Yielding of Suspensions in Compression

Yielding of Suspensions in Compression

Matthew D. Green and David V. Boger*

Advanced Mineral Products Special Research Center, Department of Chemical Engineering,University of Melbourne, Parkville, 3052 Victoria, Australia

The compressive yield stress, Py(φ), is an important rheological parameter for the characterizationof concentrated flocculated suspensions. It is a measure of the compressive strength ofinterparticle bonds in a strongly networked suspension structure and is used in the design ofprocesses for the dewatering of fine particle suspensions. There are several techniques availableto determine the compression characteristics of a particular suspension. Three techniques aredescribed and compared: two based on centrifugal consolidation and one based on pressurefiltration. Results for well-characterized ZrO2 and Al2O3 suspension systems are presented,showing the effect of flocculation conditions, sample preparation methods, and the initialsuspension concentration on the compression rheology. The application of these findings to thedesign of a compression thickener for the concentration of bauxite residue or red mud for semidrydisposal in the alumina industry is also explained.

Introduction

The use of compression to produce highly concen-trated particle suspensions in large-scale industrialconsolidation processes such as thickeners and pressurefilters has become very important over the last fewdecades (e.g., Dixon, 1981; Chandler, 1983; Marunczynand Laros, 1992; Eberl et al., 1995). Until recently,industry has often been reluctant to make use ofcompression for dewatering suspensions, fearing aninability to be able to handle the highly concentratedproduct from such a process. The innovative use ofadditives to reduce the viscosity or break down thestructure of such a product under shear, however, canmake pumping and handling of the product feasible (deGuingand, 1986; Green et al., 1992; Leong, 1994).An important application of highly concentrated

mineral suspensions is in the rapidly expanding ceram-ics industry where the wet processing of concentratedsuspensions has become prevalent (Lange, 1989; Horn,1990; Ulrich, 1990). In this technique, a ceramic moldis filled with a suspension at the highest possibleconcentration. When the wet ceramic is fired, minimalshrinkage will then occur, which is the major cause ofceramic cracking and strength reduction. The objectivethen is to produce a suspension of the highest concen-tration that will still flow. This objective can beachieved by precisely controlling the surface chemistryof the particles (Horn, 1990; Leong, 1994) and byapplying a compressive pressure until the suspensionis sufficiently dewatered. A question of interest is, whatis the compressive pressure required to produce asuspension of a certain concentration? At present, thisquestion is answered empirically using a full-scale filterpress or vacuum filter. With the techniques outlinedin this paper, this question can be answered in thelaboratory and other conditions and variables that affectdewatering may be evaluated without the costly inter-ruption of an operating plant.The mining industry is another growing user of

compression technology for the production of highlyconcentrated suspensions in tailings disposal. Tradi-tionally, mine tailings are pumped into large settlingponds from which the supernatant is recycled back to

the process while the solids slowly settle and eventuallyfill the pond. Given the huge volumes of waste producedby mining operations, this disposal technique hasnumerous environmental and economic problems (Nguy-en and Boger, 1986). An alternative disposal techniquethat is increasingly viable is to highly concentrate thetailings in a large thickener and then pump the slurryor paste to the disposal area in a “semidry” state(Robinsky, 1975; Cooling and Glenister, 1992). Thereare several compelling reasons for this trend in tailingsdisposal. As the ore yields from mining operationsdecrease, the volume of tailings generated from theextraction of the ore will increase. Adequate watersupply and available land for disposal of these tailingsare often scarce. There is also strong pressure on theindustry to reduce the amount of waste expelled intothe environment. A semidry disposal technique dra-matically reduces the landfill area required and reducesthe time required to reclaim the land and revegetate it.These arguments support the adoption in certain in-stances of a semidry disposal strategy in which minetailings are pumped as a highly concentrated slurry orpaste. The question considered here is how can com-pression be used to dewater fine particle suspensionsto produce a material suitable for semidry disposal? Thisquestion can be answered using the laboratory tech-niques and results described in this paper.

