH, C = 0.02%

HVED, C = 0.012%

Fig. 9. Influence of optimal flocculant dose on absorbance spectra of supernatant solution for HPH and HVED disrupted yeast suspensions

(Z = 0.9); HPH: solid line C = 0%, dashed line C = Copt = 0.02%; HVED: solid line C = 0%,

dashed line C = Copt = 0.012%.


175

Conclusions

It was shown in the Paper III that continuous treatment of yeast suspension by HVED

results in disruption of the yeast cell walls and extraction of intracellular bio-products.

However, it also results in formation of cell debris and decrease of filtration rate. Filtration of

the intact (Z = 0) and moderately HVED-treated (Z ≤ 0.7) yeast suspensions is governed by

cake-formation and increase of the treatment intensity results in the decrease of the filter-cake

permeability. Filtration of the maximally disrupted suspension (Z = 0.99) is governed by

internal membrane fouling that may be explained by high concentration of small cell debris in

the treated suspensions. The membrane fouling results in the steep decrease of filtration rate;

therefore, maximal HVED disruption of yeast is undesirable.

Comparison of the HVED-treatment with HPH-treatment (carried out in the Paper IV)

shows that HPH-treatment is more effective disruption method than HVED, since it results in

higher extraction of proteins and other bio-products at the same value of disintegration index

of yeast cells Z. However, if the value of disintegration index Z is above 0.9, filtration of

HPH-disrupted yeast suspension is governed by pore blocking mechanism. It results in very

low rates of filtration of the maximally HPH-treated suspensions.

Addition of an optimal dose of polycationic flocculant promoted formation of flocks and

accelerated filtration, but reduced concentration of bio-products in the filtrate.

III.4. Determination of compression-permeability using analytical centrifugation

176

Paper V: “Compression-permeability characteristics of mineral sediments

evaluated using analytical photocentrifuge”

Introduction

Paper V is focused on determination of compression-permeability characteristics of

mineral suspensions.

The main characteristics determining compression and permeability of mineral

suspensions are:

• volume fraction of particles φ;

• specific filtration resistance ; and

• coefficient of consolidation C.

Knowing of these characteristics is important for modeling of filtration and compression

of mineral suspensions, as well as for prediction of filtration and compression time and final

dryness of the filter-cakes.

All these characteristics are pressure-dependent. The dependencies may be presented in

the form, so-called, constitutive equations:

• φ = φo(1 + ps/pa)β,

• = o(1 + ps/pn)n,

• C = Co(1 + ps/po)γ,

where ps is the local solid pressure in the filter-cake or consolidate, (φo, pa, β), (o, pn, n), and

(Co, po, γ) are the sets of parameters characterising the particles volume fraction, specific

filtration resistance and consolidation coefficient, respectively. Determination of these

parameters makes the prime interest of the Paper V.

Many methods were proposed for determination of these parameters (analysis of dead-end

filtration, analysis of compression-permeability process, and analysis of the gravity

consolidation of mineral suspensions). These methods are based on the experimental

techniques available for measurement of filtration or compression of the mineral suspensions.

The most developed techniques are: dead-end filtration in the dead-end filtration cell

equipped with pressure probes, mechanical consolidation of the sediment in the, so-called,

compression-permeability cells, and gravity sedimentation at various initial heights of the

sediments. However, limitations of these methods (e.g., limited pressure range available for

the measurement, necessity of long and numerous experiments) encourage seeking of new

methods for determination of the compression-permeability parameters from the experimental

data.


177

Summary

The Paper V deals with new experimental technique available for measurements of

compression of mineral suspensions: analytical centrifugation. This technique is based on

experiments carried out in the, so-called, analytical photocentrifuge. This device allows

studying of sedimentation or consolidation of mineral suspensions at various centrifugal

rotation speeds, while the height of the sediment may be registered continuously during the

centrifugation.

Two types of important dependencies may be measured using this device:

• dependencies of sediment height on centrifugation time; and

• dependencies of ultimate sediment height on centrifugal rotation speed.

The Paper V is devoted to analysis of these dependencies and determination of parameters

of the constitutive equations for volume fraction of particles, specific filtration resistance and

consolidation coefficient from data on centrifugal consolidation. The centrifugal experiments

were carried out for aqueous suspension of calcium carbonate.

Chemical Engineering Science 66 (2011) 1296–1305


Chemical Engineering Science

0009-25

doi:10.1

n Corr

E-m

journal homepage: www.elsevier.com/locate/ces

Compression–permeability characteristics of mineral sediments evaluatedwith analytical photocentrifuge

M. Loginov a,b, E. Vorobiev a,n, N. Lebovka a,b, O. Larue a

a Unite Transformations Integrees de la Matiere Renouvelable, Universite de Technologie de Compiegne, Centre de Recherche de Royallieu, B.P. 20529-60205

Compiegne Cedex, Franceb Institute of Biocolloidal Chemistry named after F. D. Ovcharenko, NAS of Ukraine, 42, blvr. Vernadskogo, Kyiv 03142, Ukraine

a r t i c l e i n f o

Article history:

Received 24 June 2010

Received in revised form

19 December 2010

Accepted 23 December 2010Available online 30 December 2010

Keywords:

Analytical centrifugation

Concentrated suspension

Consolidation

Compressibility

Calcium carbonate

Specific filtration resistance

09/$ - see front matter & 2010 Elsevier Ltd. A

016/j.ces.2010.12.041

esponding author. Fax: +33 344 231980.

ail address: [email protected] (E. Vorob

a b s t r a c t

This work discusses applications of analytical photocentrifuge LUMiSizer for estimation of the low-

pressure compression–permeability characteristics of aqueous calcium carbonate sediments. Two

approaches for estimation of compressibility–permeability parameters were tested. These approaches

are based on (1) analysis of equilibrium height of sediment HN versus centrifugal rotation speed O and

(2) analysis of kinetic curves of the consolidation ratio U(t) at different rotation speeds O. The approach

(1) allowed fair fitting of experimental HN (O) data with parameters pa¼70.970.9 Pa and

b¼0.177770.0005 in Tiller’s equation relating the volume fraction j and solid pressure ps. The two

independent approaches (1) and (2) evidenced the presence of the scaling law relating consolidation

coefficient C and solid pressure ps, Cppsg with the similar exponents gE0.8570.03 (for the studied

solid pressure region 5 kParpsr75 kPa).

& 2010 Elsevier Ltd. All rights reserved.

1. Introduction

Compression–permeability (CP) characteristics of a particulatelayer are essential for prediction of solid–liquid separations bygravity sedimentation, filtration, expression and centrifugation.The basic filtration equations introduce the notion of averagespecific cake resistance aav by analogy with electrical resistance(Sperry, 1916). This characteristic depends on the overall filtrationproperties of the filter cake and is very useful for the equipmentscaling (Rushton et al., 1996; Wakeman and Tarleton, 1999).However, the average specific cake resistance aav is insufficient forcharacterization of the local liquid flow within the compressibleparticulate layer. Grace (1953), Tiller (1953) and Okamura andShirato (1955) developed methods for experimental determinationof local porosity e, local permeability k and local specific cakeresistance a, as functions of the local compressive pressure ps

representing the stress developed by frictional loss inside theparticulate layer. Similarly to soil mechanics, the stress balance ina particulate layer can be presented in the form of p¼ plðx,tÞþpsðx,tÞ(Tiller, 1953; Okamura and Shirato, 1955), where p is the appliedpressure, pl is the local liquid pressure in the pores, t is the time andx is the coordinate. The constitutive relationship of the particulatelayer parameters versus ps are often expressed as power lawfunctions (Tiller, 1953; Tiller and Shirato, 1964; Shirato et al., 1985;

ll rights reserved.

iev).

