Complex Fluids & Molecular Rheology Lab., Department of Chemical Engineering

An Introduction to Rheology:

Phenomenon, Concept, Measuring, and Case Study

TA 成大講稿 4/16/2013

Non-Newtonian Fluid Mechanics

Advanced Experimental Methods

Materials Processing

Polymer Solutions, Melts and Blends

Biopolymers, Biofluids and Foods

Constitutive and Computational Modeling

Rheology of Bio-Pharmaceutical Systems

Rheology of Nano- and Natural Composites

Interfacial Rheology, Micro-rheology & Microfluidics

Associative Polymers, Surfactants and Liquid Crystals

Professor Ken Walters Commemorative Symposium

The XVIth International Congress on Rheology

Colloids and Suspensions

Emulsions and Foams

Solids and Granular Materials

Industrial Rheology

Complex Flows

General Rheology

Frequent Q & A

Q: Rheometer = Rheology? A: Unfortunately, the answer is, to a large extent, negative!

Q: How to judge the correctness of rheological data and

know the physical meanings?

A: Mostly, it’s all about the theories

Q: A practical processing issue can be well characterized by a set of rheological parameters?

A: Well,…………………………………………..let’s see!

Rheology is the science of fluids or—more precisely—deformable materials

牛頓流體- 水、有機小分子溶劑等

非牛頓流體- 高分子溶液、膠體等

yx Y

VV

YNewton’s law of viscosity

V

黏度 η 為定值

黏度不為定值( 尤其在快速流場下 )

Small moleculeMacromolecule

●Deformable

V

非牛頓流體的三大特徵

特徵時間與無因次群分析

非牛頓黏度 (Non-Newtonian Viscosity) - Shear Thinning

非 牛 頓 流 體 的 特 徵

p

牛頓流體( 甘油加水 )

非牛頓流體( 高分子溶液 )

Flow curve for non-Newtonian Fluids

正向力差的效應 (Normal Stress Differences) - Rod-Climbing

牛頓流體 ( 水 ) 非牛頓流體 ( 稀薄高分子溶液 )

記憶效應 (Memory effects) - Elastic Recoil

- Open Syphon Flow

A decrease (thixotropy) and increase (anti-thixotropy) of the apparent viscosity with time at a constant rate of shear, followed by a gradual recovery when the motion is stopped

Thixotropy behavior Anti-thixotropy behavior

The distinction between a thixotropic fluid and a shear thinning fluid: A thixotropic fluid displays a decrease in viscosity over time at a constant shear rate. A shear thinning fluid displays decreasing viscosity with increasing shear rate.

Time-dependent effects ( 搖變性 )

非 牛 頓 流 體 的 不 穏 定 性 : 黏 彈 性 效 應

收縮流道

De 0 0.2 1 3 8

牛頓流體( 葡萄糖漿 )

非牛頓流體(0.057% 聚丙烯醯胺 / 葡萄糖 溶液 )

flowDe or We = t Elastic forceViscous force

:

Re 310( in all cases)

- 描述非牛頓流體行為之程度流體的特徵或 “鬆弛” 時間流動系統的特徵時間tflow : : 剪切速率

“The mountains flowed before the Lord” [From Deborah’s Song, Biblical Book of Judges, verse 5:5], quoted by Markus Reiner at the Fourth International Congress on Rheology in 1963

典型製程之流場強度範圍

-1 ( ) s

High-speed coating

Injection molding

Lubrication

Sedimentation

Rolling

Pipe flow

Extrusion

Spraying

Chewing

710510310110110310510

Typical viscosity curve of a polyolefin- PP homopolymer, melt flow rate (230 C/2.16 Kg) of 8 g/10 min- at 230 C with indication of the shear rate regions of different conversion techniques. [Reproduced from M. Gahleitner, “Melt rheology of polyolefins”, Prog. Polym. Sci., 26, 895 (2001).]