Materials and Methods

Two metal oxide aqueous suspension systems wereexamined; zirconia, ZrO2, and alumina, Al2O3. The ZrO2(mean volumetric particle diameter, d50 ≈ 0.47 µm, F ≈5.72 g/cm3) was supplied by ICI Advanced Ceramics,Australia. The Al2O3 was an AKP-30 alumina (d50 ≈0.40 µm, F ≈ 4.0 g/cm3) supplied by Sumitomo ChemicalCo. Ltd., Japan. The metal oxide systems were chosento represent “model” suspensions of polydisperse indus-trial particulate systems.The preparation of both metal oxide systems was

carefully controlled to obtain reproducible suspensions.A procedure similar to that of Leong et al. (1993) wasused. Appropriate amounts of the powder and additiveswere mixed with Milli-Q-filtered distilled water with0.01 M salt (KNO3 and NaCl for ZrO2 and Al2O3,respectively). Poly(acrylic acid) (PAA) of 2000 MW(molecular weight), at 1.0 dwb % (dry weight base), was

* Author to whom correspondence should be addressed.E-mail: [email protected].

4984 Ind. Eng. Chem. Res. 1997, 36, 4984-4992

S0888-5885(97)00141-3 CCC: $14.00 © 1997 American Chemical Society

used in some samples as a dispersant (Aldrich ChemicalCo.). All samples were prepared in the dispersed stateusing concentrated HNO3 or HCl to adjust the pH. Twomethods for dispersal of the powder were used; smallsamples (less than 100 mL) were sonicated for 2 minusing an ultrasonic horn (Branson Sonifier 450W,operated at 30-40% of the maximum power output),while larger samples (up to 400 mL) were mixed usinga high shear mixer for 5 min (Janke and Kunkel, Ultra-Turrax operated at 10 000 rpm). Both methods ofdispersion produced good suspensions exhibiting repro-ducible rheological results. The samples were adjustedto their correct pH using 1-5 M KOH or NaOH andthen rested for at least 24 h.The shear yield stress, τy, was directly measured

using the vane technique prior to any compressionmeasurements. In the vane technique, a vane con-nected to a spring is placed in the sample, the spring isslowly tightened, the maximum torque correspondingto the point of yielding (the vane begins to move) ismeasured, and the shear yield stress is calculated(Nguyen and Boger, 1983, 1985). With the vane tech-nique the stress at which the material begins to flow ismeasured. Compared to other shear yield stress tech-niques, the technique is relatively nondestructive andthus is a good measurement of the shear yield stress ofhighly concentrated and structured suspensions.

Compressive Yield Stress, Py(O), Measurement

The compressive yield stress, Py, quantifies thestrength of a networked suspension structure that issubjected to compressive forces. If the applied stressexceeds the compressive yield stress for that particularconcentration of suspension, φ, the suspension willirreversibly consolidate to a new equilibrium concentra-tion corresponding to the new stress. The compressiveyield stress is thus an intrinsic function of the localsolids concentration of the suspension. The compressiveyield stress is also a function of the structural state ofthe suspension. The suspension structure is deter-mined, for example, by the surface chemistry of theparticles, the initial conditions of the suspension, andthe method of compression. Three techniques for mea-suring Py(φ) are described: two based on centrifugalconsolidation and one based on pressure filtration.Multiple-Speed Equilibrium Sediment Height

Technique. The multiple-speed equilibrium sedimentheight technique was developed by Buscall and White(1987). Preliminary experiments using a polystyrenelatex were performed to demonstrate the technique(Buscall, 1983). It was first used in an industrialapplication by de Guingand (1986), who studied thecompression characteristics of bauxite residue or redmud. In that work, an optimum flocculant dosage wasfound that significantly enhanced the compressibilityof the red mud. The technique has also been success-fully used at the University of Melbourne in the designof several thickening operations for the Australianmining industry (unpublished work). The compressiondewatering of fine coal tailings containing a significantproportion of clay was investigated by de Kretser (1995;de Kretser et al., 1997). The clay in these tailings wasfound to control the rheology and dewatering charac-teristics of the system, and precise manipulation of thesuspension chemistry enabled improved compression.Recent work on cement pastes and alumina suspensionsby Miller et al. (1995) found a dependence of Py(φ) onthe initial concentration of the sample and only a weak

dependence on the compressive history of the suspen-sion. Miller et al. (1996) focused on evaluating themeasurement of Py(φ) using alumina and zirconiasuspensions. The technique has also been used byEckert et al. (1996) to examine the consolidation of finetailings from tar sands. Most of the results in this paperwere determined using the multiple-speed equilibriumsediment height technique.The multiple-speed equilibrium sediment height tech-

