TA 成大講稿
4/16/2013
An Introduction to Rheology:
Phenomenon, Concept, Measuring, and Case Study
Complex Fluids & Molecular Rheology Lab., Department of Chemical
Engineering
The XVIth International Congress on Rheology

Non-Newtonian Fluid Mechanics
 Colloids and Suspensions

Advanced Experimental Methods
 Emulsions and Foams

Materials Processing
 Solids and Granular Materials

Polymer Solutions, Melts and Blends
 Industrial Rheology

Biopolymers, Biofluids and Foods
 Complex Flows

Constitutive and Computational Modeling
 General Rheology

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
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
Y
牛頓流體
- 水、有機小分子溶劑等
V
Newton’s law of viscosity
V
 yx    V
Y
黏度η為定值
非牛頓流體
- 高分子溶液、膠體等
Small molecule
Macromolecule
V
●
Deformable
黏度不為定值
(尤其在快速流場下)
 非牛頓流體的三大特徵
 特徵時間與無因次群分析
非牛頓流體的特徵
 非牛頓黏度 (Non-Newtonian Viscosity)
- Shear Thinning
p

Flow curve for non-Newtonian
Fluids
牛頓流體
(甘油加水)
非牛頓流體
(高分子溶液)
 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
Time-dependent effects (搖變性)
Thixotropy behavior
Anti-thixotropy behavior
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
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.
非 牛 頓 流 體 的 不 穏 定 性: 黏 彈 性 效 應
“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
De 
(Re  103 in all cases)
Elastic force
  tflow or We =  - 描述非牛頓流體行為之程度
Viscous force
 : 流體的特徵或 “鬆弛” 時間
tflow : 流動系統的特徵時間
 : 剪切速率
De  0
0.2

牛頓流體
(葡萄糖漿)
3
1
收
縮
流
道
非牛頓流體
(0.057% 聚丙烯醯胺/葡萄糖 溶液)
8

典型製程之流場強度範圍
Lubrication
High-speed coating
Rolling
Spraying
Injection molding
Pipe flow
Chewing
Extrusion
Sedimentation
105
103
101
101
 (s-1 )
103
105
107
Typical viscosity curve of a polyolefin- PP
homopolymer, melt flow rate (230 C/2.16 Kg) of 8
g/10 minat 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
Sharkskin
Melt fracture
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)]
 Instability for dilute solutions
Taylor vortex
R1
R2
[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).]
Flow visualization of the elastic Taylor-Couette
instability in Boger fluids.
[http://www.cchem.berkeley.edu/sjmgrp/]
 剪切流與非剪切流
 基礎流變量測模式與功能
典型均勻流場
 Two standard types of flows, shear and shearfree, are frequently used to
characterize polymeric liquids
(b) Shearfree
(a) Shear
vx   y
Steady simple shear flow
vx   yx y; v y  0; vz  0
Shear rate
Streamlines for elongational flow (b=0)
Elongation
rate
vx  
vy  

2

2
vz   z
x
y
 The Stress Tensor
y
x
z
Shear Flow
Elongational Flow
Total stress
tensor*
Stress tensor
 yx
 p   xx
  p       yx
p   yy



 0
0

Hydrostatic pressure forces


0 
p   zz 
0
 p   xx
  p      0



 0

0
p   yy
0
Shear Stress :  yx
First Normal Stress Difference :  xx   yy
Second Normal Stress Difference :  yy   zz
Tensile Stress :  zz   xx


0 
p   zz 
0
 流變夾具種類與適用範圍
(a) Shear
Concentrated Regime







Homogeneous
deformation:*
Cone-andPlate
Nonhomogeneous
deformation:
(b) Elongation
Dilute Regime
103
Concentric Cylinder
Parallel
Plates
Capillary
102 101 100
Moving clamps
101
102
103
104
γ (s-1 )
105
 (s-1 )
For Melts & High-Viscosity Solutions
*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:
0  GN(0)  d , where GN(0) the "plateau modulus" is temperature insensitive
Newtonian
Power law
Zero-shear
viscosity, 0
     0 
Relaxation time,   1 / critical
Relative Viscosity:
 rel 

s
: Solution viscosity
s : Solvent viscosity
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:
  s 
[ ]  lim 