Koenders and Wakeman, 1996; Stamatakis and Tien, 1991)

j¼joð1þps=paÞb

ð1Þ

k¼ koð1þps=pkÞd

ð2Þ

a¼ aoð1þps=pnÞn

ð3Þ

where j¼ 1e is the volume fraction of solids (solidosity) in aparticulate layer, jo, ko, ao ¼ 1=ðeokoÞ, b, d, n¼db are empiricalconstants, and pa, pk, pn are constants that may be considered asreference threshold pressures. In this case, jo, ko and ao correspondto parameter values before stress application to the cake (at ps¼0).Experimentally determined values of pa, pk and pn can differ (Sedinet al., 2003). Consolidation coefficient C, which is the generalized CPcharacteristic of particulate layer, can be represented on the analogywith mass and thermal diffusivities as (Vorobiev and Fedotkin,1984; Iritani et al., 2009)

C ¼ G=ðamrsÞ ð4Þ

where G¼@ps=@e is the compressibility modulus, e¼(1j)/j isthe void ratio, m is the viscosity of liquid and rs is the density ofsolids.

Carman (1938) and Ruth (1946) introduced into laboratorypractice a CP chamber consisting of a cylinder with a piston. TheCP procedure comprises the piston loading up to ultimatestabilization of a particulate layer under increasing pressures.

www.elsevier.com/locate/ces

dx.doi.org/10.1016/j.ces.2010.12.041


dx.doi.org/10.1016/j.ces.2010.12.041

0 1 2 3 40

0.5

1

1.5

SDF

[%

]

d [m]

Fig. 1. Volume-based size distribution of CaCO3 particles in an aqueous

suspension.

M. Loginov et al. / Chemical Engineering Science 66 (2011) 1296–1305 1297

The ultimately compressed layer has a uniform structure withthe same porosity e (or solidosity j) dependent upon theapplied compressive pressure ps. This procedure is well adoptedfor the determination of j(ps) relation, for example, in theconstitutive Eq. (1). However, determination of k(ps) or a(ps)relations (constitutive Eqs. (2) and (3)) is based on very longpermeability experiments with liquid flowing through the pre-viously consolidated layer. To avoid the long permeability experi-ments, different models relating the layer permeability k withthe porous structure, such as Kozeny–Carman and Happel–Brennermodels (Happel and Brenner, 1965), can be used. Inverse methodcan also be applied for determination of particulate layercharacteristics from the solution of theoretical consolidationequation (Iritani et al., 2009).

Different methods such as use of pressure sensors, NMR,gamma and X-ray devices (Fathi-Najafi and Theliander, 1995; LaHeij et al., 1996; Sedin et al., 2003) were recently tested forimprovement of the CP chamber procedure. Nevertheless, utiliza-tion of CP chamber has several drawbacks: experiments are verylong (sometimes several days are needed for attainment of theultimate layer compression); using of only one sample in CPchamber; side-wall friction effect between the piston and cylin-der (Wakeman, 1978).

Low-pressure compressibility of particulate layer can be esti-mated from the gravity consolidation experiments (Shirato et al.,1970b, Iritani et al., 2009). Centrifugal settling methods can beadvantageous as compared to gravity consolidation: severalsamples may be studied simultaneously and different centrifugalaccelerations may be varied in the wide range corresponding todifferent compressive pressures. Murase et al. (1989) had pro-posed a procedure for estimation of the parameters of constitu-tive Eq. (1) (presented in a simplified form j¼joðps=paÞ

b) basedon compression experiments with different centrifugal accelera-tions. Dependence of the equilibrium average solidosity oncentrifugal acceleration was also studied by Green et al. (1996)and Lee et al. (2003) for estimation of the compressive yield stressof sediments.

Recently, a new tool was developed for centrifugal sedimenta-tion. It is so-called, analytical photocentrifuge (Lerche, 2002;Lerche and Sobisch, 2007). This technique was applied forestimation of colloidal stability of mineral suspensions (Sobischand Lerche, 2000; Kuentz and Rothlisberger, 2003; Mende et al.,2007; Badolato et al., 2008), determination of the particle sizedistribution (Detloff et al., 2007), determination of the dispersa-bility of carbon nanotubes in aqueous surfactant solutions(Krause et al., 2009), characterization of sludge dewatering (VonHomeyer et al., 1999; Sobisch and Lerche, 2004), consolidation,packing and compression behavior (Sobisch et al., 2006a; Lercheand Sobisch, 2007; Sobisch and Lerche, 2008), quantification ofthe particle porosity (Sobisch et al., 2006b), particle interactionand particle aggregation (Lerche and Fromer, 2001).

The analytical photocentrifuge was recently used for estima-tion of the specific cake resistance a on the basis of sedimentconsolidation experiments and Happel’s relation for a(e) (Iritaniet al., 2007). Curvers et al. (2009) proposed a procedure for theestimation of the parameters of constitutive Eq. (1) using theanalytical photocentrifuge. This new tool opens interesting pro-spects for rapid determination of the CP characteristics of mineralsediments.

Our paper presents the overall procedure for determination ofthe main CP characteristics of sediments (j, k, a, G, C) usinganalytical centrifugation. In this work, the CP characteristics ofsediments were initially estimated by direct method (usingconstitutive Eqs. (1)–(3)), then compared with ones estimatedby inverse method (using theoretical consolidation equation) andby filtration experiments.

2. Materials and methods

2.1. Materials

The aqueous suspension of calcium carbonate with solidcontent of 19.8 wt% (particle volume fraction j¼0.0827) wasprovided by OMYA (France). The density of CaCO3 particles rs wasequal to 2730 kg/m3.

The volume-based function of particle size distribution SDF (%)and specific surface area of particles in suspension S weremeasured using an analytical photocentrifuge LUMiSizer 610.0–135 (L.U.M. Gmbh, Germany). Rectangular plastic optical cells,supplied by the photocentrifuge manufacturer, with the opticalpath length of 10 mm and cross-sectional area of 710–5 m2,were used. The measurements required considerable dilution ofthe suspension (down to 104 wt%). SDF and S were calculatedusing the original software SEPView 5.1 (L.U.M. Gmbh, Germany)for granulometric analysis. The SDF of calcium carbonate versusparticle diameter d is presented in Fig. 1. The measured values ofspecific surface area S and mean diameter of particles dm are2.270.2 m2/g and 1.170.4 mm, respectively.

2.2. Analytical centrifugation

Twelve samples of aqueous suspension with initial mass of1.81 g and volume fraction j of 0.0827 were subjected toconsolidation in an analytical photocentrifuge LUMiSizer 610.0–135 (L.U.M. Gmbh, Germany). Rectangular plastic optical cells,supplied by the photocentrifuge manufacturer, were used. Theoptical path length was 10 mm and cross-sectional area was710–5 m2.