nique is a method for the determination of the compres-sive yield stress function, Py(φ), for flocculated suspen-sions using a centrifuge. Suspension samples are placedin cylindrical, transparent, flat-bottomed, centrifugetubes, and the equilibrium sediment height, Heq, ismeasured for various increasing values of the gravita-tional acceleration, g, at the bottom of the tube. Ini-tially, the volume fraction solids concentration of thesuspension is uniform throughout and equal to φ0. Rawdata required are the initial height of the suspension,H0, the density difference between the solid and the fluidphases, ∆F, and the centrifuge radius from the centerto the internal base of the tube, R. A typical plot ofHeq-(g) raw data is shown in Figure 1a (the effect ofcentrifuge tube diameter is discussed later). The datafor the Heq(g) curves are exponentially decreasing withincreasing g and are approximately linear when plottedon semilogarithmic coordinates.The conversion of the Heq versus g raw data to a Py-

(φ) curve is not trivial. The basic theory was developedby Buscall and White (1987). There are two available

Figure 1. (a) Typical raw multiple-speed equilibrium sedimentheight data; ZrO2, pH 7.1, φ0 ) 0.150. Effect of tube diametershown. (b) Corresponding compressive yield stress curves, Py(φ),determined from the raw data in part a. The symbols aredetermined using the approximate solution. The lines are deter-mined from the full iterative solution.

Ind. Eng. Chem. Res., Vol. 36, No. 11, 1997 4985

solution techniques: a full iterative algorithm and anapproximate solution. An improved iterative algorithmhas also been developed and evaluated by Green et al.(1996). It was shown there that the approximatesolution is an acceptable technique if only limited dataare available. The theory for these techniques is fullydetailed in the above references and is not consideredfurther.In Figure 1b are results comparing the full iterative

solution with the approximate solution. The symbolson the Py(φ) curves were determined using the ap-proximate solution on the raw data in Figure 1a; thelines were determined using the iterative solution. Inall cases, the approximate solution gives slightly lowervalues of the concentration for a given Py but isadequate for most engineering purposes. Both solutionmethods are shown in the subsequent results of thispaper.A certain minimum centrifuge tube diameter must be

used to minimize any possible wall effects on thecompression results. Figure 1b shows the effect of thecentrifuge tube diameter on the results for a stronglyflocculated ZrO2 suspension. These results show asignificant shift of the Py(φ) curve to the right as thecentrifuge tube diameter is increased. de Guingand(1986) observed a similar effect for bauxite residue.Narrow tubes thus apparently restrict the compress-ibility of the suspension and generate unrealistically lowresults. The minimum diameter required is related tothe shear yield stress, τy, of the suspension. The greaterthe τy, the wider the centrifuge tube that must be used.Michaels and Bolger (1962) have theoretically computedfor dilute suspensions the minimum diameter at whichcompression will occur for a suspension with a givenτy. Applying their formulation to our results, however,give unrealistically high minimum centrifuge tubediameters. An additional effect to consider is that, asthe suspension compresses, τy increases and wall effectsthus become more important. Minimization of thiseffect would require even wider centrifuge tubes. Theinitial τy of the strongly flocculated ZrO2 used in Figure1, with φ0 ) 0.15, was measured to be 198 Pa. Theconcentration of this suspension is near the maximumpossible to prepare for strongly flocculated ZrO2 withno additives. Thus, the tube diameter effects seen inFigure 1b would be the greatest observed for the resultspresented herein. A tube diameter of 26.5 mmwas usedin all experiments, this being the widest practical tubediameter for the centrifugal measurements made here.The results do not indicate that the tube diameter effectis eliminated using this tube diameter, but possible walleffects on the compressive behavior of the suspensionsare minimized.Concentration Profile Technique. The compres-

sive yield stress function may be determined from themeasurement of the concentration profile of a samplecentrifuged to an equilibrium height at a given g. Themeasured concentration profile is integrated from thetop of the sediment downward to determine the stressdeveloped by the weight of the overlying sediment. Thiscorresponds to the compressive yield stress at theconcentration at that particular height, z. A completePy(φ) curve is thus determined. This technique was firstused by Bergstrom et al. (1992) and is a more directmethod of determining Py(φ) than the multiple-speedequilibrium sediment height technique.The transmission of γ-rays through a suspension has