c 0
 cs 
c: Mass concentration
Intrinsic viscosity of dilute polystyrene
Solutions, With various solvents, as a function
of reduced shear rate β
小振幅反覆式剪切流: 黏性與彈性檢定
Exp b: Small-Amplitude Oscillatory Shear Flow
The shear stress oscillates with frequency  ,
but is not in phase with either the shear strain
or shear rate
Shear Stress : yx   A() 0 sin(t   )
strain rate:  yx (t )   0 cos t
strain:  yx (t )   0 sin t
Oscillatory shear strain, shear rate, shear stress, and first normal stress difference in
small-amplitude oscillatory shear flow
It is customary to rewrite the above equations to display the in-phase and
out-of-phase parts of the shear stress
Storage modulus
 yx  G() 0 sin t  G() 0 cos t
Loss modulus
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 solid
curves are calculated from the generalized Maxwell model, Eqs. 5.2-13 through 15
Molecular Architecture—The Fingerprints
Linear Polymer
Star Polymer
Pom-Pom Polymer
polybutadiene
Polyisoprene
Polyisoprene
C. C. Hua, H. Y. Kuo, J Polym Sci Part B: Polym Phys 38,
248-261 (2000)
S. C. Shie, C. T. Wu, C. C. Hua,
Macromolecules 36, 2141-2148 (2003)
拉伸流黏度量測與特徵
 Shearfree Flow Material Functions
For Uniaxial Elongational Flow (b  0,   0):
Zero - elongation - rate
elongational viscosity 0
 zz   xx   ( )
 : Elongational viscosity
 : Elongation rate
Zero - shear - rate
viscosity 0
Elongation viscosity  and viscosity
 for a polystyrene melt as functions of elongation
rate and shear rate, respectively
Elongational Stress Growth Function  
H. Munstedt, J. Rheol. 24, 847-867 (1980)
Hua and Yang, J Polym Res 9, 79-90 (2002)
The Rheology of Colloidal Dispersions
Onset of shear thickening : the Péclet number
 Fluid drag on the particle leads to the Stokes-Einstein relationship:
D
kBT
6 a
a: particle's hydrodynamic radius
2
x
 Dt
 The mean square of the particle’s displacement is
Accordingly, the diffusivity sets the characteristic time scale for the
particle’s Brownian motion.
a2
t particle 
D
 A dimensionless number known as Péclet number, Pe

Pe 
 a2
D

a 3
kBT
Lubrication hydrodynamics and hydroclusters
Pe~1
Pe<<1
 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>>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
Case Study I: 導電金屬漿流變性質的鑑定
1.
Steady-state Viscosity
2.
First normal stress difference
3.
Linear viscoelasticity
The Viscosity Curves of Steady Shear Flow
1e+6
1e+6
1e+5
1e+5
1e+4
1e+4
Viscosity ( Pa s )
Viscosity ( Pa s )
A
1e+3
1e+2
1e+1
1e+3
1e+2
1e+1
PP 25(TEK)
1e+0
0.0001
0.001
0.01
PP 25(TEK)
0.1
1
10
100
1e+0
0.0001
1000
0.001
0.01
Shear Rate ( 1/s )
0.1
10
100
1000
10
100
1000
D
1e+6
1e+6
1e+5
1e+5
1e+4
1e+4
Viscosity ( Pa s )
Viscosity ( Pa s )
1
Shear Rate ( 1/s )
C
1e+3
1e+2
1e+1
1e+3
1e+2
1e+1
PP 25(TEK)
PP 25(TEK)
1e+0
0.0001
B
0.001
0.01
0.1
1
Shear Rate ( 1/s )
10
100
1000
1e+0
0.0001
0.001
0.01
0.1
1
Shear Rate ( 1/s )
A
A
The 1st Normal Stress Curves of Steady Shear Flow
6000
3000
6000
PP
25
CP 25(TEK)
25-4
PP
4000
2000
1000
Normal Stress ( Pa )
Normal
Normal Stress
Stress (( Pa
Pa ))
4000
2000
0
0
-2000
-1000
-4000
-2000
-6000
-3000
-8000
-4000
0.001
0.0001
PP
PP25(TEK)
25
2000
0
-2000
-4000
-6000
0.01
0.001
0.010.1
0.1
1
1
10 10
100
100
-8000
0.0001
1000
1000
0.001
0.01
Shear Rate
Shear
Rate (( 1/s
1/s ))
0.1
100
1000
1000
PP 25
PP 25(TEK)
800
PP 25
25(TEK)
PP
600
2000
Normal Stress ( Pa )
Normal Stress ( Pa )
10
D
6000
0
-2000
-4000
400
200
0
-200
-6000
-8000
0.0001
1
Shear Rate ( 1/s )
C
4000
B
-400
0.001
0.01
0.1
1
Shear Rate ( 1/s )
10
100
1000
-600
0.0001
0.001
0.01
0.1
1
Shear Rate ( 1/s )
10
100
1000
A
B
PP 25(TEK)
PP 25(TEK)
1e+6
10000
1e+5
10000
1e+3
1e+4
1000

G' ; G'' ( Pa )
1000
Complex Viscosity  Pa s )
1e+4
G' ; G'' ( Pa )

