M

ω

Rotation

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

Part I: Rotational Rheometry

How to measure Shear Viscosity correctly?

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 flowproperties, Polymer Melt Rheology

B) Time-dependent Flow BehaviourYield Stress of Dispersions and it`s relation to Zeta Potential, Thixotropy, Structure Recovery

- with Live Tests on Kinexus Rheometer

Basic Terms in Shear Basic Terms in Shear RheometryRheometry

TangentialTangential--force Fforce F

ss

displacement udisplacement u

aa bb

area = a area = a ·· bbGap = s Gap = s

AFdtdsu

tan=

=

=

τ

γγ

γ

.

strainstrain [][]

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

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

TypicalTypical ShearShear Rate RangesRate Ranges

1010--111010--33

SaggingSagging, , LevellingLevelling

101044101011

Extrusion, Extrusion, InjectionInjection MouldingMoulding

101000 101022

MixingMixing, Blade , Blade CoatingCoating, , BrushingBrushing

101033 101066

Roll Roll CoatingCoating, , SprayingSpraying

ss--11

RotationalRotational--RheometerRheometer

High Pressure CapillaryHigh Pressure Capillary--RheometerRheometerSample: Water up to high viscousSample: Water up to high viscousResults: ShearResults: Shear--Viscosity, Viscosity, ElongationalElongational--Viscosity, Wall Slip...Viscosity, Wall Slip...

Sample: Water up to solidsSample: Water up to solidsResults: ShearResults: Shear--Viscosity, Yield Viscosity, Yield StessesStesses, , ViscoVisco--Elasticity, Relaxation...Elasticity, Relaxation...

Shear ViscosityShear Viscosity

τη =γ.

γ − Shear RateShear Rate.τ − Shear StressShear Stress

η − Shear ViscosityShear Viscosity

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

Typical Shear ViscositiesTypical Shear Viscosities

MaterialMaterial

AirAirAcetonAcetonWaterWaterOlive OilOlive OilGlycerolGlycerolMolten PolymersMolten PolymersBitumenBitumenGlass at 500Glass at 500°°CCGlass at ambientGlass at ambient

ShearShear--Viscosity (Pas)Viscosity (Pas)

1010--66

1010--44

1010--33

1010--11

101000

101033

101088

10101212

10104040

Units: RememberPascal second Pas (SI) 1 Pas = 10 PPoise P (CGS) 1 mPas = 1 cP

ShearShear--Viscosity depends onViscosity depends on……

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

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

•• PressurePressure

•• TimeTime

•• Shear RateShear Rate

τη (Τ, p, t, γ) =

γ.

.

SteadySteady--State Flow BehaviourState Flow Behaviour

..

Shear Rate

Silicon Oil, Suspension Inks, Paints Cornflower

Stre

ss

Shear Rate

Newtonian Shear Thinning Shear Thickening

Stre

ss

Shear Rate

Stre

ss

Shear Rate

Vis

cosi

ty

Vis

cosi

ty

Shear Rate

Vis

cosi

ty

Shear Rate

Principle of Operation: Rotational Rheometer

• The drive is situated above the sample, not below.

• The driven spindle is air bearing supported 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

Air bearing

Motor

Stress- and Strain Control

possible.

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 Thumbfor dispersions:

Gap Size > 10 * D90

Cone-Plate / Plate-Plate

0s-1 10s-1

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

• Cone Adv: Const Shear Rate alongthe complete gap, easy cleaning, low sample volume, wide viscosityrange

• Cone DisAdv: only forhomogeneous samples, fordisperse 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 rate dependency, solvent evaporation

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 of inertia limits oscillation and transientsteps, high cleaning effort, large sample volumes (ca 2ml – 15ml)

• Double Gap Adv: highest sensitivity forlow viscous samples, lower inertiacompared to cup&bob, nearly no impact on loading errors

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

Cup&BobCup&Bob accacc DIN53019DIN53019

Double GapDouble Gap

Basic Basic ViscometryViscometry: How to run a flow curve: How to run a flow curveCSCS--Mode: Steady state and nonMode: 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

Newton:τη =γ.

CR-Mode CS-Mode

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

. .

equivalentShear ViscosityCurve: η = η (γ) η = η (τ)

.

1. Steady State Flow Properties

SteadySteady State ConditionState Condition

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

Kinexus Rheometer

τγ

=J

SteadySteady State State CalculationCalculation( )

( )( ) ( )

( ) ( )

( )

( )

.1lnln

lnln

lnln

lnln

lnln

lnln

lnln

lnlnln

lnln

lnln

ln

ln

lnln

ln

ln

lnln

lnln

,

:

lnln

lnln

lnlnln

ln

ln

lnln

0

statesteadyfortdJd

tdd

tdtd

tdd

tdd

tdd

tdtd

tdd

tdd

tdtd

td

d

tdd

td

td

tdd

tdtd

consttconstt

tdtLawNewtons

tdd

tdtd

tdtd

td

td

tdJd

t

=⇒

−+−=

−+−

=

=−+⎟⎟⎠

⎞⎜⎜⎝

⎛

=−⎟⎟⎠

⎞⎜⎜⎝

⎛⋅

=−=

⇒==

⋅=⋅=

−=−

=⎟⎠⎞

⎜⎝⎛

=

∫

τητ

τητ

τητ

τητ

τγ

τηητ

ητγ

τγτγτγ

ComparisonComparison StressStress-- and Rate and Rate ControlledControlled TestTest

Shower Gel: Comparison CS □ und CR ∆ Shear Viscosity Curve

Live Measurement on Live Measurement on KinexusKinexus: : Shower Gel Flow CurveShower Gel Flow Curve

Normal Stress Normal Stress DifferenceDifference N1N1

⇒⇒ AlwaysAlways watchwatch thethe Normal Stress Normal Stress duringduring a a ShearShear ViscosityViscosity MeasurementMeasurement!!