been used to measure the equilibrium concentration

profile (Bergstrom, 1992; Bergstrom et al., 1992). Adestructive testing method used here and by Miller etal. (1995, 1996) involves taking multiple sections fromthe sediment (typical spacing 0.5-2.0 mm). The solidsconcentration of each section is measured by mass losson drying. The value determined by drying is taken asthe concentration at the midpoint height of the section.A similar technique has been used on filter cakes bySherwood et al. (1991) and Meeten (1993).To determine Py(φ), the raw concentration profile data

may be integrated using trapezoidal constructions;otherwise, curves may be fitted to the raw data whichare then integrated either analytically or numerically.The difference between the solution methods is smalland largely dependent on the curve fitting of the rawφ(z) data.Filtration Technique. Filtration of a suspension

through a membrane by a piston operated at constantpressure is a direct measure of the compressive yieldstress at the final concentration of the filter cake afterequilibrium is attained (Landman and White, 1994). Byoperation of the filtration device at a range of pressureson separate samples for each pressure, a complete Py-(φ) curve is generated. This technique was successfullyused byMiller et al. (1996). Miller’s apparatus was usedto obtain the results that are part of Figure 2; the readeris referred to Miller et al. for details of the apparatusand its operation.Comparison of Measurement Techniques. Com-

bined results from all three measurement techniquesare compared in Figure 2. The results are for ZrO2 inthe strongly flocculated state (pH 7.6). The results spana substantial range of solids concentration (φ ) 0.10-0.45) and compressive yield stress (4 orders of magni-tude). Three centrifuges were used to obtain resultsover this large range using the multiple-speed equilib-rium sediment height technique. These are referencedin Figure 2 as the low-, medium-, and high-speedcentrifuges (LSC, MSC, and HSC). Concentrationprofiles were determined from the high- and low-speedcentrifuged samples, and the resulting Py(φ) curvesagree well with those from the multiple-speed equilib-rium sediment height technique. The pressure filtration

Figure 2. Plot comparing each technique for determining Py(φ);ZrO2, pH 7.6, φ0 ) 0.15.

4986 Ind. Eng. Chem. Res., Vol. 36, No. 11, 1997

results are also consistent with the two centrifugetechniques; however, only the upper range of pressureswas accessed due to experimental constraints.The agreement between the three measurement

techniques is good evidence that the compressive yieldstress is a material property of a suspension. The twocentrifuge techniques and the filtration technique com-press by different consolidation mechanisms. In cen-trifugation, the expelled water from the suspensionnetwork is forced upward through the structure andhinders consolidation. However, in pressure filtration,the expelled water flows downward and contributes tothe compression. In both cases, at equilibrium, it is thesediment structure that supports the applied stress. Theagreement between the results thus suggests that thecompressive yield stress is independent of the pathtaken to reach the final condition (that is, it is a materialproperty).Which technique should be used? Given that all three

techniques agree reasonably well, the accuracy of eachtechnique, the ease of use, and the time to obtain resultsmust be considered. A comparison of each technique isgiven in Table 1. The multiple-speed technique is timeconsumingsattainment of the equilibrium state for 5or 6 speeds can require over a month for the mineralsuspensions studied here. Measurement time per sampleis low, but data analysis is moderately complex andaccuracy is moderate. The concentration profile tech-nique requires a suspension to reach an equilibriumheight at a single centrifuge speedsabout a week.Sectioning of the sediment is laborioussrequiring aboutan hour per samplesbut the accuracy of the concentra-tion profile and the resulting Py(φ) curve is good sincemany sections can be taken. Pressure filtration requiresa custom-built apparatus, but results of moderateaccuracy can be obtained in a day for a single sampleof low volume. As an industrial engineer, the concen-tration profile technique is clearly the method of prefer-ence to use. Centrifuges are widely available, multiplesamples can be tested simultaneously, data analysis issimple and straightforward, and results can be obtainedin just over a week. The disadvantage is the laborioussectioning of each sample; this could be automated ifnecessary. If the number of samples is large and resultsare not urgent, then the multiple-speed techniqueshould be used. Therefore, the technique to be appliedis dictated by the particular circumstance.

