FUNDAMENTALS of RHEOLOGY - From Deformation to Flow of Materials
Abel Gaspar-Rosas TA Instruments, Inc. – USA 2003 Sales Meeting Marbella, Spain
-
Objective Objectives
• Review of fundamental concepts of rheology • Practical issues • Advances in rheometry • Advanced evaluation methods
Key points • Deformation • Flow • Practical view • Rheology equipment • Evaluation methods
Definition of Rheology
• Rheology is the science of flow and deformation of matter.
?
“”
(everything flows)
-
Heraclitus de Samos (500
B.C.)
Time scale in rheology Deborah Number
De = / texp
material
texp us (you and me)
Flow and Deformation
???
Interest: Rheological Properties Classical Extremes Ideal Solid -- [External Force] -Ideal Fluid STEEL
WATER Strong structure Weak structure Rigidity Deform Retain/recover shape Store Energy
(purely Elastic – R. Hooke, 1678)
[Energy]
Fluidity Flow Lose shape Dissipate Energy (purely Viscous – I. Newton, 1687)
ELASTICITY Storage Modulus
VISCOSITY Loss Modulus
REAL Behavior Apparent Solid [Energy + time] Apparente Fluid
- viscoelastic materials -
Flow and Deformation Parameters: [Shear Stress, Shear Strain, Shear Rate]
Stress: Force per unit area. Symbol: Units: Pa (SI) or dynes/cm² (cgs)
Shear Strain: Relative deformation in shear. Symbol: Units: None
Shear Rate: Change of shear strain per unit time. Symbol: Units: [1/s] = s-1
Simple Shear Deformation and Flow Shear Deformation
x(t)
F = A h
y
A z
Strain
V =
x(t) h
Shear Flow Strain Rate
. = V = 1 x(t) h h t
x
Rigidity G =
Viscosity = .
Summary of Types of ‘Flow’
Shear Stress,
flow
y
Bingham (Newtonian with yield stress) Bingham Plastic (shear-thinning with yield stress) Shear Thinning (Pseudoplastic)
Newtonian Shear Thickening (Dilatant)
deformation
Shear Rate,
Model Fitting - Shear Stress vs. Shear Rate Summary of Viscosity Models
Newtonian
K
n
Pseudoplastic
( n 1)
Dilatant
K
n
( n 1)
Bingham
y
Casson Herschel-Bulkley
1 2
1 2
0
n
1 2
1
c
y K
n
2
log
The Idealized Flow Curve 1) Sedimentation 2) Leveling, Sagging 3) Draining under gravity 4) Chewing and swallowing 5) Dip coating 6) Mixing and stirring 7) Pipe flow 8) Spraying and brushing 9) Rubbing 10) Milling pigments in fluid base 11) High Speed coating
4 5 6 1 1.00E-5
1.00E-4
3
2 1.00E-3
0.0100
0.100
8
7 1.00
10.00
shear rate (1/s)
9 11
10 100.00
1000.00
1.00E4
1.00E5
1.00E6
Models Fit to log-log Plots Predicts the shape of the complete Flow Curve Cross
0 - -
=(K ) m
Sub-sets of the Cross Equation which predict portions of the complete Flow Curve Power Law Sisko
= K1
1 n
= + K1 n-1
Williamson
= o - K1 n 1
Rotational Testing Deformation and Flow
upper plate ‘moving’ sample lower plate ‘fixed’
Newtonian and Non-Newtonian Behavior of Fluids 1.000E5
Non-Newtonian Region
Newtonian Region Independent of
1.000E5
= f()
10000
(Pa)
(Pa.s)
1000
100.0
10.00
Flow dependence 10000 1.000E-5
1.000E-4
1.000E-3
0.01000
shear rate (1/s)
0.1000
1.000 1.000
CMT - Stress Ramp Test - Continuous Ramp Stress is applied to material at a constant rate.
Stress (Pa)
Stress (Pa)
Resultant strain is monitored with time.
m = Stress rate (Pa/min)
flow
y deformation
time (min.) USES Yield stress ‘Scouting’ Viscosity Run
Shear Rate,
Automotive Paint Samples: Data fit to Herschel-Bulkley Model 10000
SMT Sample
Viscosity (Pa.s)
1000
LMT Sample
a: yield stress: 6.582 Pa b: viscosity: 0.3777 Pa.s c: rate index: 0.8319
a: yield stress: 5.207 Pa b: viscosity: 0.2909 Pa.s c: rate index: 0.8426
100.0
10.00 Short milling time Long milling time
1.000
0.1000
0.01000
0
50.00
100.0
150.0
200.0
Shear Stress (Pa)
250.0
300.0
Automotive Paint Samples: Viscosity vs. Shear Stress 10000
Viscosity (Pa.s)
1000
Short milling time Long milling time
100.0
10.00
1.000
0.1000
0.01000 1.000
10.00
100.0
Shear Stress (Pa)
1000
SMT Technology - Step Rate
In a step rate test (stress growth), a step strain rate is applied to the material and the stress and normal force is recorded over time.