Fn

Ft

Shower Gel

Edge failure

SteadySteady State State 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 latexparticles in a pressure sensitive adhesive 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.

Reason for Shear Rate DependencyEntanglement Network / Particle-Particle-Interaction

Log γ

Log

η

Equilibrium

Molecules / Particles

Entanglements / Particle Interaction

Destruction >Recovery

No Entanglements

..

Changing the Volume Fraction of Particles…

Log

Zer

o S

hear

Vis

cosi

ty1.0<

mφφ 5.01.0 <<

mφφ 5.0>

mφφ

Volume Fraction

Newtonian Shear Thinning Shear Thickening

[ ] m

mmedium

φη

φφ

ηη

−

⎟⎟⎠

⎞⎜⎜⎝

⎛−= 1

Krieger-Dougherty:

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

ShearShear ThickeningThickening of of concentratedconcentrated dispersionsdispersions

⇒⇒ thosethose shearshear thickeningthickening effectseffects cancan havehave negative negative impactimpact on on processabilityprocessability ––seesee sectionsection capillarycapillary rheometryrheometry

Kinexus Rheometer

We keep the volume fraction (φ) constantBut 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

Vol

ume

(%)

SteadySteady State State FlowFlow CurvesCurves: Impact of : Impact of PolydispersityPolydispersity

Impact of Impact of PolydispersityPolydispersity on on FlowFlow BehaviourBehaviourFine talc of different D50, mixed into an epoxy resin

Increasing amount of 175 Increasing amount of 175 µµmm particlesparticles

Zero

She

ar V

isco

sity

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

φη

φφ

ηη

−

⎟⎟⎠

⎞⎜⎜⎝

⎛−= 1

Krieger-Dougherty

==> ==> the higher the concentration of the 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]

Shea

r vis

cosi

ty[P

as].

1%0.5%0.3%0.1% CP0.1% DG

1%

0.1%

0.3%

0.5% [ ]ηπ 3

310 h

AR

NM ⋅⋅=

[ ] [ ] ckc hsp 2ηη

η+=Mw= 2.400.000 g/mol

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

Further Factors Influencing Dispersion Rheology

volume fraction, φ Particle size Particle size distribution

Particle shapeElectrostatic interactions

Vs

- - - - - -+ + + +

+ + + +

Steric Hindrance

Laser Diffraction

Digital MicroscopyLight Scattering

Size and Zeta

Spray ParticleAnalyzer

Wet

Dry

Polymer Melt Rheology: Determination of Mw from Flow Curves

γγ.

Polymer Melt Rheology: Effect of Molecular Weight Distribution

Narrow MWD

Broad MWD

Log Shear Rate (1/s)

Log

Visc

osity

(Pa.

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

2. Time Dependent Flow Properties

Viscosity 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.

Thixotropic Example

Two samples… one very thixotropic, one not so thixotropic.

Time

She

ar ra

teV

isco

sity

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.

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 shear2 = high shear phase (time-and rate dependent)

3 = Recovery

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.

Log

Vis

cosi

ty

Log Shear Rate

“YIELD STRESS”

An ever increasing viscosity as the shear rate approaches zero, i.e. a does not flow / solid like when stationary.

ZERO SHEAR VISCOSITY

The viscosity plateau’s as the shear rate approaches zero, i.e. flows / liquid likewhen stationary.

10-6 106

Studying weakerinteractions

Studying strongerinteractions

Rheometer measurement range

ViscometerMeasurement range

THIXOTROPIC

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

Relation to Flow CurvesRelation to Flow Curves

UsuallyUsually Stress Stress RampRamp isis usedused as a as a prepre--testtest, , whereaswhereas Multiple Multiple CreepCreepgivesgives preciseprecise YieldYield StressStress

Fließgrenze = 3Pa

Schubspannungen1Pa, 1.5Pa, 2Pa, 2.5Pa

Schubspannung3Pa

Viskoses Fleßen

Energy absorbed - strong association - no flow

Linear Linear oror logarithmiclogarithmic Stress Stress RampRamp MutlipleMutliple CreepCreep Tests at different Tests at different StressesStresses

Yield Stress Determination by Stress Ramp and Creep Tests

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 to counter the effect of gravityon these large particles…

Particle Size

Sample characterised on a Mastersizer 2000, showing a particle size greater the 1 micrometer.

Laser Diffraction

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.

Steady-Shear Viscosity vs Zeta-Potential

At isoelectric point the zero shear viscosity gets infiniteStronger associated structures which resist even high shear stresses.

Log

Vis

cosi

ty

Log Shear Stress

Associated structure strong enough to induce a yield stress.

Suspension withsub-micron particlesand high zeta potential

Suspension with micron particlesand zeta potential -> 0mV

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.

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

Thank you for your attention!

Please join our sessions on:

Capillary Rheometry and Oscillatory Rheometry.

AnyAny QuestionsQuestions? ? torsten.remmler@malvern.detorsten.remmler@malvern.de