fundamentals of rheology

FUNDAMENTALS of RHEOLOGY- From Deformation to Flow of Materials -

Abel Gaspar-RosasTA Instruments, Inc. – USA

2003 Sales MeetingMarbella, Spain

• Review of fundamental concepts of rheology

• Practical issues

• Advances in rheometry

• Advanced evaluation methods

ObjectiveObjectives

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

Judges 5:5

material texp us (you and me)

Flow and Deformation???

Interest: Rheological PropertiesClassical Extremes

Ideal Solid -- [External Force] -- Ideal Fluid

STEEL WATER Strong structure Weak structure Rigidity Fluidity Deform Flow Retain/recover shape Lose shape Store Energy Dissipate Energy (purely Elastic – R. Hooke, 1678) [Energy] (purely Viscous – I. Newton, 1687)

ELASTICITY VISCOSITY Storage Modulus 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

= FA

h

x(t)

1 x(t)

h t

Strain =

x(t)h

Strain Rate = . Vh

Rigidity G =

V

y

x

Az

Shear Deformation

Viscosity =.

=

Shear Flow

Summary of Types of ‘Flow’

Newtonian

Bingham Plastic(shear-thinning with yield stress)

Shear Thickening (Dilatant)

Shear Thinning (Pseudoplastic)

Bingham (Newtonian with yield stress)

Shea

r St

ress

,

Shear Rate,

y

deformation

flow

Model Fitting - Shear Stress vs. Shear Rate

K

K

K

n

n

y

n

c

y

n

n

n

( )

( )

1

1

12

0

Newtonian

Pseudoplastic

Dilatant

Bingham

Casson

Herschel-Bulkley

Summary of Viscosity Models

12

12

12

The Idealized Flow Curve

1

1) Sedimentation2) Leveling, Sagging3) Draining under gravity4) Chewing and swallowing5) Dip coating6) Mixing and stirring7) Pipe flow8) Spraying and brushing9) Rubbing10) Milling pigments in fluid base11) High Speed coating

2 3

6

5

8 9

1.001.00E-5 1.00E-4 1.00E-3 0.0100 0.100

shear rate (1/s)

10.00 100.00 1000.00 1.00E4 1.00E5

log

1.00E6

117

4

10

Models Fit to log-log Plots

0 =(K--

)m

= K 1n 1

= + K1n-1

= - Ko 1n 1

Predicts the shape of the complete Flow Curve

Cross

Sub-sets of the Cross Equation which predict portions of the complete Flow Curve

Power Law

Sisko

Williamson

Rotational Testing Deformation and Flow

upper plate‘moving’

lower plate‘fixed’

sample

Newtonian and Non-Newtonian Behavior of Fluids

Newtonian Region Independent of

Non-Newtonian Region

= f()

1.0001.000E-5 1.000E-4 1.000E-3 0.01000 0.1000

shear rate (1/s)

1.000E5

10000

(P

a.s)

1.000E5

1.000

10.00

100.0

1000

10000

(P

a)

Flow dependence

CMT - Stress Ramp Test - Continuous Ramp

Stress is applied to material at a constant rate. Resultant strain is monitored with time.

Str

ess

(P

a)

time (min.)

m = Stress rate (Pa/min)

USES Yield stress ‘Scouting’ Viscosity Run

Str

ess

(P

a)

Shear Rate,

y

deformation

flow

300.00 50.00 100.0 150.0 200.0 250.0

Shear Stress (Pa)

10000

0.01000

0.1000

1.000

10.00

100.0

1000

Vis

cosi

ty (

Pa.

s)

SMT Samplea: yield stress: 6.582 Pab: viscosity: 0.3777 Pa.sc: rate index: 0.8319

LMT Samplea: yield stress: 5.207 Pab: viscosity: 0.2909 Pa.sc: rate index: 0.8426

Short milling timeLong milling time

Automotive Paint Samples: Data fit to Herschel-Bulkley Model

10001.000 10.00 100.0Shear Stress (Pa)

10000

0.01000

0.1000

1.000

10.00

100.0

1000

Vis

cosi

ty (

Pa.

s)


Automotive Paint Samples: Viscosity vs. Shear Stress

SMT Technology - Step Rate

Select the step rate test to measure the transient viscosity or normal stress difference

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.

The strain rate ramp is ideal for a fast viscosity scan as a function of shear rate for lower to medium viscosity fluids

In a thixotropy experiment, the strain rate is varied linear with time up and down and the stress is recorded over time.