Select the step rate test to measure the transient viscosity or normal stress difference
SMT Technology - Thixotropy
In a thixotropy experiment, the strain rate is varied linear with time up and down and the stress is recorded over time.
The strain rate ramp is ideal for a fast viscosity scan as a function of shear rate for lower to medium viscosity fluids
SMT Technology - Steady Rate Sweep Test
In a steady rate experiment the equilibrium stress upon application of a step strain rate is measured. The equilibrium stress or viscosity is recorded as a function of the strain rate.
In a steady experiment, only the equilibrium value is measured over a manual selected time period
Stress
Creep Recovery Experiment
t1 tim t2 e Response of Classical Extremes
Strain
Strain
t1
tim
t2
Stain rate for t>t1 is constant – Strain for t>t1 increase with time – Strain rate for t >t2 is 0 –
Strain for t>t1 is constant – Strain for t >t2 is 0 –
t1
tim t2
Automotive Paint Samples: Creep / Recovery Test 80.0
?
2
70.0
Recovery
% strain
60.0 50.0
Creep
Long milling time Short milling time
40.0
?
30.0
?
2
1
Recovery
20.0 10.0 0
0.0
global time (s)
600
Automotive Paint Samples:
Creep Recovery Test 30.0
25.0
% strain
20.0
Long milling time Short milling time
inside the ? 1
Elastic Ringing
15.0
10.0
5.00
0 1.000E-3
0.01000
0.1000 time (s)
1.000
10.00
SMT Technology - Creep Test
In a creep test, a step stress is applied to the material and the deformation is recorded over time. If the stress is removed after a time t1 the recoverable deformation (recoil) is obtained.
The recoil test is the most sensitive test to determine aq material’s elasticity
Oscillatory Testing Deformation and Flow
upper plate ‘moving’ sample
lower plate ‘fixed’
Dynamic Flow Testing
An oscillatory (sinusoidal) deformation (stress or strain) is applied to a sample. The material response
Deformatio n Response
(strain or stress) is measured. The phase angle , or phase
shift, between the control and the response is measured.
Phase angle
Fundamentals of Rheology The fundamental definition of rheology indicates that for a material to flow its original structural composition must first exceed a critical limited deformation. Rheology, the science of deformation and flow of materials characterizes materials through parameters such as; • • • • •
storage modulus (G’) loss factor (Tan ) viscosity ( ) characteristic times ( ) ...
loss modulus (G”) critical deformation c yield point ( y) flow index (n)
With exquisite presicion, rheology describes the behavior of materials as viscoelastic fluids (G”>G’ and -> 90°) to viscoelastic solids (G’>G” and -> 0°) Information commonly used to improve formulations optimize processes, select aplication conditiosn, evaluate product performance, determine shelf life, evaluate product economy, and more.
Linear and Non-Linear Stress-Strain Behavior of Solids 1000
Linear Region G is constant
Non-Linear Region
G = f() osc. stress (Pa)
G' (Pa)
100.0
G
10.00
Deformation
1.000 0.010000
0.10000
100.0
Flow
1.0000 10.000 % strain
100.00
0.01000 1000.0
Automotive Paint Samples: Stress Sweep after Time Sweep 100.0
10.00
G' (Pa)
Elastic Component 1.000
0.1000
Short milling time Long milling time 0.01000
Yield Stress y
Frequency = 6.28 rad/s 1.000E-3 1.000E-3
0.01000
0.1000
1.000
10.00
osc. stress (Pa)
100.0
1000
SMT Technology - Strain Sweep Test
In a strain sweep, the strain is varied linear or logarithmic over the selected range. Strain, stress amplitude and phase shift are recorded.