The schema of centrifugal experiments is presented in Fig. 2.The radial distance of the centrifugal cell bottom from the axis ofrotation R was equal to 0.13 m. The initial height of the sample inthe cell Hi was equal to 2.2710–2 m. Centrifugation experimentswere carried out at different rotor speeds O in the interval of240–4000 rpm. The corresponding centrifugal accelerations at thebottom of the cell were within (8.3–2320)g, where g¼9.81 m/s2 isthe gravity acceleration.

t

H

H0

H∞

320 rpm 4000 rpm

R

Hi

H∞

H0

Initial suspension

Before consolidation

After consolidation

Pre-consolidation Consolidation

Fig. 2. Schema of the consolidation experiment. After the stage of pre-consolidation at low rotation speed O¼320 rpm (E14.9g), the sediment compresses at higher

rotation speed (here O¼4000 rpm) and its height H decreases from the initial (Ho) to the final (HN) value.

H∞

Δi, i = (ps,i)

Δi + 1, i + 1 = (ps,i+1)

Δi-1, i-1 = (ps, i-1)

Compressed sediment

o

= 0

M. Loginov et al. / Chemical Engineering Science 66 (2011) 1296–13051298

The experiments were done using pre-consolidated sedimentsdirectly prepared inside the centrifugal cells from the initial suspen-sions. Pre-consolidation of the initial suspensions was done at asufficiently low rotation speed O of 320 rpm (E14.9g) during60 min. It resulted in formation of sediment with the initial heightHoE1.610–2 m and flat vertical interface between solids andsupernatant. The rotor speed variation within 240–460 rpm(8.3g30.1g) had no noticeable impact on kinetics of the followingconsolidation. Then rotation speed O was increased to a higher level(10004000 rpm), and consolidation experiment was carried out ata constant value of O. The radial position of the sediment surfacewas measured and evolution of the sediment height H (m) with timet (s) was recorded during the consolidation experiment. Experi-ments were finished when the constant equilibrium sedimentheight HN was reached (Fig. 2).

All the experiments were done at the constant temperature25 1C and were replicated, at least, three times. The mean valuesand the standard deviations were calculated. The error bars infigures correspond to the standard deviations.

Fig. 3. Schematic presentation of the material coordinate o. Volume fraction of

solids ji is constant within the certain finite element Do and is related to solid

pressure ps according to the constitutive equation ji¼j (ps).

2.3. Estimation of CP characteristics from analytical centrifugation

experiments

Numerical method of Curvers et al. (2009) was used in ourwork for estimation of parameters in the constitutive Eq. (1). Theinput data for this method gives the equilibrium sediment heightHN dependence on rotation speed O. The outputs of this methodare parameters of the Eq. (1) relating the local solid pressure ps

and the local volume fraction j in the sediment.The calculation uses a one-dimensional material coordinate o

instead of Euclidian coordinate H. Material coordinate o isdefined as the height of solids (that is the volume of solidsdivided by the cross-sectional area) measured from the bottomof the sediment. The height of the sediment HN corresponds tothe maximal value of material coordinate oo (Fig. 3). According tothis method, the total height of the sediment is divided in N finiteelements having the height Do¼oo/N (see Fig. 3). The volumefraction of particles j and the solid pressure ps are assumedconstant within each finite element.

The value of jo in the constitutive Eq. (1) was estimated fromthe gravitation sedimentation experiments and was set to0.085970.0009. For pa and b estimation, the numerical algorithmproposed by Curvers et al. (2009) with N¼200 was used.

The specific filtration resistance a of the sediment was thencalculated as (Wakeman and Tarleton, 1999)

a¼ 1=ðkrsjÞ ð5Þ

where k is the local permeability of the sediment defined as(Happel and Brenner, 1965)

k¼1

ðrsSÞ2U

69j1=3þ9j5=36j2

jð3þ2j5=3Þð6Þ

Substitution of Eqs. (1) and (6) into Eq. (5) yields local valuesof specific resistance a at various solid pressures ps. Now validityof the constitutive Eq. (3) can be verified.

The local consolidation coefficient C¼C(ps) was calculatedusing Eq. (4). Another constitutive equation was used in thiswork for C¼C(ps) in order to fit the calculated C(ps) dependence

C ¼ Coð1þps=poÞg

ð7Þ

where Co, po and g are the empirical constants. Note that at psbpo

Eq. (7) may be reduced to

C ¼ Cupgs ð8Þ

where C0ECo/pog.


2.4. Estimation of CP characteristics by inverse method using

solution of consolidation equation

Dewatering of consolidated sediment is controlled by Darcy’slaw (Shirato et al., 1970a; Iritani et al., 2009)

u¼1

mars

@pl

@o ð9Þ

where u is the upward liquid velocity, pl is the excess hydraulicpressure, m is the viscosity of liquid, a is the specific resistance ofthe sediment, rs is the density of particles and o is the materialcoordinate measured from the bottom of the sediment. Here pl

may be calculated from the force balance over the differentialelement of the sediment do (Leung, 1998)

@pl

@o þ@ps

@o ¼ðrsrlÞRO2

ð10Þ

where ps is the solid pressure and RO2 is the centrifugalacceleration.

The continuity equation is expressed as (Shirato et al., 1970a)

@u

@o ¼@e

@tð11Þ

The first differentiation of Eq. (9) with respect to o andsubsequent combination with Eqs. (10) and (11) results in thebasic consolidation equation (Shirato et al., 1970b)

@ps

@t¼ G

@

@o1

amrs

@ps

@o

ð12Þ

where the compressibility modulus G is defined as G¼qps/qe

(Vorobiev and Fedotkin, 1984).In Eq. (12), G¼G(ps), a¼a(ps). However, quite frequent is the

assumption that both G and a may be treated as constants formoderately compressible materials (Shirato et al., 1987; Iritaniet al., 2009). Therefore, Eq. (12) may be represented as (Shiratoet al., 1970a; Iritani et al., 2009)

@ps

@t¼ C

@2ps

@o2ð13Þ

where C is defined as in Eq. (4).Eq. (12) can be solved with the next initial and boundary

conditions, related to the centrifugal consolidation (Shirato et al.,1970b; Iritani et al., 2009)

ps ¼ 0 at t¼ 0 ð13:1Þ

ps ¼ 0 at o¼oo ðat the surface of a sedimentÞ ð13:2Þ

@ps

@o ¼ðrsrlÞO2R at o¼ 0 ðat the bottom of a sedimentÞ

ð13:3Þ

Solving Eq. (13) with conditions (13.1)–(13.3), one obtains ananalytical solution (Carslaw and Jaeger, 1959)

ps ¼ ðrsrlÞRO2oo ð1o=ooÞ

8

p2

X1m

ð1Þm1

ð2m1Þ2sinð2m1Þp

2ð1o=ooÞ

"

exp ð2m1Þ2p2

4

Ct

o2o

( )!#ð14Þ

Eq. (14) has the same form as the solution obtained by Iritaniet al. (2009) for the gravity consolidation.

Then, time dependence of the consolidation ratio U (relativechange in the height of the consolidated sediment) can be

calculated as (Iritani et al., 2009)

U ¼ ðHoHÞ=ðHoH1Þ ¼

Z t

0uoðpsÞdt

Z 10

uoðpsÞdt ð15Þ

where uo is the apparent upward liquid velocity at the surface ofthe sediment (o¼oo). Now Eq. (15) gives (Iritani et al., 2009)

U ¼ 132

p3

X1m

ð1Þm1

ð2m1Þ3exp

ð2m1Þ2p2

4

Ct

o2o

!ð16Þ

Eq. (13) and its analytical solutions (14) and (16) are valid inapproximation of C remaining constant during the consolidation–sedimentation process. However, the consolidation coefficient ispressure dependent, C¼C(ps), and increases throughout the con-solidation time (Shirato et al., 1970b). So, Eq. (13) may be usedonly as approximation with a proper mean value of C (Shiratoet al., 1970a). In this work the pressure dependence of C wasapproximated by the power law equation (7). The finite differencesolution method was used for solving Eq. (13) with the boundaryconditions (13.1)–(13.3) and power-law approximation (Eq. (7))was supposed. The details of this method are presented in theAppendix A.