Melt instability

Photographs of LLDPE melt pass through a capillary tube under various shear rates. The shear rates are 37, 112, 750 and 2250 s-1, respectively.[Reproduced from R. H. Moynihan, “The Flow at Polymer and Metal Interfaces”, Ph.D. Thesis, Department of Chemical Engineering, Virginia Tech., Blackburg, VA, 1990.]

[Retrieved from the video of Non-Newtonian Fluid Mechanics(University of Wales Institute of Non-Newtonian Fluid Mechanics,2000)]

Sharkskin Melt fracture

Instability for dilute solutions

Flow visualization of the elastic Taylor-Couetteinstability in Boger fluids.[http://www.cchem.berkeley.edu/sjmgrp/]

Taylor vortex

R1R2

[S. J. Muller, E. S. G. Shaqfeh and R. G. Larson, “Experimental studies of the onset of oscillatory instability in viscoelastic Taylor-Couette flow”, J. Non-Newtonian Fluid Mech., 46, 315 (1993).]

剪切流與非剪切流

基礎流變量測模式與功能

Two standard types of flows, shear and shearfree, are frequently used to characterize polymeric liquids

典 型 均 勻 流 場

Steady simple shear flow

xv y

; 0; 0x zy yxv y v v

Streamlines for elongational flow (b=0)

2

2

x

y

z

v x

v y

v z

(a) Shear (b) Shearfree

Shear rate

Elongationrate

The Stress Tensor

x

y

z

0

0

0 0

xx yx

yx yy

zz

p

p p

p

0 0

0 0

0 0

xx

yy

zz

p

p p

p

Shear Flow Elongational Flow

yx

xx yy

yy zz

Shear Stress:

First Normal Stress Difference:

Second Normal Stress Difference:

zz xx Tensile Stress:

Total stresstensor*

Hydrostatic pressure forces

Stress tensor

流變夾具種類與適用範圍

-1γ (s )

Homogeneousdeformation:*

Nonhomogeneousdeformation: Parallel

Plates

(a) Shear

(b) Elongation

Capillary

3 2 1 0 1 2 3 4 510 10 10 10 10 10 10 10 10

Cone-and-Plate

Concentric Cylinder

Concentrated Regime Dilute Regime

-1 (s )

For Melts & High-Viscosity Solutions

Moving clamps

*Stress and strain are independent of position throughout the sample

基礎流變量測之物理解析與應用

According to the Reptation Theory:

Newtonian Power law

Zero-shearviscosity, 0

critical/1 time,Relaxation

0

(0)N0 d

(0)N, where the "plateau modulus" is temperature insensitiveG G

0

s

s

] lim[c c

srel

Master curves for the viscosity and first normal stress difference coefficient as functions of shear rate for the low-density polyethylene melt shown in previous figure

Intrinsic viscosity of dilute polystyrene Solutions, With various solvents, as a function of reduced shear rate β

Intrinsic Viscosity:

Relative Viscosity:

s

:

:

Solution viscosity

Solvent viscosity

: c Mass concentration

小振幅反覆式剪切流 : 黏性與彈性檢定Exp b: Small-Amplitude Oscillatory Shear Flow

Oscillatory shear strain, shear rate, shear stress, and first normal stress difference in small-amplitude oscillatory shear flow

0( ) sinyx t t strain:

0( ) cosyx t t strain rate:

The oscillates with frequency ,

but is not in phase with eith shear s

shear s

traier the

o

n

shea

tre

r

ss

r rate

0( ) sin( )yx A t Shear Stress:

Storage and loss moduli, G’ and G”, as functions of frequency ω at a reference temperature of T0=423 K for the low-density polyethylene melt shown in Fig. 3.3-1. The solidcurves are calculated from the generalized Maxwell model, Eqs. 5.2-13 through 15

0 0( ) sin co( ) syx GG t t

It is customary to rewrite the above equations to display the in-phase and out-of-phase parts of the shear stress