The non-linear monitor (NLM) senses the end of the linear viscoelastic range
Frequency Sweep: Material Response
log G'and G"
Terminal Region
Rubbery Plateau Region
Transition Region
Glassy Region
1
2
Storage Modulus (E' or G') Loss Modulus (E" or G")
log Frequency (rad/s or Hz)
Dynamic Moduli of a Polymer Melt vs. Frequency 1000000
1000000
1.00E7
PDMS at 20°C 100000
100000 1000000 10000
1000
1000
100.0
100.0
10.00
10.00
1.000
1.000
*
100000
10000
G "
1000
G'
0.1000 0.1000 1.000E-3 1.000E-4
0.01000
0.1000
1.000
10.00
ang. frequency (rad/sec)
100.0
100.0 1000
* (Pa.s)
G'' (Pa)
G' (Pa)
10000
SMT Technology - Temperature Sweep Test
In a temperature sweep, the temperature is varied continuously or discrete over the selected range. Strain, stress amplitude and phase shift are recorded.
In all temperature dependent test, the AutoTension function is available
Practical Issues • Sample handling • Sample handling • Sample handling
Non-Newtonian, Time Dependent Fluids Thixotropy A decrease in apparent viscosity with time under constant shear rate or shear stress, followed by a gradual recovery, when the stress or shear rate is removed. Rheopexy An increase in apparent viscosity with time under constant shear rate or shear stress, followed by a gradual recovery when the stress or shear rate is removed. Also called Anti-thixotropy or negative thixotropy. Reference:Barnes, H.A., Hutton, J.F., and Walters, K., An Introduction to Rheology, Elsevier Science B.V., 1989. ISBN 0-444-87469-0
Non-Newtonian, Time Dependent Fluids
Viscosity
Rheopectic Shear Rate = Constant Thixotropic
time
Automotive Paint Samples: Structural Change – Structure Rebuild (Thixotropy) 100.0
Osc. –> Rotat. -> osc
Elasticidad G' (Pa)
10.00
Short milling time Long milling time
1.000
Pre_shear: 1000 1/s for 60 sec Stress = 0.1 Pa Frequency = 6.28 rad/s 0.1000 0
100.0
200.0
300.0
400.0
500.0
600.0
time (s)
700.0
800.0
900.0
1000
No-Newtonian rheological behavior (shear-thinning) must produce a balance of properties during the formation of the coating film. • formulation, estability, aplication • satisfactory leveling • uniform thickness • resistance to sag/drainage
ADDITIVES - can cause non desired effects. • too much elasticity (rapid contraction of structure) • extreme shear-thinning • flocculation of pigment
Response for a Viscoelastic Material At short times (high frequencies) the
response is solid-like At long times (low frequencies) the response
is liquid-like THE HISTORY OF LOADING IS CRUCIAL
Exponential Close
Gap Rapid Close
~ 1000 - 2000 microns from final gap
Controlled Close
Time
Squeeze Flow effect is less pronounced
Comparison of Standard and Exponential Sample Gap Close on Paint 250
Exponential Close
G' (Pa)
200 150
Fast Linear Close
100 50 0
0
200
400
600
Time (s)
800
1000
Solvent Trap System • Reduces errors due to solvent evaporation • Available for cones, plates, and concentric
cylinders [cover only]
Visual confirmation of Material’s Response Steady State Rotational Flow
Shear Rate
Tim e
(ddt)
Steady State Oscillatory Flow
Advances in Rheology Equipment
Interest: Rheological Properties Classical Extremes Ideal Solid -- [External Force] -Ideal Fluid STEEL
WATER Strong structure Weak structure Rigidity Deform Retain/recover shape Store Energy
(purely Elastic – R. Hooke, 1678)
[Energy]
Fluidity Flow Lose shape Dissipate Energy (purely Viscous – I. Newton, 1687)
ELASTICITY Storage Modulus
VISCOSITY Loss Modulus
REAL Behavior Apparent Solid [Energy + time] Apparente Fluid
- viscoelastic materials -
TA’s New Concept - “SMT”
“CMT” Technology The Rheometric Series
• • •
and
Historically - Controlled Stress or Controlled Strain rheometers Today - Instruments can do both - to a greater or lesser degree TA’s Rheometry Technology Concept
• SMT • CMT -
Separate Motor & Transducer
- Controlled Strain
Combined Motor & Transducer - Controlled Stress
SMT
CMT
‘ARES’
‘AR’
5 models
5 models
SMT RHEOMETRY - The ARES “from water to steel and everything in between!”
• Independent measure of Torque & Strain • System inertia has no effect on Measurement • Force Rebalance transducer (spring for RDA) • Controlled Strain • Oscillatory testing on low viscosity fluids • Simultaneous measurements • Rheo-Optical • System Optimized for Application • Best Normal Force • LCD display for status information • ARES – a highly recognized name • Powerful Software and Analysis • Powerful, $$$
CMT RHEOMETRY - The AR2000 “from water to steel and everything in between!”
