Rotational Rheometry

8/18/2019 Rotational Rheometry

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M

ω

Rotation

Brno, 28-29th march 2012 – School of Rheology

Part I: Rotational Rheometry

How to measure Shear Viscosity correctly?


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Outline

• Basic terms in shear rheometry

• Principle of Operation: Rotational Rheometer

• Applications:

A) Steady State Flow Curves using a Rotational Rheometer:Impact of particle size, volume fraction and polydispersity on dispersion flow

properties, Polymer Melt Rheology

B) Time-dependent Flow Behaviour

Yield Stress of Dispersions and it`s relation to Zeta Potential, Thixotropy,Structure Recovery

- with Live Tests on Kinexus Rheometer


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Basic Terms in ShearBasic Terms in Shear RheometryRheometryTangentialTangential--force Fforce F

ss

displacement udisplacement u

aa b b

area = aarea = a ·· b bGap = sGap = s

A

F

dt d

s

u

tan=

=

=

τ

γ γ

γ

.

strainstrain [][]

Shear stress [Pa=N/mShear stress [Pa=N/m22]]

Shear rate [1/s]Shear rate [1/s]


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Shear ViscosityShear Viscosity

τ

η =γ

.

γ Shear RateShear Rate

.τ Shear StressShear Stress

η Shear ViscosityShear Viscosity

Resistance of a sample against the flow Resistance of a sample against the flow


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Typical Shear ViscositiesTypical Shear Viscosities

MaterialMaterial

Air Air AcetonAceton

Water Water

Olive OilOlive Oil

GlycerolGlycerolMolten PolymersMolten Polymers

BitumenBitumen

Glass at 500Glass at 500°°CC

Glass at ambientGlass at ambient

Shear Shear --Viscosity (Pas)Viscosity (Pas)

1010--66

1010--44

1010--33

1010--11

101000101033

101088

10101212

10104040

Units: Remember

Pascal second Pas (SI) 1 Pas = 10 P

Poise P (CGS) 1 mPas = 1 cP


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Shear Shear --Viscosity depends onViscosity depends on……

•• PhysicalPhysical--chemical structure of the samplechemical structure of the sample

•• Temperature (up to 20% / K)Temperature (up to 20% / K)

•• PressurePressure

•• TimeTime

•• Shear RateShear Rate

τ

η (Τ, p, t, γ) =

γ

..


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SteadySteady--State Flow Behaviour State Flow Behaviour

..

Shear Rate

Silicon Oil, Suspension Inks, Paints Cornflower

S t r e s s

Shear Rate

Newtonian Shear Thinning Shear Thickening

S t r e s s

Shear Rate

S t r e s s

Shear Rate

V i s c o s i t y

V i s c o s

i t y

Shear Rate

V i s c o s i t y

Shear Rate


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Principle of Operation: Rotational Rheometer

• The drive is situated above the sample,

not below.

• The driven spindle is air bearingsupported so torque can be measured.

• The separate torque transducer is

eliminated!

Advantages:

• Wide Torque Range 10e-9 to 10e-1 Nm

• Short Response times

• Small inertia design

• Direct Stress and Direct Strain

Sample

Upper Measuring

Plate

Temperature

Controller

Position

sensor

Ai r bearing

Motor

Stress- and

Strain Control

possible.


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Choice of Geometry: From Fluids to Solids

R

M

ω

Apply Torque /Measure Torque

Measure Displ.

Apply Displacement

δ

Parallel Plates Cup&Bob Solids Fixture

• the higher the viscosity,the smaller the geometry

• the higher the shear rate,

the smaller the gap.