Results and Discussion

Having ascertained that Py(φ) is a material propertyof concentrated suspensions, results are now presentedshowing how Py(φ) depends on the state of flocculation,the sample preparation, the initial concentration, and

the surface chemistry of the suspension. Model metaloxide suspensions are used to demonstrate these effects.Except where noted, the majority of the compressiveyield stress results to be presented have been obtainedusing the multiple-speed equilibrium sediment heighttechnique.Flocculation Effect. The compressive behavior of

metal oxide suspension systems can be controlled bymanipulating the degree of flocculation of the sample.The suspension pH fixes the surface charge on theparticles, which, in turn, determines the magnitude ofelectrostatic repulsion between them. When the par-ticles are electrically neutral, the repulsion is minimizedand the suspension is strongly flocculated. This is theisoelectric point (iep) or point of zero charge. For pH’snot far removed from the iep, the suspension is weaklyflocculated due to repulsive surface charges on theparticles. Shown in Figure 3a is the effect on compres-sion of varying the pH for ZrO2 suspensions. When theZrO2 is strongly flocculated at pH 7.2, the suspensionis the least compressible. When weakly flocculated, thesuspension can be compressed to a higher concentrationfor the same applied stress. At pH’s far from the iep,suspensions are fully dispersed, which on settling (muchslower than flocculated suspensions) form a hard, highlyconcentrated layer on the bottom. A sharp interfacebetween the supernatant and the sediment also cannotbe seen; thus, measurement of the compressibility ofdispersed systems is not possible using both centrifugetechniques and, although not tried, pressure filtrationwould be difficult due to the formation of the hard layer.These same trends are also seen for Al2O3, althoughthose results are not reported here.

Table 1. Comparison of Py(O) Measurement Techniques(Times Are per Sample)a

technique

multiplespeed

concentrationprofile

pressurefiltration

samples per run 2-28a 2-8a 1conc. accuracy (%) (4 (0.5 (1pressure accuracy (%) (2 (5 (2measurement time (min) 30 60 5equipment time 4-5 weeks 1 week 1 dayanalysis time (min) 10 15 5no. of data pointsb 5-6 15-30 5-6

a Dependent on centrifuge size. b Minimum data pointsrequiredsgreater accuracy achieved with more points, but timesincrease proportionally.

Figure 3. (a) Effect of pH on compressive yield stress, Py(φ); ZrO2,φ0 ) 0.15. (b) Plot of Py vs pH for lines of constant concentrationstaken from part a plus additional data.


The effect of flocculation is better shown in Figure3b by replotting the data of Figure 3a as Py versus pHfor a series of constant concentrations. The leastcompressible condition is thus clearly at the iep (pH 7.2).Figure 3b may be compared with the corresponding plotof shear yield stress, τy, versus pH shown in Figure 4.In both plots, the pH’s of maximum Py and τy areidentical. This suggests that the mechanism of break-ing bonds between particles to cause motion by shearis related to that of the mechanism of breaking bondsin compression. A relationship between Py and τy issuggested later in the paper.Sample Preparation Effects. The method of sus-

pension preparation for rheological and compressionalstudy is extremely important. For suspensions bothstrongly and weakly flocculated by only electrostaticforces (pH and ionic strength), the measured Py(φ) wasunaffected by the method used to prepare the samples(results not shown). Dilution of these suspensions aftersonication or high shear mixing also had no effect onthe measured Py(φ). In contrast, the Py(φ) measured forsuspensions sterically stabilized by low molecular weightpolymer was affected by the sample preparation methodand by dilution before compression.In Figure 5, a concentrated stock suspension of ZrO2

(φ0 ) 0.26) sterically stabilized with 1.0 dwb % 2000MW PAA was prepared in the weakly flocculated state(pH 6.0) using the high-shear Ultra-Turrax mixer (solidline). Subsamples of 50 mL were then sonicated for 1min (dotted line). The Py(φ) curve is shifted to the rightfor the additionally sonicated sample, indicating thatthe structure of the suspension is further broken down

by the sonication and has become more compressible.Samples of weakly flocculated, sterically stabilizedsuspensions thus should be sonicated separately beforecompression to separate the particles as much aspossible.In Figure 6, 100 mL samples of the stock suspension