• Controlled Stress • Creep / Recovery test • High Angular Resolution • Advanced Electronics • Mobius Drive – Strain • Smart Swap technology • Very low Shear Rate FC • Signals for each point • Status window • Powerful Software & Analysis • Easy Manual measurements • Versatile, Powerful, great $$$
Rheometrics Series - Labels
TA is the ONLY company that offers SMT & CTM technology with the best technical support
The AR2000 • Advanced design !!! – Mobius™ Drive – Smart Swap™ - Interchangeable Peltier Plate, Peltier Concentric Cylinder, and ETC – Air bearing drive – Normal force sensor – Optical encoder resolution – Casting – Fast Electronics
AR2000 Smart Swap™ • Push button to release and attach temperature • • • •
systems Firmware automatically senses type of system and configures software accordingly All connectors are on front of unit Takes less than 30s to exchange temperature systems All systems are powered and controlled from the main electronics
Smart Swap - Removal Press ‘Release’ button Flashing green status light indicates it is safe to unplug Press ‘Release’ button again
Continuous green status light indicates attachment can be removed
: Specifications • Torque range CS:
0.1N.m to 200mN.m
• Torque range CR:
0.03N.m to 200mN.m
• Speed range CS:
1E-8 to 300rad/s
• Speed range CR:
1E-4 to 300rad/s
• Inertia:
~15N.m2
• Frequency range:
1.2 E-7 to 100Hz
• Step change in speed:
< 30ms
• Step change in strain: < 60ms • Step change in stress:
<1ms
and much more…
AR2000: Angular Resolution - 40nRad 0.1000
0.0100
resolution check-0002o resolution limit
d i s p l a c e m e n t ( r a d )
1.00E-3
1.00E-4
1.00E-5
1.00E-6
1.00E-7
1.00E-8
1.00E-9 0.10
1.00
10.00
100.00 1000.00 osc. torque (micro N.m)
10000.00
1.00E5
1.00E6
Oscillation – Amp. Sweep 20.00
10000.00
17.50 1000.00
15.00
100.00
|n*| (Pa.s)
10.00
10.00
7.500 1.00
5.000
0.10 2.500
0 1.00E-7
0.03 Nm
1.00E-6
1.00E-5 1.00E-4 displacement (rad)
1.00E-3
0.01 0.0100
osc. torque (micro N.m)
12.50
Performance on ~1Pa.s Oil 1000
100.0
velocity (rad/s)
10.00
1.000
0.1000
0.01000
1.000E-3
1.000E-4 1.000E-3
0.01000
[rad/s]
Time to 10% [s]
Time to 1% [s]
0.1
0.015
0.018
1.0
0.014
0.022
10
0.017
0.025
100
NA
NA
0.1000
1Pa.s oil [ 0.1 rad per sec 1Pa.s oil [1.0 rad per sec 1Pa.s oil [10 rad per sec 1.000
time (s)
10.00
100.0
Real Rheological Data 1000
1.000E5
Certified value 1.43Pa.s 100.0 10000
1000 1.000
0.1000 100.0
0.01000 1Pa.s oil 0.1 rad per sec 1Pa.s oil 1.0 rad per sec 1Pa.s oil 10 rad per sec
1.000E-3
1.000E-4 1.000E-3
0.01000
0.1000
1.000
time (s)
10.00
10.00
1.000 100.0
viscosity (Pa.s)
velocity (rad/s)
10.00
Stress Relaxation on PDMS 1.2 1
% strain
0.8 0.6 0.4 0.2 0 0.001
0.01
0.1
1
10
100
• Within 1% of set value in 30ms
time [s]
6 5
% strain
4
• Within 1% of set value in 30ms
3 2 1 0 0.001
0.01
0.1
1
10
100
time [s]
• Within 1% of set value in 30ms
12 10 % strain
8 6 4 2 0 0.001
0.01
0.1
1 time [s]
10
100
Visual confirmation of Material’s Response Steady State Rotational Flow
Shear Rate
Tim e
(ddt)
Steady State Oscillatory Flow
Visual confirmation of Steady State Flow
time
strain
1.000E7 strain
viscosity (Pa.s)
strain
1.000E8
1.000E6
time
time
Carreau a: zero-rate viscosity: 4.982E7 Pa.s b: infinite-rate viscosity: 0.4928 Pa.s c: consistency: 2.007E5 s d: rate index: 0.5756 standard error: 7.506
1.000E5
10000 1.000E-7
1.000E-6
1.000E-5
1.000E-4 1.000E-3 shear rate (1/s)
0.01000
0.1000
1.000
Visual Confirmation - Oscillation Frequency Sweep PDMS
1.000E6 1.000E5
1.000E6
1.000E5
1.000E5 10000 1000
100.0
100.0
| n * | ( P a . s )
10000 1000
10.00 1000
10.00
1.000
1.000
0.1000
G '' ( P a )
G ' ( P a )
10000
0.1000 PDMS Extended frequency sweep-0001o, Frequency sweep step
0.01000 100.0 1.000E-5 1.000E-4 1.000E-3 0.010000.1000 1.000 frequency (Hz)
10.00
0.01000 100.0
Evaluation Methods Viscoelastic Transformations
Background
• Each material has a unique set of viscoelastic properties •
• •
investigated by oscillatory flow, creep/recovery test, or stress relaxation test. If each test is performed within the linear viscoelastic region of the material, the information should be the same even though each test provides different sections of the total rheological characterization profile. Polymer transformation software as a tool may interconvert linear viscoelastic functions. It is now possible to easily transform data obtained from one technique into another.