Rule of Thumb

for dispersions:

Gap Size > 10 * D90


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Cone-Plate / Plate-Plate

0s-1 10s-1

10s-1 10s-1 10s-1

• Cone Adv: Const Shear Rate along

the complete gap, easy cleaning,low sample volume, wide viscosityrange

• Cone DisAdv: only for homogeneous samples, for disperse samples D90 < 10 x gap,

solvent evaporation

• Plate Adv: flexible gap, auto-tensionpossible, low sample volume, oftenused for temperature dependenttests, good for disperse systems

• Plate DisAdv: shear ratedependency, solvent evaporation


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Cup & Bob / Double Gap• Cup&Bob Adv: large gap, works well

for disperse systems, also for samplesshowing sedimentation, large surfacearea, nearly no evaporation effects,

good for low viscous samples, lessimpact of loading errors

• Cup&Bob DisAdv: high moment ofinertia limits oscillation and transientsteps, high cleaning effort, largesample volumes (ca 2ml – 15ml)

• Double Gap Adv: highest sensitivity for low viscous samples, lower inertiacompared to cup&bob, nearly noimpact on loading errors

• Double Gap DisAdv: large samplevolume (ca. 15ml – 30ml), difficultcleaning

Cup&BobCup&Bob accacc DIN53019DIN53019

Double GapDouble Gap


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BasicBasic ViscometryViscometry: How to run a flow curve: How to run a flow curveCS CS -- Mode: Steady state and non Mode: Steady state and non--steady state measurementssteady state measurements

Steady state:Steady state:

nonnon--steady state:steady state:

τ

τ

γγ

γγ

.

.

tt tt

tttt

Table of stressesTable of stresses

Linear rampLinear ramp


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Newton:τη =γ

.

CR-Mode CS-Mode

. equivalentFlow Curve: τ = τ (γ) γ = γ (τ). .

equivalentShear Viscosity

Curve: η = η (γ) η = η (τ).

1. Steady State Flow Properties


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SteadySteady State ConditionState Condition

⇒⇒ dLnJ/dLntdLnJ/dLnt = 1= 1 for for pure pure viscousviscous flowflow!!⇒⇒ DeviationsDeviations showshow measurementmeasurement errorserrors!!

Kinexus Rheometer

τ

γ = J


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SteadySteady StateState CalculationCalculation

( )( )( ) ( )

( ) ( )

( )

( )

.1ln

ln

ln

ln

ln

ln

ln

ln

ln

ln

ln

ln

ln

ln

ln

lnln

ln

ln

ln

ln

ln

ln

ln

ln

ln

ln

ln

ln

ln

ln

,

:

ln

ln

ln

ln

ln

lnln

ln

ln

ln

ln

0

statesteady for t d

J d

t d

d

t d

t d

t d

d

t d

d

t d

d

t d

t d

t d

d

t d

d

t d

t d

t d

d

t d

d

t d

t d

t d

d

t d

t d

const t const t

t dt Law Newtons

t d

d

t d

t d

t d

t d

t d

t d

t d

J d

t

=⇒

−+−=

−+−

=

=−+⎟⎟ ⎠

⎞⎜⎜⎝

⎛

=−⎟⎟ ⎠

⎞⎜⎜⎝

⎛ ⋅

=−=

⇒==

⋅=⋅=

−=−

=⎟ ⎠ ⎞

⎜⎝ ⎛

=

∫

τ η τ

τ η τ

τ η

τ

τ η

τ

τ γ

τ η

η τ

η τ γ

τ γ τ γ τ

γ


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ComparisonComparison StressStress-- and Rateand Rate ControlledControlled TestTest

Shower Gel:

Comparison CS □ und CR ∆ Shear Viscosity Curve

Live Measurement onLive Measurement on KinexusKinexus::

Shower Gel Flow CurveShower Gel Flow Curve


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Normal StressNormal Stress DifferenceDifference N1N1

⇒⇒ AlwaysAlways watchwatch thethe Normal Stress Normal Stress duringduring aa Shear Shear ViscosityViscosity MeasurementMeasurement!!

Fn

Ft

Shower Gel

Edge failure


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SteadySteady StateState FlowFlow CurvesCurves: Impact of: Impact of ParticleParticle SizeSize

10-1

100

101

102

103

104

105

106

γ (s-1)

10-2

10-1

100

101

102

η

( P a . s

)

Increase the size of latex

particles in a pressure sensitiveadhesive from D50=175µm to

D50=750mm

Polydispersity and Volume

Fraction similar

175 µm

750 µm

.

Smaller size means an increase in number of particles which causes an

increase in particle-particle interactions. Hence an increase in low shear

viscosity.