Storage modulus

Loss modulus

Linear Polymer Star Polymer Pom-Pom Polymer

Molecular Architecture—The Fingerprints

polybutadiene Polyisoprene Polyisoprene

S. C. Shie, C. T. Wu, C. C. Hua, Macromolecules 36, 2141-2148 (2003)

C. C. Hua, H. Y. Kuo, J Polym Sci Part B: Polym Phys 38, 248-261 (2000)

拉 伸 流 黏 度 量 測 與 特 徵

Shearfree Flow Material Functions

( )zz xx

0 0b For Uniaxial Elongational Flow ( , ) :

Elongation viscosity and viscosity

for a polystyrene melt as functions of elongation

rate and shear rate, respectively

0Zero-elongation-rate

elongational viscosity

0Zero- shear-rate

viscosity

:

:

Elongational viscosity

Elongation rate

H. Munstedt, J. Rheol. 24, 847-867 (1980)Hua and Yang, J Polym Res 9, 79-90 (2002)

Elongational Stress Growth Function

The Rheology of Colloidal Dispersions

Onset of shear thickening : the Péclet number

Fluid drag on the particle leads to the Stokes-Einstein relationship:

The mean square of the particle’s displacement is

Accordingly, the diffusivity sets the characteristic time scale for the particle’s Brownian motion.

A dimensionless number known as Péclet number, Pe

B : particle's hydrodynamic radius6

k TD a

a

Dtx 2

D

at particle

2

Tk

a

D

a

B

Pe32

Lubrication hydrodynamics and hydroclusters

The flow-induced density fluctuations are known as hydroclusters which lead to an increase in viscosity.

The formation of hydroclusters is reversible, so reducing the shear rate returns the suspensions to a stable fluid

Pe<<1Pe~1

Pe>>1

At (Pe<<1) regime, random collisions among particles make them naturally resistant to flow.

As the shear rate increase (Pe~1), particles become organized in the flow, which lowers their viscosity.

At (Pe>>1) regime, the strong hydrodynamic coupling between particles leads to the formation of

hydroclusters (red particles) which cause an increase in viscosity.

Controlling shear thickening fluids: to modify colloidal surface

The addition of a polymer “brush” grafted or absorbed onto the particles’ surface can prevent particles from getting close together.

The figure shows that shear thickening is suppressed by imposing a purely repulsive force field.

With the right selection of grafted density, molecular weight, and solvent , the onset of shear thickening moves out of the desired processing regime

1. Steady-state Viscosity

2. First normal stress difference

3. Linear viscoelasticity

Case Study I: 導電金屬漿流變性質的鑑定

Shear Rate ( 1/ s )

0.0001 0.001 0.01 0.1 1 10 100 1000

Vis

cosi

ty (

Pa

s )

1e+0

1e+1

1e+2

1e+3

1e+4

1e+5

1e+6

PP 25(TEK)

Shear Rate ( 1/ s )

0.0001 0.001 0.01 0.1 1 10 100 1000

Vis

cosi

ty (

Pa

s )

1e+0

1e+1

1e+2

1e+3

1e+4

1e+5

1e+6

PP 25(TEK)

Shear Rate ( 1/ s )

0.0001 0.001 0.01 0.1 1 10 100 1000

Vis

cosi

ty (

Pa

s )

1e+0

1e+1

1e+2

1e+3

1e+4

1e+5

1e+6

PP 25(TEK)

Shear Rate ( 1/ s )

0.0001 0.001 0.01 0.1 1 10 100 1000

Vis

cosi

ty (

Pa

s )

1e+0

1e+1

1e+2

1e+3

1e+4

1e+5

1e+6

PP 25(TEK)

A

D

B

C

The Viscosity Curves of Steady Shear Flow

PP 25(TEK)

PP 25(TEK)PP 25(TEK)

PP 25(TEK)

A

Shear Rate ( 1/ s )

0.0001 0.001 0.01 0.1 1 10 100 1000

Nor

mal

Str

ess

( Pa

)