2.5. Estimation of specific cake resistance from filtration

experiments

The average specific resistance aav of calcium carbonate cakewas experimentally estimated using the filtration cell Amicon8200 (Millipore, USA). The nylon membrane with pore size0.2 mm (Biodyne A, Pall Co) was used as a filter medium. Ruth–Carman’s equation was applied for calculation of aav (Wakemanand Tarleton, 1999)

t

V¼

aavrlmws

2A2Dpð1ws=wcÞVþRm

mADp

ð17Þ

where Dp is the filtration pressure difference, rl and m are densityand viscosity of filtrate, respectively, ws is the weight fraction ofsolids in suspension, wc is the weight fraction of solids in thefilter cake, A is the filter medium surface area, Rm is hydraulicresistance of the filtration medium, and t and V are filtration timeand filtrate volume, respectively. The calculated value of aav

corresponds to a certain average solid pressure ps in the filtercake. The average value of solid pressure in the filter cake may beestimated from the liquid pressure redistribution in the filter cake(Vorobiev, 2006)

pl

pa¼ 1þ

Dp

pa 1þ

Dp

pa

1n

1

" #1

x

L

þ1

( )1=ð1nÞ

ð18Þ

where x is the coordinate and L is the filter cake thickness. Thenps¼Dppl and the average solid pressure in the filter cake may beestimated as

ps ¼pa

ð1þDp=paÞ1n1

U1n

2nU ð1þDp=paÞ

2n1

h i1 ð19Þ

Note that this equation may be reduced to a more simple formfor non-compressible sediments (at n51)

ps ¼Dp=2 ð20Þ


3.1. CP characteristics of calcium carbonate sediment obtained from

ultimate settling experiments

Fig. 4 shows dimensionless equilibrium sediment height HN/Ho

as a function of rotational speed O. Experimental data (symbols)


were used as input in application of the numerical method ofCurvers et al. (2009) for estimation of parameters in the constitutiveEq. (1). The presented solid line is the result of calculations. Theobtained parameters of the constitutive Eq. (1) are pa¼70.970.9 Paand b¼0.177770.0005 for the solid pressure region 5 kParpsr75kPa. A relatively low value of b (b0.15) suggests that the studiedsediment is moderately compressible (Tiller and Leu, 1980). Theestimated value of b falls within the range of bE0.07–0.20,obtained for aqueous suspensions of CaCO3, calcium silicate andkaolin (Sedin et al., 2003; Johansson and Theliander, 2007; Teohet al., 2006b). Inset in Fig. 4 shows the local module of compressi-bility G calculated versus solid pressure ps.

Fig. 5 shows the local specific resistance a and local consolidationcoefficient C versus solid pressure ps. The value of a is calculated

0 1000 2000 3000 40000.2

0.4

0.6

0.8

1

H∞

/ H

0 [–

]

102 104

102

104

ps [Pa]

G [

Pa]

slope = 1.18

[rpm]

Fig. 4. Dimensionless equilibrium sediment height HN/Ho versus rotational speed

O. Symbols are experimental data, solid line was obtained by data fitting with

application of the numerical method proposed by Curvers et al. (2009). Insert shows

calculated local module of sediment compressibility G versus local solid pressure ps.

0 20000 40000 600000

1

2

3

4

5

6

7

0

0.2

0.4

0.6

0.8

1

C [

10–6

, m2 /s

]

[1

010, m

/kg]

ps [Pa]

C

Fig. 5. Local specific resistance a and local consolidation coefficient C versus solid

pressure ps. The dependence of a(ps) was calculated from Eqs. (5) and (6) (symbols),

solid line is the result of least square fitting by the constitutive Eq. (3). The C(ps)

dependence was estimated from a(ps) and j(ps) with the help of Eq. (4) (symbols).

The solid line is the result of least square fitting by the power law Eq. (7).

from Eqs. (5) and (6). Note that for estimation of k and a we used thevalue of the specific surface area of particles S¼2.2 m2/g measuredusing LumiSizer.

Tiller’s power law Eq. (3) was also used for approximation of a(ps)dependence. Taking in account that ko¼2.510–13 m2 at jo¼0.0859(Eq. (2)), we estimated that ao¼1.71010 m/kg (Eq. (3)). The leastsquare fitting yields pn¼645755 Pa, n¼0.25970.005 with correla-tion coefficient r of 0.996.

Finally, a(ps) and j(ps) data were used in Eq. (4) for estimation ofthe local consolidation coefficient C (Fig. 5). Fitting of the calculatedC(ps) dependence with the help of Eq. (7) yields the followingparameters: Co¼7.310–10 m2/s, po¼34.371.5 Pa, g¼0.9170.04with correlation coefficient r¼0.995. Since estimated value of po ismuch lower than values of ps used in our experimental study, po5ps,the calculated dependence C(ps) may be fitted by means of Eq. (8)with fitting parameters C 0 ¼(2.970.3)10–11 m2/(s Pa0.91) andg¼0.9170.04 and correlation coefficient r¼0.995.

3.2. CP characteristics of calcium carbonate sediment obtained from

solution of consolidation equation

Fig. 6 presents experimental results (symbols) for the timedependence of consolidation ratio U¼(HoH)/(HoHN) at differ-ent values of the angular speed of centrifugal rotation O. In thisfigure, solid lines correspond to the best fitting of experimentaldata by the analytical solution (16). The correlation coefficientswere rather low (within the range of 0.9710.987), so, theexperimental data could not be fitted satisfactory by means ofEq. (16). Fig. 7 presents the same experimental data fitted usingthe fitting function (Eq. (A1)); here, correlation coefficients rwere considerably higher (within the range of 0.995–0.999). Itevidences in favor of the model with pressure-dependent con-solidation coefficient and application of numeric procedure foranalysis of consolidation kinetics.

Fig. 8 shows parameters of Eq. (A1) a(O) and b(O) versus theinverse angular speed of centrifugal rotation O1 estimated fromthe experimental data presented in Fig. 7. The dependences of botha(O) and b(O) evidence that predicted relations, described by Eqs.(A2) and (A4), can be fairly used for fitting the experimental data.

101 102 1030

0.2

0.4

0.6

0.8

1

U [

−]

, rpm C/ωo, s-1

-1000 0.0092-2000 0.0195-3000 0.025-4000 0.027

2

t [s]

Fig. 6. Consolidation ratio U versus sedimentation time t at different values of

angular speed of centrifugal rotation O. Symbols are experimental data and solid

lines were obtained using the least square fitting by Eq. (16). The best values of

parameters C=o2o are presented.

1010

0.2

0.4

0.6

0.8

1

U [

−]

-1000-2000-3000-4000

t [s]102 103

, rpm

Fig. 7. Consolidation ratio U versus sedimentation time t at different values of the

angular speed of centrifugal rotation O. Symbols are experimental data, and solid

lines were obtained by fitting these data using Eq. (A1).