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Reason for Shear Rate Dependency

Entanglement Network / Particle-Particle-Interaction

Log γ

L o g

Equilibrium

Molecules / Particles

Entanglements / Particle Interaction

Destruction >

Recovery

No Entanglements

..


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Changing the Volume Fraction of Particles…

L o g

Z e r o S h e a r V i s

c o s i t y

1.0<mφ

φ 5.01.0 mφ

φ

Volume Fraction

Newtonian Shear Thinning Shear Thickening

[ ] m

mmedium

φ η

φ φ

η η

−

⎟⎟ ⎠ ⎞⎜⎜

⎝ ⎛ −= 1

Krieger-Dougherty:

SteadySteady StateState FlowFlow CurvesCurves: Impact of: Impact of ParticleParticle LoadingLoading


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Shear Shear ThickeningThickening ofof concentrated concentrated dispersionsdispersions

⇒⇒ thosethose shear shear thickeningthickening effectseffects cancan havehave negativenegative impactimpact onon processability processability – – seesee sectionsection capillarycapillary rheometryrheometry

Kinexus Rheometer


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We keep the volume fraction (φ ) constant

But changing polydispersity…

What happens to the viscosity?

Particle Size Distribution

0.1 1 10 100 1000 3000

Particle Size (µm)

0

5

10

15

20

V o l u m e ( % )

SteadySteady StateState FlowFlow CurvesCurves: Impact of: Impact of PolydispersityPolydispersity


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Impact ofImpact of PolydispersityPolydispersity onon FlowFlow Behaviour Behaviour Fine talc of different D50, mixed into an epoxy resin

Increasing amount of 175Increasing amount of 175 µµmm particlesparticles

Z

e r o S h e a r V i s c

o s i t y

100%

175 µm

100%

750 µm

Increasing amount of 750Increasing amount of 750µµm particlesm particles

0%0%

100%100%

100%100%

0%0%

If you want to increase the solid content of the sample but keep the viscosity the same,

increase the particle size distribution (polydispersity) as well.

Conversely, narrow the particle size distribution to increase the viscosity.

[ ] m

mmedium

φ η

φ

φ

η

η −

⎟⎟ ⎠

⎞

⎜⎜⎝

⎛

−= 1

Krieger-Dougherty


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==>==> the higher the concentration ofthe higher the concentration of XanthanXanthan, the higher the zero shear viscosity., the higher the zero shear viscosity.

Xanthan Solution - measured with Cone Plate and Double Gap

0,001

0,01

0,1

1

10

100

1000

1,0E-04 1,0E-03 1,0E-02 1,0E-01 1,0E+00 1,0E+01 1,0E+02 1,0E+03

Shear Rate [1/s]

S h e a r v i s c o

s i t y [ P a s ] .

1%

0.5%

0.3%

0.1% CP

0.1% DG

1%

0.1%

0.3%

0.5% [ ]η π

3

3

10 h

A

R N M ⋅⋅=

[ ] [ ] ck c

hsp 2η η η +=Mw= 2.400.000 g/mol

SteadySteady StateState FlowFlow CurvesCurves: Impact of Matrix: Impact of Matrix AdditivesAdditives


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Further Factors Influencing Dispersion Rheology

volume fraction, φ Particle size Particle size distribution

Particle shapeElectrostatic interactions

Vs

- - - - - -+ + + +

+ + + +

Steric Hindrance

Laser Diffraction

Digital Microscopy

Light Scattering

Size and Zeta

Spray Particle

Analyzer

Wet

Dry


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Polymer Melt Rheology: Determination of Mw from Flow Curves

γγ.


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Polymer Melt Rheology: Effect of Molecular Weight Distribution

Narrow MWD

Broad MWD

Log Shear Rate (1/s)

L o g

V i s c o s i t y

( P a . s

)

A Polymer with a broad MWD exhibits non-

Newtonian flow at a lower rate of shear than a

polymer with the same η0 but has a narrow MWD


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2. Time Dependent Flow PropertiesViscosity is not only dependent on shear rate it is

also time dependent.

Think of paint. Thick in the can when left in the

shed for months, but thins when stirred.