-4000

-3000

-2000

-1000

0

1000

2000

3000

CP 25-4

Shear Rate ( 1/ s )

0.0001 0.001 0.01 0.1 1 10 100 1000

Nor

mal

Str

ess

( Pa

)

-8000

-6000

-4000

-2000

0

2000

4000

6000

PP 25

Shear Rate ( 1/ s )

0.0001 0.001 0.01 0.1 1 10 100 1000

Nor

mal

Str

ess

( Pa

)

-8000

-6000

-4000

-2000

0

2000

4000

6000

PP 25

Shear Rate ( 1/ s )

0.0001 0.001 0.01 0.1 1 10 100 1000

Nor

mal

Str

ess

( Pa

)

-600

-400

-200

0

200

400

600

800

1000

PP 25

Shear Rate ( 1/ s )

0.001 0.01 0.1 1 10 100 1000

Nor

mal

Str

ess

( Pa

)

-8000

-6000

-4000

-2000

0

2000

4000

6000

PP 25

A

D

B

C

The 1st Normal Stress Curves of Steady Shear Flow

PP 25(TEK) PP 25(TEK)

Angular Frequency ( 1/s )

0.01 0.1 1 10 100

Com

plex

Vis

cosi

ty P

a s

)

1e+1

1e+2

1e+3

1e+4

1e+5

1e+6

G' ;

G''

( P

a )

100

1000

10000

Angular Frequency ( 1/s )

0.01 0.1 1 10 100

Com

plex

Vis

cosi

ty P

a s

)

1e+1

1e+2

1e+3

1e+4

1e+5

G' ;

G''

( P

a )

10

100

1000

10000

Angular Frequency ( 1/s )

0.01 0.1 1 10 100

Com

plex

Vis

cosi

ty P

a s

)

1e+1

1e+2

1e+3

1e+4

1e+5G

' ; G

'' (

Pa

)

10

100

1000

10000

Angular Frequency ( 1/s )

0.01 0.1 1 10 100

Com

plex

Vis

cosi

ty P

a s

)

1e+1

1e+2

1e+3

1e+4

1e+5

G' ;

G''

( P

a )

10

100

1000

10000

Complex Viscosity

Storage Modulus G' Loss Modulus G''

G’ & G’’A

D

B

C

1. The screen is fixed just above the board, and the medium lies in front of the flexible squeegee.2. The mesh of the screen is pushed down into contact with the board by the squeegee as it moves

across the screen, rolling the medium in front of it.

Starting position for a screen printer

The screen printing process

http://www.ami.ac.uk/courses/topics/0222_print/index.html#1

3. The squeegee blade first presses the medium into the open apertures of the image, and then removes the excess as it passes across each aperture.

4. The screen then peels away from the printed surface behind the squeegee, leaving the medium that was previously in the mesh aperture deposited on the board beneath

gauze

gap (‘snap-off’)

board holder

board

emulsion mask

framemedium

squeegee

medium

snap-off

medium drawn from open mesh

Screen Printing Technique

Angular Frequency ( 1/s )

0.01 0.1 1 10 100

G' ;

G''

( P

a )

101

102

103

104

105

Storage Modulus G' ( Pa )Loss Modulus G" ( Pa )

Angular Frequency ( 1/s )

0.01 0.1 1 10 100

G' ;

G''

( P

a )

101

102

103

104

105

Storage Modulus G' ( Pa )Loss Modulus G" ( Pa )

Angular Frequency ( 1/s )

0.01 0.1 1 10 100

G' ;

G''

( P

a )

10-1

100

101

102

103

104

105

Storage Modulus G' ( Pa )Loss Modulus G" ( Pa )

Angular Frequency ( 1/s )

0.01 0.1 1 10 100

G' ;

G''

( P

a )

10-1

100

101

102

103

104

105

Storage Modulus G' ( Pa )Loss Modulus G" ( Pa )