10-3 10-2

101

102

0.002 0.004 0.006 0.008 0.01

1

1.5

2

2.5

a [s

]b

[−]

Slope = 1.33 ± 0.06

–1 [s/rad]

–1 [s/rad]

Fig. 8. Experimentally derived parameters a and b versus inverse angular speed of

centrifugal rotation O1.

0 20000 40000 60000 800000

0.2

0.4

0.6

0.8

1

1*

2

1

C [

10–6

, m2 /s

]

ps [Pa]

Fig. 9. Consolidation coefficient C versus solid pressure ps estimated by the first

(1, 1n) and second (2) approaches. The dashed line (1n) corresponds to the

corrected data accounting for the error in determination of the specific surface

area of particles.


Such satisfactory description of the experimental data evidences infavor of approximations used in Eqs. (7), (9) and (13).

The exponent g1¼1.3370.04 was obtained from fitting of theexperimental dependence of a(O1) by Eq. (A2).Then exponent gin the power law model (Eq. (7)) was estimated from Eq. (A3) asg¼0.8570.03. Fitting of the experimentally derived dependenceof b(O–1) by the linear equation

b¼ k1eþk2eO1

ð21Þ

gave k1e¼0.7170.02 and k2e¼16374.

From the other side, fitting of theoretically derived depen-dence of b(O–1) by linear equation Eq. (A4) at the given value ofg¼0.8570.03 resulted in k1t¼0.7270.04 and k2t¼2.9370.06.Note that consistency between k1t and k1e was within the errorsof estimations. Equalization of k2e and k2t

ffiffiffiffiffiffiffiffiffiffipo=f

pallowed estima-

tion of po as 12507100 Pa. Then adjustment of theoretical andexperimental a(O–1) dependences at the given values ofg¼0.8570.03 and po¼12507100 Pa yields to¼225728 andCo ¼o2

o=to ¼ ð1:570:3Þ 108 m2=s. Note that psbpo in theexperimentally studied range of solid pressures and Eq. (7) maybe reduced to Eq. (8) with the fitting parameters C0ECo/po

g¼

(3.571.0)10–11 m2/(s Pa0.85) and g¼0.8570.03.

4. Discussion and concluding remarks

The discussed two approaches can be used for estimation of CPcharacteristics of the sediments. The first approach is based onanalysis of the equilibrium height of sediment HN versus rotationspeed O (Curvers et al., 2009). It allows estimation of the particlevolume fraction j profiles in the layer ultimately consolidatedunder the given pressure ps. Then parameters of the constitutiveEqs. (1)–(3) and (7)–(8) can be determined. The obtained depen-dence C(ps) is presented by solid line 1 in Fig. 9.

The second approach is based on determination of the experi-mental consolidation ratio U(t)¼(Ho–H)/(Ho–HN) at different rota-tion speeds O and its comparison with the theoretical consolidationratio obtained from solution of consolidation equation. Thisapproach assumes validity of the simplified form of consolidationEq. (13) resulting from Terzaghi model (Shirato et al., 1970a) andutilizes numerical calculations accounting for the pressure depen-dence of a local consolidation coefficient C(ps). Validity of the simplepower law relation (8) was demonstrated and the following para-meters for the calcium carbonate sediments were obtained:C0 ¼(3.571.0)10–11 m2/(s Pa0.85), g¼0.8570.03. The calculatedC(p) dependence is presented by solid line 2 in Fig. 9.

However, as Fig. 9 shows, the first approach gives considerablylarger values of C as compared with the second approach. Thisdiscrepancy is not surprising accounting for the number of


approximations used. For example, the first approach assumesvalidity of Happel’s Eq. (6) for the local permeability k of sediments.Moreover, we used specific surface area of particles S estimated fromgranulometric experiments, which is usually underestimated ascompared with the surface area determined from hydraulic perme-ability experiments (Konert and Vandenberghe, 1997). For theparticles with non-spherical shape or rough surface, the correctioncoefficient n (S-n S, n41) may be rather high. This underestimationmay result in underestimation of the specific resistance a (ap1/n2,see Eqs. (5) and (6)) and overestimation of the consolidationcoefficient C (Cpn2 Eq. (4)).

For the adjustment of C(ps) behavior estimations by differentapproaches, we used only one fitting parameter n2, accounting forcorrection of the specific surface area of particles. The corrected C(ps)dependence is presented by dashed line (1n) in Fig. 9. The best fitresulted in n¼1.2370.02 with correlation coefficient r¼0.998. Wesee that corrected C(ps) dependence (line 1n), obtained by the firstapproach, is in good correspondence with C(ps) dependence,obtained by the second approach (line 2). It reflects good applic-ability of the power law relation (8) to data obtained by bothapproaches with the same parameters C0 and g. It was shown earlierthat the power law relation (8) can approximate the experimentaldata for different filter cakes (Vorobiev et al., 1993; Zaiats et al.,1993). So, the two independent approaches evidenced the presenceof the simple scaling law relating the consolidation coefficient C andthe solid pressure ps (Eq. (8)) with practically the same scalingexponent gE0.8570.03.

It is possible to use the developed method for better estima-tion of specific cake resistance a. Fig. 10 presents example of a(ps)dependence calculated from Eqs. (1), (5) and (6). Here, the solidand dashed lines correspond to the uncorrected (So¼2.2 m2/g)and corrected (So¼v 2.2 m2/g, nE1.23) data, respectively. Theconstitutive Eq. (3) can be used for approximation of a(ps) withthe following parameters: ao¼1.71010 m/kg (Eq. (18)),n¼0.25970.005, pn¼645755 Pa (uncorrected) or ao¼2.61010

m/kg (corrected). The correlation coefficient of such estimation isr¼0.996.

0 20000 40000 600000

5

10

15

20

[1

010, m

/kg]

ps [Pa]

Fig. 10. Local specific resistance a versus solid pressure ps. The a(ps) dependence

was calculated from Eqs. (1), (5) and (6). Here, the solid and dashed lines

correspond to the uncorrected (S¼2.2 m2/g) and corrected (S¼v 2.2 m2/g,

nE1.23)) data, respectively. Symbols correspond to the experimental data

estimated from filtration experiments, the average solid pressure in the filter

cake was calculated by Eq. (19) (filled symbols) and Eq. (20) (open symbols).

The values of specific cake resistance a were independentlyestimated from the filtration experiments with the filter cellAmicon 8200. The values of average specific cake resistance aav

were calculated from Ruth–Carman Eq. (17). The average solidpressure in the filter cakes was calculated using Eqs. (19)and (20).

These values of aav (symbols in Fig. 10) were noticeablyhigher than the values predicted from Eqs. (1), (5) and (6) withuncorrected So¼2.2 m2/g (solid line in Fig. 10) and were in bettercorrespondence with the corrected values of a with So¼v 2.2m2/g, nE1.23 (dashed line in Fig. 10). However, despite of thiscorrection, the differences between the values of a estimatedfrom centrifugal consolidation experiments and measured valuesof aav were still noticeable. Overestimation of aav values can beexplained by application of the simplified Eq. (17) for analysis offiltration data (Teoh et al., 2006a). Moreover, these differencesmay also originate from the various complex effects related with‘‘cell wall’’ factor (Tiller et al., 1972), presence of creep (Cristensenand Kieding, 2007) and resistance of filtration membrane (Teohet al., 2006b), which were neglected in present analysis.