Interconversion routes oscillation GG
relaxation spectrum H() stress relaxation G(t)
creep compliance J(t)
Stress Relaxation vs. FrequencySweep Transformed Data •
The black line on the plot was calculated by transforming a frequency sweep file through the discrete relaxation spectrum and then on to a stress relaxation file 1.00E5
G t (P a )
10000.000 1000.000 100.000 10.000 1.000 0.01000
0.1000
1.000 time (s)
10.00
100.0
Creep Test Data vs. Frequency Sweep Transformed Data c o m p lia n c e ( m ^ 2 / N )
2.5000E-3 2.2500E-3 2.0000E-3 1.7500E-3 1.5000E-3 1.2500E-3 1.0000E-3 7.5000E-4 5.0000E-4
Real data - shows creep ringing Transformed data – no ringing
2.5000E-4 0 0
0.10000.20000.30000.40000.50000.60000.70000.80000.90001.000 time (s)
Evaluation Methods From H() MWD oscillation GG
relaxation spectrum H() stress relaxation G(t)
creep compliance J(t)
MWD
Blend of ‘Low’ and ‘High’ Mw 1.000E6
1.000E6
1.000E5
1.000E5
115k 1150k Blend 10000 G '' (P a )
G ' (P a )
10000
1000
1000
100.0
100.0
10.00 1.000E-5 1.000E-4 1.000E-3
0.01000 0.1000 1.000 ang. frequency (rad/sec)
10.00
100.0
10.00 1000
Resultant Continuous Spectrum 1.000E7
Recipricol plus e^(PI/2) 1.000E6
1.000E5
H (P a )
10000
1000
100.0
10.00
1.000 1.000E-41.000E-3 0.01000 0.1000
1.000
10.00 Tau (s)
100.0
1000
10000
1.000E5 1.000E6
Resultant MWD 0.3000 Calculated Rouse subtraction
0.2500
w (M )
0.2000
0.1500
0.1000
0.05000
0
4
5
6 Log [Molar mass (g/Mol)]
7
* Comparison 1.000E9 Molecular weight (WLF) n0: 1.365E8 Pa.s Mw: 1.164E6 g/mol 1.000E8
115k 1150k 115k 1150k Blend
1.000E7
|n * | ( P a . s )
Molecular weight (WLF) n0: 2.020E7 Pa.s Mw: 6.613E5 g/mol
1.000E6
1.000E5
Molecular weight (WLF) n0: 1.691E5 Pa.s Mw: 1.606E5 g/mol
10000
1000 1.000E-5
1.000E-4
1.000E-3
0.01000 0.1000 1.000 ang. frequency (rad/sec)
10.00
100.0
1000
Key Points - (review) • Deformation • Flow • Practical view • Advances in rheology equipment • Advances in evaluation methods
CONCLUSIONS….. - Rheology describes the structural behavior and physical properties of materials - SMT and CMT technology provide the most complete rheological characterization of materials - Rheological testing is a very practical and versatile tool - Viscoelastic transformation add more power to rheology instrumentation - TAI is the ONLY company that offers SMT & CMT technology with best technical support and service next …
(Know)
Interest: Rheological Properties Classical Extremes Ideal Solid -- [External Force] -Ideal Fluid STEEL
WATER Strong structure Weak structure Rigidity Deform Retain/recover shape Store Energy
(purely Elastic – R. Hooke, 1678)
[Energy]
Fluidity Flow Lose shape Dissipate Energy (purely Viscous – I. Newton, 1687)
ELASTICITY Storage Modulus
VISCOSITY Loss Modulus
REAL Behavior Apparent Solid [Energy + time] Apparente Fluid
- viscoelastic materials -
WE ARE a company operating at…