were diluted to φ0 ) 0.10 in two ways: first, by stirringin water (dotted line); second, by stirring in water andthen sonicating for 2 min (dashed line). The resultingcurves lie significantly to the left of the original con-centrated suspension (solid line). Dilution of the weaklyflocculated suspension thus irreversibly alters the struc-ture of the particle network in some way, becoming farless compressible than the original concentrated sus-pension. Sonication of the diluted suspension onlypartially recovers the original structure.In Figure 7, 50 mL samples of the stock suspension

were diluted by stirring in water as before. The pH wasthen adjusted to the strongly flocculated state (pH 4.5-4.6 for this sterically stabilized sample containing PAA).One sample was subsequently sonicated for 20 s (dottedline), while the other sample was stirred (dashed line).The strongly flocculated suspensions are less compress-ible than the weakly flocculated suspension (solid line)in agreement with the previous section. The stronglyflocculated structure also appears stable since the Py-(φ) curve is unchanged by further sonication. The

Figure 4. Effect of pH and φ on shear yield stress, τy, for ZrO2.

Figure 5. Effect of dispersion technique on Py(φ); ZrO2 with 1.0dwb % 2000 MW PAA, pH 6.0, φ0 ) 0.263.

Figure 6. Effect of dilution on Py(φ); ZrO2 with 1.0 dwb % 2000MW PAAsweakly flocculated: (b) base suspension Ultra-Turrax5 min; (O) diluted by just stirring in water; (0) diluted and thensonicated for 2 min.

Figure 7. Effect of dilution on Py(φ); ZrO2 with 1.0 dwb % 2000MW PAAsstrongly flocculated; (b) base suspension Ultra-Turrax5 min; (O) diluted by just stirring in water and adjusted pH; (0)diluted, adjusted pH, and then sonicated for 20 s.


compression results of these strongly flocculated sus-pensions thus appear to be independent of their methodof preparation.Consideration of the results in Figures 5-7 indicates

that the compression rheology of sterically stabilizedsuspensions is sensitive to their preparation method.An important industrial problem is the optimization ofthe flocculation of mineral particles entering a thick-ener, which usually occurs in a feed-well at the thick-ener center. The flocculation efficiency in the feed-welldetermines the throughput (from the settling rate) andthe underflow concentration (from the suspension com-pressibility) of the thickener (Landman et al., 1988).Samples for compression measurements for the optimi-zation of an existing process thus should be taken fromthe thickener feed-well after flocculation. For the designof a new thickener, flocculation conditions of the sus-pension in the laboratory should closely match those inthe plant. In these ways, the compression rheologymeasured will best represent the actual suspensionused.Initial Concentration. It has been found here that

the initial concentration, φ0, of the suspension is adetermining factor in the final bottoms concentrationachievable. A significant dependence of Py(φ) on φ0 isshown in Figure 8 for strongly flocculated Al2O3 at itsiep; that is, when φ0 increases, the suspension becomesless compressible. The same effect of φ0 on Py(φ) isapparent for both strongly and weakly flocculated ZrO2as seen in Figures 9 and 10. The initial concentration

effect thus appears to be a universal property of thesemetal oxide suspensions.Several explanations are postulated for these initial

concentration effects. First, if the initial state is aweakly structured, open network of particles with fewconnecting bonds, then under compression the particleswould have room to move to a semiordered state of ahigh concentration. However, if the initial suspensionis already highly concentrated, then a strong structuremay be already present which may constrain the move-ment of particles under compression. The concentrationachieved will thus be lower since the particles cannotpack as well compared with if they had started in thediluted state. Another possible mechanism that woulddescribe these initial concentration effects is based onthe suspension microstructure. Two suspensions of thesame initial concentration may have very differentmicrostructures. A suspension may consist of denseaggregates of particles joined by relatively few bondsand contain large void spaces between the aggregates.Compression of such a structure would involve theyielding of relatively few bonds. Conversely, a suspen-sion that is a homogeneous structure of single particleswould require the yielding of many more bonds forcompression to occur. The compressive yield stresswould thus be proportional to the number of bondsbetween either aggregates or particles depending on thestructure of the suspension (Kapur et al., 1997). As theinitial concentration of the suspension changes, theinitial microstructure may change, which would directlyaffect the compression rheology.The effect of the initial concentration of the suspen-

sion used in compression tests has important ramifica-tions when industrial processes are examined. Forexample, in the optimization or design of thickeners,samples for compression tests should be either takenfrom the thickener feed-well directly after flocculationor prepared at the concentration that is or will be used.The suspension sample to be tested under compressionwill thus have a representative structure of that in theactual process. It should be noted, however, that if thefeed concentration is below the gel point, φg (theconcentration at which particles form a continuousnetwork), then the final compression height in thecentrifuge or filter press will be low and hence measure-ment accuracy will suffer.Effect of Additives. Polymeric additives change the

surface chemistry of suspended particles and dramati-cally affect the compression rheology. The addition of