In summary, two independent methods were used for estima-tion of the low-pressure compression–permeability characteris-tics of sediments These approaches are based on (1) analysis ofthe equilibrium height of sediment HN versus centrifugal rotationspeed O and (2) analysis of kinetic curves of the consolidationratio U(t) at different rotation speeds O. It was shown thatconsolidation curves may be fitted satisfactory by two-parame-trical Eq. (A1). These allowed estimation of dependence C¼C(ps).The two independent approaches (1) and (2) evidenced thepresence of the scaling law relating the consolidation coefficientC and solid pressure ps, Cpps

g with practically the same scalingexponent gE0.8570.03 (for the studied solid pressure region5 kParpsr75 kPa). Proposed procedure may be useful for ana-lysis of the CP characteristics of sediments using analyticalphotocentrifuge.

Nomenclature

Symbols

A membrane surface area, m2

a parameter of Eq. (A1), sb parameter of Eq. (A1), dimensionlessC consolidation coefficient, m2/sC0 parameter of Eq. (8), m2/(s Pag)Co parameter of Eq. (7), m2/sd diameter of particles, mmdm mean diameter of a particles, mme void ratio, dimensionlessf ¼(rsrl)Roo, kg/mG compressibility modulus, Pag gravitational acceleration, 9.81 m/s2

H height of sediment in centrifugal cell, mHi initial height of suspensions in centrifugal cell, mHo height of sediment in centrifugal cell before consoli-

dation, mHN equilibrium height of sediment in centrifugal cell after

consolidation, mk local permeability of sediment, m2

k1e, k2e parameters of Eq. (21)k1t, k2t parameters of Eq. (a4)ko parameter in constitutive Eq. (2), m2

L thickness of filter cake, mN number of finite differences used, dimensionlessn parameter in Eq. (3), dimensionless

10-2 10-1 1000

0.2

0.4

0.6

0.8

1

t/o [−]

U [

−]

0.50.2

0

= 1.0

Fig. A1. Consolidation ratio U versus reduced time tn¼t/to, where to ¼o2o=Co at

different values of g and constant value of po=ðfO2Þ ¼ 0:01. Symbols correspond to

numerical solution of Eqs. (13)(13.3) with the pressure dependent C described

by Eq. (7); solid lines were obtained by fitting these data by Eq. (16).


p applied pressure, Papa parameter in constitutive Eq. (1), Papk parameter in constitutive Eq. (2), Papl local liquid pressure, Papn parameter in constitutive Eq. (3), Papo parameter of Eq. (7), Paps local solid compressive pressure, Paps average solid compressive pressure, PaDp filtration pressure, PaR radial distance from the center of rotation to bottom of

centrifugal cell, mS specific surface area of CaCO3 particles, m2/gt time, stn ¼t/to, reduced time, dimensionlessU consolidation ratio, dimensionlessx coordinate, m

Greek letters

a local specific resistance, m/kgaav average specific resistance, m/kgao empiric constant in Eq. (3), m/kgb parameter in constitutive Eq. (1), dimensionlessg parameter in Eq. (7), dimensionlessg1 parameter in Eqs. (A2) and (A3), dimensionlessd parameter in Eq. (2), dimensionlesse local porosity, dimensionlessm viscosity of liquid, Pa sn correction coefficient for specific surface area, dimen-

sionlessr correlation coefficient, dimensionlessrl density of liquid, kg/m3

rs density of CaCO3, kg/m3

t consolidation time factor, sto ¼o2

o=Co, sj volume fraction of particles, dimensionlessjo parameter in Eq. (1), dimensionlessO angular rotational speed, rad/so height of solids measured from the bottom of the

sediment, moo total height of solids in the sediment, m

Abbreviations

CP compression–permeabilitySDF volume-based size distribution function, %

Acknowledgement

The authors would like to acknowledge OMYA for providingraw materials for this study.

Appendix A

A.1. Details of the finite difference solution method used for solving

the Eq. (12) with the power law dependence C(ps) (Eq. (7)).

The value of oo was divided into 64 grids (Do¼oo/64) andpressure ps,i was calculated in all the grid points. At each timestep, the value of C was averaged and calculated as C ¼

1=64P64

i ¼ 1 Cðps,iÞ. The convergence of the numerical scheme was

maintained by sufficiently small level of Courant number Cr¼CDt/

Do2¼0.01, where Dt is the time step (Smith, 1977).

As far as in our experiments RbHo (0.13 mb1.610–2 m),the centrifugal acceleration inside the sediment was assumed tobe constant and was calculated as O2R, where O is the angularrotational speed.

Fig. A1 presents examples of the time dependence of consolida-tion ratio U(t) obtained by numerical solution of Eqs. (13) with theboundary conditions (13.1)–(13.3) for the pressure and time depen-dent consolidation coefficient C(ps) (symbols). Consolidation ratio U

is plotted versus reduced time tn (defined as tn¼t/to) for differentvalues of g and constant value of po=fO2. Here to ¼o2

o=Co is theconsolidation time factor, and f¼(rsrl)Roo.

The direct using of Eqs. (7), (13) and (13.1–13.3) for fitting ofthe experimental U(t) data requires a rather complex non-linearfitting procedure and can result in an inaccurate estimation of theparameters po and g in Eq. (7). To avoid this difficulty, the two-parametric function

UðtÞ ¼ 1expðt=aÞ

1b1ð1expðt=aÞðA1Þ

was used in this work for the curve-fitting of U(t) data. Here a andb are the parameters. This function increases monotonically fromU¼0 at t¼0 to U¼1 at t¼N. It was used as an approximation fordescription of the consolidation–sedimentation kinetics.

The solid lines in Fig. A1 were obtained using Eq. (A1) for theleast square fitting of the numerical U(t) data. The correlationcoefficients r were rather high (r40.9999); it evidences in favorof the applied approximation. The tabulated parameters a and b

may be useful for analysis of the experimental U(t) data atdifferent O.

Fig. A2 presents dependencies of the parameters a/to (a) andb (b) versus the dimensionless parameter O1


pat different

values of g. The obtained results evidence that a(O) dependence(Fig. A2(a)) can be fairly approximated (with correlation coeffi-cients r40.9996) by the power equation

apOg1 ðA2Þ

10-2 10-1 100

10-2

10-1

0.00.10.20.30.61.0

0 0.2 0.4 0.6 0.8 1

2

4

6

8

a/ o

[−]

b [−

]

γ

[−]po / f−1

[−]po / f−1

Fig. A2. Parameters a/to and b versus dimensionless parameter O1ffiffiffiffiffiffiffiffiffiffipo=f

pat

different values of g. The values of a/to and b were obtained from fitting of the

numerically derived U(t) data. Here to ¼o2o=Co .


where exponents g and g1 are related as

g¼m1g1ð1þm2g1Þ ðA3Þ

Here m1¼0.5370.02 and m2¼0.1570.03 were obtained by theleast square fitting procedure and correlation coefficient r was0.9993.

From the other side, parameter b increases approximatelylinearly with increase of O1:

b¼ k1tþk2t


qO1

ðA4Þ

and decreases with increase of g (Fig. A2(b)). Here, k1t and k2t areadjustable parameters, which are dependent upon g.

So the dependences of both a and b parameters versus theangular speed of centrifugal rotation O may be described byrather simple laws represented by Eqs. (A2)–(A4). We used thisapproach for simplification of numerical analysis of the experi-mental U(t) data on and estimation of the parameters Co, po and gin Eq. (7).