However, it is thixotropic as it does not rebuild

straight away on stopping the stirring.


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Thixotropic Example

Two samples… one very thixotropic, one not so

thixotropic.

Time

S h e a r r a t e

V i s c o s i t y

Time

Bad paint – leaves brush

marks.Rebuilds too thick too quickly.

Good paint – leaves smooth

finish.

Rebuilds quite slowly. Enough

time to allow ridges to smooth

out.


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Thixotropy 3- Step-Shear profile

Thixotropy: Decrease of viscosity vs. time at

constant shear + complete recovery under rest

11 22 33

1 = Initial Viscosity at low shear

2 = high shear phase (time-and rate dependent)

3 = Recovery


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Another Time Dependent Property: Yield Stress

Some samples require a certain stress until they

flow – a yield stress.

A transition to go from solid to liquid. Or…

Why toothpaste needs to be squeezed to get

out of the tube.

However, does not flow into bristles on tooth

brush.

Why Heinz tomato sauce needs a whack.

But still looks thick on the plate.

Or why pumps take time to get going.


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L o g V i s c o s i t y

Log Shear Rate

“YIELD STRESS”

An ever increasing viscosity as theshear rate approaches zero, i.e. a does

not flow / solid like when stationary.

ZERO SHEAR VISCOSITY

The viscosity plateau’s as the shear rateapproaches zero, i.e. flows / liquid like

when stationary.

10-6 106

Studying weaker

interactions

Studying stronger

interactions

Rheometer measurement range

Viscometer Measurement range

THIXOTROPIC

Both materials can be, and tend to be“thixotropic” – viscosity depends on time.

Relation to Flow CurvesRelation to Flow Curves


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UsuallyUsually StressStress Ramp Ramp isis used used as a as a pre pre-- test test , , whereaswhereas Multiple Multiple CreepCreep

gives gives precise precise Yield Yield StressStress

Fließgrenze = 3Pa

Schubspannungen

1Pa, 1.5Pa, 2Pa, 2.5Pa

Schubspannung3Pa

Viskoses Fleßen

Energy absorbed - strong association - no flow

Linear Linear or or logarithmiclogarithmic StressStress Ramp Ramp Mutliple Mutliple CreepCreep Tests at differentTests at different

StressesStresses

Yield Stress Determination by Stress Ramp and

Creep Tests


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Example: Stable Metal Oxide Dispersions

In this case study we have a sample of silica

(silicon oxide) which has an average particle size

greater than 1 micrometer.

Conventional colloidal theory of

increasing the zeta potential

to ±30mV is insufficient tocounter the effect of gravity

on these large particles…


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Particle Size

Sample characterised on a Mastersizer 2000,

showing a particle size greater the 1 micrometer.

Laser Diffraction


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Zeta Potential

Titrating a silica sample with HCl on a

Zetasizer Nano with MPT-2 autotitrator.

The isoelectric point (where the zeta potential is

zero) is in the very acidic (pH 1) region.


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Steady-Shear Viscosity vs Zeta-Potential

At isoelectric point the zero shear viscosity gets infinite

Stronger associated structures which resist even

high shear stresses.

L

o g V i s c o s i t y

Log Shear Stress

Associated structure

strong enough to induce

a yield stress.

Suspension with

sub-micron particles

and high zeta potential

Suspension with micron particles

and zeta potential -> 0mV


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Resultant Rheology for the Silica Supsension

As the particles associate more, with pH’s closer

to the iso-electric point, the viscosity increases.

pH2.42

pH3.52pH3.97

Materials with higher low shear viscosities are

regards as more resistance to separation.


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Resulting Yield Stress for the Silica Suspension

Yields stress measurements (the stress at the peak of

instantaneous viscosity) is a measurement of the internal

strength of material.

pH2.42 – yield stress = 15.8 Pa

pH3.52 – yield stress = 2.5 Pa

pH3.97 – no yield stress


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Thank you for your attention!

Please join our sessions on:

Capillary Rheometry and Oscillatory Rheometry.

Any Any QuestionsQuestions?? [email protected]@malvern.de

Documents

Rotational Rheometry