Figure 8. Effect of initial concentration on Py(φ) for stronglyflocculated Al2O3 (iep pH 9.3-9.4).

Figure 9. Effect of initial concentration on Py(φ) for stronglyflocculated ZrO2 (iep pH 6.8-7.2).

Figure 10. Effect of initial concentration on Py(φ) for weaklyflocculated ZrO2 (pH 5.6-5.7).


low MW PAA coats the particles with a thin layer ofpolymer that reduces the attractive forces betweenthe particles by a steric separation (Leong et al., 1993).In Figure 11, 1.0 dwb % of 2000 MW PAA is addedto a ZrO2 suspension and Py versus pH is plotted for arange of φ and compared with that of no additive. Theeffect on the compression behavior of the suspensionsis to shift the pH of maximum flocculation and makethem substantially more compressible. The shear yieldstress is likewise reduced by such an addition (Leong,1994).A longer-chained polymer has the effect of flocculating

the particles through a bridging mechanism. The shearand compressive rheology of this system has beenexamined by Leong (1994). Figure 12 is reproducedhere to illustrate the effect of adding a 750 000 MW,1.0 dwb % PAA compared with the same suspensionwith no polymer. For comparison, the effect of the 2000MW PAA is also shown. The long polymer chainsinduce a widely separated particle structure that re-stricts particle movement and hence is less compress-ible. In industry, long-chained polymer flocculants arecommonly used to quickly settle mineral suspensions.Such treatment adversely affects the compression rhe-ology of the system and should be avoided if high finalconcentrations are to be achieved.Compressive Yield Stress and Shear Yield Stress

Correspondence. It is useful to compare the shapeand order of magnitude of τy(φ) and Py(φ) curves. InFigure 13 are plots of τy(φ) and Py(φ) on log-log

coordinates for strongly and weakly flocculated ZrO2with no additives. The data can be fitted to power lawsof the forms

where A, B, m, and n are constants. For the data inFigure 13, the values for these constants are listed inTable 2. The exponents m and n are approximatelyequal (within fitting error) for both the τy(φ) and Py(φ)curves, as evidenced by their parallel nature in Figure13. The preexponential factor for Py(φ), B, are between40 and 90 times greater than that for τy(φ), A, asevidenced by the axis scales in Figure 13. From thisinformation a relation between τy(φ) and Py(φ) may bewritten by the substitution of eq 1 into eq 2 to yield

If m and n are equal, then a linear relation between Pyand τy is obtained. The prediction of Py(φ) from τy(φ)measurements is extremely useful since the determi-nation of Py(φ) can take many weeks using the com-monly available centrifuge methods, whereas τy(φ)measurements can be completed in days. From thelimited data in Figure 13 which show similar power lawexponents for both strongly and weakly flocculated ZrO2,a relation dependent on the state of flocculation of thematerial could also be developed.

Applications

An extremely useful application of Py(φ) data is in thedesign and/or optimization of thickeners containing acompression zone. Using these curves, the thickenerheight, Hi, required to produce a certain bottom con-centration, φb, from a given initial concentration, φi, inthe thickener may be estimated (de Guingand, 1986).This is easily calculated for a batch thickener at

Figure 11. Effect of Py(φ) on pH for ZrO2 with and without 2000MW poly(acrylic acid), φ0 ) 0.176; curves taken at constantconcentration.

Figure 12. Effect of low- and high-MW poly(acrylic acid) (2000and 750 000) on Py(φ) for ZrO2 at the iep, φ0 ) 0.159 (reproducedfrom Leong, 1994).

Figure 13. Comparison of shear and compressive yield stresscurves (τy(φ) and Py(φ), respectively) for strongly (open symbols)and weakly (closed symbols) flocculated ZrO2: (O) τy(φ) pH 6.9-7.2; (b) τy(φ) pH 5.6-5.7; (0) Py(φ) pH 7.2; (9) Py(φ) pH 5.7.

