Rotational Rheometry
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Transcript of 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