SMT Technology - Thixotropy

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

SMT Technology - Steady Rate Sweep Test

Creep Recovery Experiment

Response of Classical Extremes

– Strain for t>t1 is constant– Strain for t >t2 is 0

time

Str

ain

time

Str

ain

time

– Stain rate for t>t1 is constant– Strain for t>t1 increase with time– Strain rate for t >t2 is 0

t2

Str

ess

t1

t1 t2t2t1

6000.0 global time (s)

80.0

0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

% s

trai

n

Creep Long milling time Short milling time

Automotive Paint Samples: Creep / Recovery Test

Recovery

Recovery

?1

?2

?2

10.001.000E-3 0.01000 0.1000 1.000

time (s)

30.0

0

5.00

10.0

15.0

20.0

25.0

% s

trai

n

Elastic Ringing

Long milling timeShort milling time

Automotive Paint Samples:

Creep Recovery Test

insidethe ?1

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’

lower plate‘fixed’

sample

Dynamic Flow Testing

Deformation

Response

Phase angle

An oscillatory (sinusoidal) deformation (stress or strain) is applied to a sample.

The material response (strain or stress) is measured.

The phase angle , or phase shift, between the control andthe response is measured.

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 modulus (G”)• loss factor (Tan ) critical deformation c

• viscosity () yield point (y)• characteristic times () 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

Non-Linear Region

G = f()Linear Region G is constant

G

1000.00.010000 0.10000 1.0000 10.000 100.00% strain

1000

1.000

10.00

100.0

G' (

Pa

)

100.0

0.01000

os

c. s

tres

s (

Pa

)

Deformation Flow

10001.000E-3 0.01000 0.1000 1.000 10.00 100.0

osc. stress (Pa)

100.0

1.000E-3

0.01000

0.1000

1.000

10.00

G' (

Pa)

Frequency = 6.28 rad/s


Automotive Paint Samples: Stress Sweep after Time Sweep

Elastic Component

Yield Stress y

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

Terminal Region

Rubbery PlateauRegion

TransitionRegion

Glassy Region

12

Storage Modulus (E' or G')

Loss Modulus (E" or G")

log Frequency (rad/s or Hz)

log

G'a

nd G

"

Dynamic Moduli of a Polymer Melt vs. Frequency

10001.000E-4 1.000E-3 0.01000 0.1000 1.000 10.00 100.0

ang. frequency (rad/sec)

1000000

0.1000

1.000

10.00

100.0

1000

10000

100000

G' (

Pa)

1000000

0.1000

1.000

10.00

100.0

1000

10000

100000

G''

(Pa)

1.00E7

100.0

1000

10000

100000

1000000

* (

Pa

.s)

G"

G'

*

PDMS at 20°C

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

time

Vis

cosi

ty

Thixotropic

Rheopectic

Shear Rate = Constant

10000 100.0 200.0 300.0 400.0 500.0 600.0 700.0 800.0 900.0

time (s)

100.0

0.1000

1.000

10.00

G' (

Pa)

Pre_shear: 1000 1/s for 60 secStress = 0.1 PaFrequency = 6.28 rad/s


Automotive Paint Samples: Structural Change – Structure Rebuild (Thixotropy)

Elasticidad

Osc. –> Rotat. -> osc

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

Time

~ 1000 - 2000 micronsfrom final gap

Squeeze Flow effectis less pronounced

Rapid Close

Controlled Close

Comparison of Standard and Exponential Sample Gap Close on Paint

0 200 400 600 800 10000

50

100

150

200

250

Time (s)

G' (

Pa)

Fast Linear Close

Exponential Close

• Reduces errors due to solvent evaporation• Available for cones, plates, and concentric cylinders [cover only]

Solvent Trap System

Shear Rate

Time

(ddt)

Visual confirmation of Material’s Response

Steady State Rotational Flow

Steady State Oscillatory Flow

Advances

in Rheology Equipment

TA’s New Concept - “SMT” and “CMT” TechnologyThe Rheometric Series

• Historically - Controlled Stress or Controlled Strain rheometers• Today - Instruments can do both - to a greater or lesser degree

• TA’s Rheometry Technology Concept

• SMT - Separate Motor & Transducer - Controlled Strain

• CMT - Combined Motor & Transducer - Controlled Stress

SMT‘ARES’5 models

CMT‘AR’

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 - RemovalPress ‘Release’ button

Press ‘Release’ button again

Continuous green status light indicates attachment can be removed

Flashing green status light indicates it is safe to unplug

• 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…

: Specifications

AR2000: Angular Resolution - 40nRad

1.00E60.10 1.00 10.00 100.00 1000.00 10000.00 1.00E5osc. torque (micro N.m)

0.1000

1.00E-9

1.00E-8

1.00E-7

1.00E-6

1.00E-5

1.00E-4

1.00E-3

0.0100

dis

pla

cem

ent

(rad)

resolution check-0002oresolution limit

Oscillation – Amp. Sweep

1.00E-7 1.00E-6 1.00E-5 1.00E-4 1.00E-3 0.0100displacement (rad)

0

2.500

5.000

7.500

10.00

12.50

15.00

17.50

20.00|n

*| (

Pa.

s)

0.01

0.10

1.00

10.00

100.00

1000.00

10000.00

osc. torque (micro N

.m)

0.03 Nm

Performance on ~1Pa.s Oil

[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 NA100.01.000E-3 0.01000 0.1000 1.000 10.00

time (s)

1000

1.000E-4

1.000E-3

0.01000

0.1000

1.000

10.00

100.0

vel

ocity

(ra

d/s)