Table 2. Power Law Constants for Fit of Data in Figure14

pH A m B n

7.2 7.4 × 106 5.6 6.3 × 108 6.75.7 1.1 × 107 6.3 4.7 × 108 6.9

τy(φ) ) Aφm (1)

Py(φ) ) Bφn (2)

Py(φ) ) B(τy(φ)A )n/m (3)


equilibrium using the equation

where g0 is the gravitational acceleration. Equation 4underestimates the height necessary for a continuousthickener since the compressive forces never reachequilibrium in continuous flow. To determine thethickener height required for a continuous thickener, asecond parameter is required that quantifies the rateof compression. This parameter is the hindered settlingfunction, r(φ). With it, the bed height and the concen-tration profile in the thickener may be exactly calculated(Landman and White, 1994). This technique is cur-rently being trialed by Alcoa of Australia on a 75 mdiameter superthickener used to concentrate bauxiteresidue for semidry disposal.In Figure 14 are compression data for bauxite residue

or red mud with various amounts of added flocculant(Green et al., 1994). Also shown is the equivalent batchthickener height required for a typical feed concentra-tion of φ ) 0.060. It can be seen that for unflocculatedred mud, in a clarifier with no compression zone, thebottom concentration is φ ) 0.20 (43 wt %). A batchthickener height of 5 m yields a bottom concentrationof about φ ) 0.27 (53 wt %). The optimum addition of145 ppm flocculant can then further increase the bottomconcentration to about φ ) 0.32 (59 wt %). Theutilization of a compression zone in a thickener togetherwith the correct dosage of flocculant can thus increasethe bottom concentration from 0.20 to 0.32 or from 43to 59 wt %. This represents significant dewatering andin this case is more than adequate for a semidry tailingsdisposal scheme (Glenister and Abbott, 1989; Ritcey,1989; Cooling and Glenister, 1992). The materialproduced from the thickener possesses a shear yieldstress but can still be pumped. In fact, pumping energyrequirements can be lower since the pipeline is nowoperating in laminar flow. Problems such as erosionand settling in the pipeline and difficulties with startupare also minimized (Thomas, 1977).Compressive yield stress curves have also been used

in the optimization of full-scale high-pressure filtrationsystems in the kaolin industry (Eberl et al., 1995). Thepressure required to achieve a certain filter cakeconcentration may be directly determined from such acurve. In conjunction with filtration rate data and thesubsequent determination of the hindered settling func-tion, r(φ), the effect of filter cake thickness and the effect

of various pressure cycles on the filtration time may alsobe calculated. The optimization and design of filtrationsystems may thus be achieved without costly planttrials. The ideal type and amount of flocculant may bedetermined in the laboratory. At the design level, theoptimal dewatering technology for the suspension sys-tem can also be found.

Conclusions

Three techniques for the determination of the com-pressive yield stress were discussed in this paper. Theconcentration profile technique was shown to be ac-curate, is theoretically sound, and is the easiest toimplement, requiring no specialized equipment otherthan a centrifuge. Factors important to the measure-ment of the compressive yield stress were identified,including the centrifuge tube diameter, the initialconcentration, and the initial structural state of thesuspension. The effect of flocculation and the effect ofpolymeric additives on the compression rheology wereexamined. All results were applied to the problem ofoptimization and design of thickeners.

Acknowledgment

We express our thanks to Dr. K. Miller and Prof. C.F. Zukoski of Chemical Engineering Department, Uni-versity of Illinois, Urbana-Champaign, for use of theirlow-speed centrifuge and pressure filtration apparatusfor some of the results presented herein. M.D.G. ac-knowledges that the results reported here were obtainedas part of doctoral research cosupervised by Prof. D. V.Boger and A/Prof. K. A. Landman at University ofMelbourne. This research was supported by the Ad-vanced Mineral Products Special Research Centre,University of Melbourne.

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Py(φb) ) ∆Fg0φiHi (4)


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Received for review February 12, 1997Revised manuscript received July 11, 1997

Accepted July 22, 1997X

IE970141I

X Abstract published in Advance ACS Abstracts, September15, 1997.


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Yielding of Suspensions in Compression