Complex Viscosity  Pa s )
1e+5
1e+3
100
1e+2
1e+2
1e+1
0.01
100
0.1
1
10
1e+1
0.01
100
10
0.1
Angular Frequency ( 1/s )
1
100
Angular Frequency ( 1/s )
C
D
10000
1e+5
1e+3
100
Complex Viscosity 
1e+2
Storage Modulus G'
1e+4
1000
G' ; G'' ( Pa )

G' ; G'' ( Pa )
1000
10000

1e+4
Complex Viscosity  Pa s )
1e+5
Complex Viscosity  Pa s )
10
1e+3
100
1e+2
Loss Modulus G''
1e+1
0.01
10
0.1
1
Angular Frequency ( 1/s )
10
100
1e+1
0.01
10
0.1
1
Angular Frequency ( 1/s )
10
100
Screen Printing Technique
Starting position for a screen printer
squeegee
gauze
medium
frame
gap (‘snap-off’)
board holder
emulsion mask
board
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.
The screen printing process
medium
medium drawn from open mesh
snap-off
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
http://www.ami.ac.uk/courses/topics/0222_print/index.html#1
105
104
104
G' ; G'' ( Pa )
G' ; G'' ( Pa )
105
103
102
103
102
Storage Modulus G' ( Pa )
Loss Modulus G" ( Pa )
101
0.01
0.1
1
Storage Modulus G' ( Pa )
Loss Modulus G" ( Pa )
10
100
101
0.01
Angular Frequency  ( 1/s )
104
104
103
103
G' ; G'' ( Pa )
G' ; G'' ( Pa )
105
102
101
Storage Modulus G' ( Pa )
Loss Modulus G" ( Pa )
0.1
1
10
100
Silver paste CM-B
105
10-1
0.01
1
Angular Frequency  ( 1/s )
Silver paste CM-A
100
0.1
Storage Modulus G' ( Pa )
Loss Modulus G" ( Pa )
102
101
100
10
Angular Frequency  ( 1/s )
Powders sample
100
10-1
0.01
0.1
1
10
Angular Frequency  ( 1/s )
Binders sample
100
106
106
105
Storage Modulus G' ( Pa )
Loss Modulus G" ( Pa )
105
104
103
104
103
102
Storage Modulus G' ( Pa )
Loss Modulus G" ( Pa )
105
G' ; G" ( Pa )
G' ; G" ( Pa )
G' ; G" ( Pa )
106
Storage Modulus G' ( Pa )
Loss Modulus G" ( Pa )
104
103
102
102
101
101
0
100
200
300
400
500
600
100
101
0
100
200
Time ( s )
300
400
500
600
0
100
200
Time ( s )
Silver paste
300
400
500
600
Time ( s )
Powders sample
Binders sample
90
90
Phase Angle ( ° )
80
60
50
40
30
20
10
70
60
50
40
30
20
10
0
0
100
200
300
400
500
Time ( s )
600
70
60
50
40
30
20
10
0
0
0
100
200
300
Time ( s )
  tan 1  G "/ G '
Phase Angle ( ° )
80
Phase Angle,  ( ° )
70
Phase Angle,  ( ° )
Phase Angle,  ( ° )
90
Phase Angle ( ° )
80
400
500
600
0
100
200
300
Time ( s )
400
500
600
 流變-光學 (Rheo-Optical) 整合量測系統:
結構 vs. 應力
Versatile Optical Rheometry
Lens
Iris PEM Iris
Objective
lens
Polarier
Pinhole
Spatial filter
& Beam expander
Flow-LS (large-angle detection)
Couette
cell

Rheology
CCD
Analyzer
Rheo-SALS

Lens
Screen with aperture
(from PEM)
1f
2f
Photodiode
Rheo-Birefringence
Lock-in amplifiers
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
 c : Onset of the shear - enhanced
concentration fluctuations
 a : Onset of the anomalies in the
rheological and scattering behaviors
FIG. A complete picture of the shear-induced phase separation and structure formation from a wide range of
techniques on the same polymer solutions
Continued
Comparisons with Mechanical Characterizations:
6.0 wt% PS/DOP solution (c c  30)
Mechanical
M w  3.84 106 ; M w M n  1.06
FIG The plots of shear viscosity ( ), birefringence (n), and dichroism (n) of the solution
as a function of shear rate ( )
Notice that the behavior of the shear viscosity is also classified into three regimes
Physics governing the fluid behavior
The Smoluchowski equation:


 (r1 , r2 ,..., t )


U

 H nm   kBT


t
R m R m 
n , m R n

subject to appropriate boundary and initial conditions
U

 sum of deterministic forces= Fmh  Fmintra  Fminter  Fmex
R m
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)!”
TA 成大講稿
4/16/2013
An Introduction to Rheology:
Phenomenon, Concept, Measuring, and Case Study
Complex Fluids & Molecular Rheology Lab., Department of Chemical
Engineering