References

Badolato, G.G., Aguilar, F., Schuchmann, H.P., Sobisch, T., Lerche, D., 2008.Evaluation of long term stability of model emulsions by multisample analy-tical centrifugation. Progress in Colloid and Polymer Science 134, 66–73.

Carman, P.C., 1938. Fundamental principles of industrial filtration. Transactions ofthe Institution of Chemical Engineers 16, 168–188.

Carslaw, H.S., Jaeger, J.C., 1959. Conduction of Heat in Solids. Clarendon Press, Oxford.Cristensen, M., Kieding, K., 2007. Creep effect in activated sludge filter cakes.

Powder Technology 177, 23–33.Curvers, D., Saveyn, H., Scales, P.J., Van der Meeren, P., 2009. A centrifugation

method for the assessment of low pressure compressibility of particulatesuspensions. Chemical Engineering Journal 148 (2–3), 405–413.

Detloff, T., Sobisch, T., Lerche, D., 2007. Particle size distribution by space or timedependent extinction profiles obtained by analytical centrifugation (concen-trated systems). Powder Technology 174, 50–55.

Fathi-Najafi, M., Theliander, H., 1995. Determination of local filtration propertiesat constant pressure. Separations Technology 5 (3), 165–178.

Grace, H.P., 1953. Resistance and compressibility of filter cakes. Chemical Engi-neering Progress 49, 303–318.

Green, M.D., Eberl, M., Landman, K.A., 1996. Compressive yield stress of flocculatedsuspensions: determination via experiment. AIChE Journal 42 (8), 2308–2317.

Happel, J., Brenner, H., 1965. Low Reynolds Number Hydrodynamics. Prentice-HallInc, Eaglewood Cliffs, USA.

Iritani, E., Katagiri, N., Aoki, K., Shimamoto, M., Yoo, K.-M., 2007. Determination ofpermeability characteristics from centrifugal flotation velocity of deformableoil droplets in O/W emulsions. Separation and Purification Technology 58 (2),247–255.

Iritani, E., Hashimoto, T., Katagiri, N., 2009. Gravity consolidation–sedimentationbehaviors of concentrated TiO2 suspension. Chemical Engineering Science 64(21), 4414–4423.

Johansson, C., Theliander, H., 2007. Validation of predicted local profiles in cakefiltration. Chemical Engineering Research and Design 85 (2), 220–228.

Koenders, M.A., Wakeman, R.J., 1996. The initial stages of compact formation fromsuspensions by filtration. Chemical Engineering Science 51 (16), 3897–3908.

Konert, M., Vandenberghe, J.E.F., 1997. Comparison of laser grain size analysis withpipette and sieve analysis: a solution for the underestimation of the clayfraction. Sedimentology 44, 523–535.

Krause, B., Petzold, G., Pegel, S., Potschke, P., 2009. Correlation of carbon nanotubedispersability in aqueous surfactant solutions and polymers. Carbon 47 (3),602–612.

Kuentz, M., Rothlisberger, D., 2003. Rapid assessment of sedimentation stability indispersions using near infrared transmission measurements during centrifu-gation and oscillatory rheology. European Journal of Pharmaceutics andBiopharmaceutics 56 (3)355361.

La Heij, E.J., Kerkhof, P.J.A.M., Kopinga, K., Pel, L., 1996. Determining porosityprofiles during filtration and expression of sewage sludge by NMR imaging.AIChE Journal 42 (4), 953–959.

Lee, S.J., Chu, C.P., Tan, R.B.H., Wang, C.H., Lee, D.J., 2003. Consolidation dewateringand centrifugal sedimentation of flocculated activated sludge. ChemicalEngineering Science 58 (9), 1687–1701.

Lerche, D., Fromer, D., 2001. Theoretical and experimental analysis of thesedimentation kinetics of concentrated red cell suspensions in a centrifugalfield: determination of the aggregation and deformation of RBC by flux densityand viscosity functions. Biorheology 38 (2–3), 249–262.

Lerche, D., 2002. Dispersion stability and particle characterisation by sedimenta-tion kinetics in a centrifugal field. Journal of Dispersion Science and Technol-ogy 23, 699–709.

Lerche, D., Sobisch, T., 2007. Consolidation of concentrated dispersions of nano-and microparticles determined by analytical centrifugation. Powder Technol-ogy 174, 46–49.

Leung, W.W.-F., 1998. Industrial Centrifugation Technology. McGraw-Hill, NY.Mende, M., Schwarz, S., Petzold, G., Jaeger, W., 2007. Destabilization of model silica

dispersions by polyelectrolyte complex particles with different charge excess,hydrophobicity, and particle size. Journal of Applied Polymer Science 103 (6),3776–3784.

Murase, T., Iwata, M., Adachi, T., Gmachowski, L., Sirato, M., 1989. An evaluation ofcompression–permeability characteristics in the intermediate concentrationrange by use of centrifugal and constant-rate compression techniques. Journalof Chemical Engineering of Japan 22, 378–384.

Okamura, S., Shirato, M., 1955. Liquid pressure distribution within cakes in theconstant pressure filtration. Kagaku Kogaku 19, 104–120.

Rushton, A., Ward, A.S., Holdich, R.G., 1996. Solid–Liquid Filtration and SeparationTechnology. VCH Publishers, Weinheim.

Ruth, B.F., 1946. Correlating filtration theory with industrial practice. Industrialand Engineering Chemistry 38 (6), 564–571.

Sedin, P., Johansson, C., Theliander, H., 2003. On the measurement and evaluationof pressure and solidosity in filtration. Chemical Engineering Research andDesign 81 (10), 1393–1405.

Shirato, M., Murase, T., Negawa, M., Senda, T., 1970a. Fundamental studies ofexpression under variable pressure. Journal of Chemical Engineering of Japan3 (1), 105–112.

Shirato, M., Kato, H., Kobayashi, K., Sakazaki, H., 1970b. Analysis of settling of thickslurries due to consolidation. Journal of Chemical Engineering of Japan 3 (1),98–104.

Shirato, M., Sambuichi, M., Murase, T., Aragaki, T., Kobayachi, K., Iritani, E., 1985.Memoirs of the Faculty of Engineering Nagoya University, vol. 37, pp. 38–92.

Shirato, M., Iwata, M., Wakita, M., Murase, T., Hayashi, N., 1987. Constant-rateexpression of semisolid materials. Journal of Chemical Engineering of Japan 20,1–6.

Smith, G.D., 1977. Numerical Solution of Partial Differential Equations: FiniteDifference Methods. Oxford Univ. Press, Clarendon, London & New York.

Sobisch, T., Lerche, D., 2000. Application of a new separation analyzer for thecharacterization of dispersions stabilized with clay derivatives. Colloid andPolymer Science 278, 369–374.

Sobisch, T., Lerche, D., 2004. Use of analytical centrifugation for evaluation ofsolid–liquid separation in decanter centrifuges: application for selection offlocculants for sludge dewatering. Filtration 4, 270–274.

Sobisch, T., Lerche, D., Detloff, T., Beiser, M., Erk, A., 2006a. Tracing the centrifugalseparation of fine particle slurries by analytical centrifugation. Filtration 6,313–321.

Sobisch, T., Lerche, D., Fischer, S., Fanter, C., 2006b. Characterization of porous beadcelluloses by analytical centrifugation. Progress in Colloid and Polymer Science133, 169–172.