1Pa.s oil [ 0.1 rad per sec1Pa.s oil [1.0 rad per sec1Pa.s oil [10 rad per sec

Real Rheological Data

100.01.000E-3 0.01000 0.1000 1.000 10.00

time (s)

1000

1.000E-4

1.000E-3

0.01000

0.1000

1.000

10.00

100.0

ve

loci

ty (

rad

/s)

1.000E5

1.000

10.00

100.0

1000

10000

vi

sco

sity

(P

a.s)

1Pa.s oil 0.1 rad per sec1Pa.s oil 1.0 rad per sec

1Pa.s oil 10 rad per sec

Certified value 1.43Pa.s

Stress Relaxation on PDMS

• Within 1% of set value in 30ms



0

0.2

0.4

0.6

0.8

1

1.2

0.001 0.01 0.1 1 10 100

time [s]

% s

tra

in

0

1

2

3

4

5

6

0.001 0.01 0.1 1 10 100

time [s]

% s

trai

n

0

2

4

6

8

10

12

0.001 0.01 0.1 1 10 100

time [s]

% s

tra

in

Shear Rate

Time

(ddt)

Visual confirmation of Material’s Response

Steady State Rotational Flow

Steady State Oscillatory Flow

time

str

ain

time

str

ain

time

str

ain

1.0001.000E-7 1.000E-6 1.000E-5 1.000E-4 1.000E-3 0.01000 0.1000shear rate (1/s)

1.000E8

10000

1.000E5

1.000E6

1.000E7

visc

osi

t y (

Pa.

s)

Carreaua: zero-rate viscosity: 4.982E7 Pa.sb: infinite-rate viscosity: 0.4928 Pa.s

c: consistency: 2.007E5 sd: rate index: 0.5756 standard error: 7.506

Visual confirmation of Steady State Flow

Visual Confirmation - Oscillation Frequency Sweep

100.01.000E-5 1.000E-4 1.000E-3 0.01000 0.1000 1.000 10.00frequency (Hz)

1.000E6

0.01000

0.1000

1.000

10.00

100.0

1000

10000

1.000E5

G' (

Pa

)

1.000E6

0.01000

0.1000

1.000

10.00

100.0

1000

10000

1.000E5

G'' (P

a)

1.000E5

100.0

1000

10000

|n*|

(P

a.s

)

PDMS

PDMS Extended frequency sweep-0001o, Frequency sweep step

Evaluation MethodsViscoelastic Transformations

•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 inter-convert linear viscoelastic functions.

• It is now possible to easily transform data obtained from one technique into another.

Background

Interconversion routes

oscillationGG

creepcompliance

J(t)

stressrelaxation

G(t)

relaxationspectrum

H()

Stress Relaxation vs. FrequencySweepTransformed 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

100.00.01000 0.1000 1.000 10.00time (s)

1.00E5

1.000

10.000

100.000

1000.000

10000.000

Gt (

Pa)

Creep Test Data vs. Frequency SweepTransformed Data

1.0000 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000

time (s)

2.5000E-3

0

2.5000E-4

5.0000E-4

7.5000E-4

1.0000E-3

1.2500E-3

1.5000E-3

1.7500E-3

2.0000E-3

2.2500E-3

com

plia

nce

(m^2

/N)

Real data - shows creep ringingTransformed data – no ringing

Evaluation MethodsFrom H() MWD

oscillationGG

creepcompliance

J(t)

stressrelaxation

G(t)

relaxationspectrum

H()

MWD

10001.000E-5 1.000E-4 1.000E-3 0.01000 0.1000 1.000 10.00 100.0ang. frequency (rad/sec)

1.000E6

10.00

100.0

1000

10000

1.000E5

G' (

Pa)

1.000E6

10.00

100.0

1000

10000

1.000E5

G'' (P

a)

115k 1150k Blend

Blend of ‘Low’ and ‘High’ Mw

1.000E61.000E-41.000E-3 0.01000 0.1000 1.000 10.00 100.0 1000 10000 1.000E5Tau (s)

1.000E7

1.000

10.00

100.0

1000

10000

1.000E5

1.000E6

H (

Pa

)

Recipricol plus e^(PI/2)

Resultant Continuous Spectrum

74 5 6Log [Molar mass (g/Mol)]

0.3000

0

0.05000

0.1000

0.1500

0.2000

0.2500

w(M

)

Calculated Rouse subtraction

Resultant MWD

10001.000E-5 1.000E-4 1.000E-3 0.01000 0.1000 1.000 10.00 100.0ang. frequency (rad/sec)

1.000E9

1000

10000

1.000E5

1.000E6

1.000E7

1.000E8

|n*|

(P

a.s

)

115k1150k115k 1150k Blend

Molecular weight (WLF)n0: 1.691E5 Pa.sMw: 1.606E5 g/mol



* Comparison

Key Points - (review)

• Deformation

• Flow

• Practical view

• Advances in rheology equipment

• Advances in evaluation methods

- 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

CONCLUSIONS…..

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