Silver paste CM-A Silver paste CM-B

Powders sample Binders sample

Time ( s )

0 100 200 300 400 500 600

G' ;

G"

( P

a )

101

102

103

104

105

106

Storage Modulus G' ( Pa ) Loss Modulus G" ( Pa )

Time ( s )

0 100 200 300 400 500 600

Pha

se A

ngle

, (

°)

0

10

20

30

40

50

60

70

80

90

Phase Angle ( ° )

Time ( s )

0 100 200 300 400 500 600

G' ;

G"

( P

a )

100

101

102

103

104

105

106

Storage Modulus G' ( Pa ) Loss Modulus G" ( Pa )

Time ( s )

0 100 200 300 400 500 600

Pha

se A

ngle

, (

°)

0

10

20

30

40

50

60

70

80

90

Phase Angle ( ° )

Time ( s )

0 100 200 300 400 500 600

G' ;

G"

( P

a )

101

102

103

104

105

106

Storage Modulus G' ( Pa ) Loss Modulus G" ( Pa )

Time ( s )

0 100 200 300 400 500 600

Pha

se A

ngle

, (

°)

0

10

20

30

40

50

60

70

80

90

Phase Angle ( ° )

Silver paste Powders sample Binders sample

1tan "/ 'G G

流變 - 光學 (Rheo-Optical) 整合量測系統 :

結構 vs. 應力

Versatile Optical Rheometry

Couettecell

Laser

CCD

Iris Iris

Spatial filter & Beam expander

Screen with aperture

Lens

Objectivelens

Pinhole

Lens

Analyzer

PolarierPEM

Photodiode

1f 2f

Lock-in amplifiers

(from PEM)

Rheo-SALS

Rheo-Birefringence

Rheology

Flow-LS (large-angle detection)

CASE STUDY II : Combined Rheo-Optical Measurements Rheo-Optical Studies of Shear-Induced Structures in Semidilute Polystyrene

Solutions [Kume et al. (1997)]

1. Shear-induced structure formation in semidilute solutions of high molecular weight polystyrene was investigated using a wide range of rheo-optical techniques

2. The effects of shear on the semidilute polymer solutions could be classified into some regimes w.r.t. shear rate

FIG. A complete picture of the shear-induced phase separation and structure formation from a wide range oftechniques on the same polymer solutions

c

a

: Onset of the shear-enhanced

concentration fluctuations

: Onset of the anomalies in the

rheological and scattering behaviors

Continued

n n

The plots of shear viscosity ( ), birefringence ( ), and dichroism ( ) of the solution

as a function of shear rate ( )

FIG

6w w n

6.0 30

3.84 10 1.06

c c

M M M

wt% PS/DOP solution ( )

;

Notice that the behavior of the shear viscosity is also classified into three regimes

Comparisons with Mechanical Characterizations:

Mechanical

Physics governing the fluid behavior

B,

h intra inter

subject to appropriate boundary and initial conditions

( , ,..., )

sum of deterministic forc

The Smoluchowski equa

es

tion:

=

nmn m n m m

m m mm

t Uk T

t

U

1 2r rH

R R R

F F F FR

exm

Tips and Recommendations of problem solving

Identify an analogous model system that had been studied earlier

Go through literature survey and read carefully and apprehensively

Design tactics for collecting preliminary data—experimental or

computational Discuss with your supervisor or counselor for the significance of

the current data and appropriate next steps. Repeat this procedure until the problem has been resolved to a

satisfactory extent.

People used to tell me,

“The problems encountered in industry are

typically too complex to be studied in a

(academic) lab (like yours)”

My response was,

“Just because the problems are so complex

that they must eventually be resolved in

a (academic) lab (like mine)!”

Complex Fluids & Molecular Rheology Lab., Department of Chemical Engineering

An Introduction to Rheology:

Phenomenon, Concept, Measuring, and Case Study

TA 成大講稿 4/16/2013