Sobisch, T., Lerche, D., 2008. Thickener performance traced by multisampleanalytical centrifugation. Colloids and Surfaces A: Physicochemical and Engi-neering Aspects 331, 114–118.

Sperry, D.R., 1916. The principles of filtration. Metallurgical and Chemical

Engineering 15 (4), 198–203.Stamatakis, K., Tien, C., 1991. Cake formation and growth in cake filtration.

Chemical Engineering Science 46 (8), 1917–1933.Teoh, S.-K., Tan, R.B.H., Tien, C., 2006a. A new procedure for determining filter cake

resistance from filtration data. Chemical Engineering Science 61, 4957–4965.Teoh, S.-K., Tan, R.B.H., Tien, C., 2006b. Analysis of cake filtration data—a critical

assessment of conventional filtration theory. AIChE Journal 52 (10),3427–3442.

Tiller, F.M., 1953. The role of porosity in filtration. I. Numerical methods. ChemicalEngineering Progress 46, 467–479.

Tiller, F.M., Shirato, M., 1964. The role of porosity in filtration: VI new definition of

filtration resistance. AIChE Journal 10 (1), 61–67.Tiller, F.M., Haynes Jr., S., Lu, W.-M., 1972. The role of porosity in filtration: VII

effect of side-wall friction in compression-permeability cells. AIChE Journal 18,13–20.

Tiller, F., Leu, W., 1980. Basic data fitting in filtration. Journal of the Chinese

Institute of Chemical Engineers 11, 61–70.

Von Homeyer, A., Krentz, D.-O., Kulicke, W.-M., Lerche, D., 1999. Optimization ofthe polyelectrolyte dosage for dewatering sewage sludge suspensions bymeans of a new centrifugation analyser with an optoelectronic sensor. Colloidand Polymer Science 227, 637–645.

Vorobiev, E.I., Fedotkin, I.M., 1984. Calculation of the optimum filtration pressureon the basis of examination of filtration parameters of suspensions. Chemicaland Petroleum Engineering 20 (5), 24–25.

Vorobiev, E.I., Anikeev, J.V., Samolyotov, V.M., 1993. Dynamincs of filtration andexpression: new methods for combined analysis and calculation of theprocesses with due account of the cake consolidation dynamics and the filtermedium compressibility. Chemical Engineering and Processing: Process Inten-sification 32 (1), 45–51.

Vorobiev, E., 2006. Derivation of filtration equations incorporating the effect ofpressure redistribution on the cake–medium interface: a constant pressurefiltration. Chemical Engineering Science 61 (11), 3686–3697.

Wakeman, R.J., 1978. A numerical integration of the differential equationsdescribing the formation of and flow in compressible filter cakes. Transactionsof IChemE 59, 260–270.

Wakeman, R.J., Tarleton, E.S., 1999. Filtration: Equipment Selection, Modelling andProcess Simulation. Elsevier, Oxford.

Zaiats, I., Vorobiev, E., Rakowsky, K., 1993. Modeling of beet pulp pressing.Zuckerindustrie 6, 437–444.


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Conclusions

The Paper V proposes two independent methods for analysis of the following

experimental dependencies measured during the centrifugal consolidation:

• ultimate sediment height versus centrifugal rotation speed (analyzed by Method I); and

• sediment height versus centrifugation time (analyzed by Method II).

These methods allow estimation of parameters of the constitutive equations for volume

fraction of particles, specific surface resistance, and coefficient of consolidation. They were

applied for estimation of the said constitutive parameters for calcium carbonate suspension.

The values of parameters of the constitutive equation for consolidation coefficient C,

estimated by two methods, are rather close:

• C = (2.9±0.3)·10–11ps0.91±0.04 (estimated by Method I),

• C = (3.5±1.0)·10–11ps0.85±0.03 (estimated by Method II).

Difference between the pre-exponential factors, estimated by Method I and Method II, is

caused by using underestimated value of specific surface area of calcium carbonate in

calculation by Method I.

IV. Concluding remarks and suggestions for future work

189


Several problems related to the influence of chemical or mechanical pre-treatment on the

filtration of mineral and biological suspensions have been investigated. It was observed that

the optimal filtration performance requires a compromise between the filtration rate and

quality of the final products (filtrate and concentrate).

Investigation of the influence of a dispersant on preparation of flowable and concentrated

suspension of kaolin showed that preparation of kaolin suspensions with concentrations above

70 % wt is unreasonable due to low fluidity of the concentrated suspensions. It was concluded

that low fluidity of concentrated suspensions is related to morphology (high aspect ratio) of

the kaolin particles. Increase of suspension concentration results in percolation of the

stabilized kaolin particles and in abrupt increase of fluidity. Though more concentrated

suspensions may be prepared by dead-end filtration in the presence of a dispersant, the

presence of a dispersant in such over-concentrated suspensions has only low effect on the

fluidity.

Continuation of this investigation may be based on idea of the adjustment of fluidity of

concentrated kaolin suspensions by addition of mineral particles with low aspect ratio.

Also, it was shown that highly concentrated (> 75 % wt) and flowable suspension of

calcium carbonate may be prepared by dynamic filtration with addition of sodium

polyacrylate. The influence of the time of dispersant addition on efficiency of filtration, final

dryness, and fluidity of suspensions was studied. It was shown that the highest dryness of

suspension, obtained by dynamic filtration with delayed addition of a dispersant, was

79.6±1.0 % wt., while its viscosity was below 0.8 Pas (at shear rate 20 s–1). The maximal

dryness of suspension obtained by filtration with initial addition of a dispersant was 77.1 %

wt.

Obviously, the results of this experimental lab-scale study must be verified in a pilot-scale

work. Also, a dispersant with stronger adsorption on the surface of particles should be found.

In addition, the maximal concentration of suspension that may be prepared by dynamic

suspension shall be estimated in the separate theoretical study.

It was shown that continuous treatment of yeast suspension by high voltage electric

discharges (HVED) may be used for disruption of the cells and extraction of intracellular bio-

products. However, it also results in formation of cell debris and decrease of filtration rate due


190

to internal membrane fouling. Comparison of the novel method of HVED-treatment with

classical method of high pressure homogenization (HPH) shows that HPH-treatment is more

effective method of disruption than HVED, as far as it results in higher extraction of proteins

and other bio-products at the same value of disintegration index of yeast cells. However, if the

value of disintegration index Z is above 0.9, filtration of HPH-disrupted yeast suspension is

governed by pore blocking mechanism. It results in very low rates of filtration of the

maximally HPH-treated suspensions.

Therefore, it is reasonable to focus further study only on filtration of HPH-treated

suspensions. It is quite interesting to study the influence of addition of intact yeast cells to the

disrupted yeast suspensions on filtration (especially, dynamic filtration) of yeast suspensions.

Intact cells may preserve the filtration membrane from the fouling by cells debris, so, the

effect of concentration of the intact cells and cells debris (or disruption degree) on the

mechanism of fouling may be investigated.

Also, two independent methods for analysis of the experimental dependencies measured

during the centrifugal consolidation were proposed. Dependencies of local compression and

permeability characteristics on solid pressure were estimated by these methods for aqueous

suspension of calcium carbonate. Obviously, the methods must be tested on other well

characterised mineral suspensions and the results of analysis must be compared with data

obtained by classical methods for estimation of compression and permeability (dead-end

filtration, compression-permeability test).

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