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How to measure the shear viscosity properly?
Torsten Remmler, Malvern Instruments
v
Capillary
p
testXpo Fachmesse für Prüftechnik 10.-13.10.2016
M
Rotation
Outline
• How is the Shear Viscosity defined?
• Principle of Operation: Rotational and Capillary Rheometer
• Choice of the Correct Geometry
• Steady State Condition
• Example for Steady State Shear Viscosity Curve
Basic Terms in Shear Rheometry
Tangential-force F
s
displacement u
a b
area = a · bGap = s
AFdtdsu
tan
.
strain []
Shear stress [Pa=N/m2]
Shear rate [1/s]
Typical Shear Rate Ranges
10-110-3
Sagging, Levelling
104101
Extrusion, Injection Moulding
100 102
Mixing, Blade Coating, Brushing
103 106
Roll Coating, Spraying
s-1
Rotational-Rheometer
High Pressure Capillary-RheometerSample: Water up to high viscousResults: Shear-Viscosity, Elongational-Viscosity, Wall Slip...
Sample: Water up to solidsResults: Shear-Viscosity, Yield Stesses, Visco-Elasticity, Relaxation...
Shear Viscosity
=.
Shear Rate. Shear Stress
Shear Viscosity
Resistance of a sample against the flow
Typical Shear Viscosities
Material
AirAcetonWaterOlive OilGlycerolMolten PolymersBitumenGlass at 500°CGlass at ambient
Shear-Viscosity (Pas)
10-6
10-4
10-3
10-1
100
103
108
1012
1040
Units: RememberPascal second Pas (SI) 1 Pas = 10 PPoise P (CGS) 1 mPas = 1 cP
Shear-Viscosity depends on…
• Physical-chemical structure of the sample • Temperature (up to 20% / K)• Pressure• Time• Shear Rate
p, t, ) =
.
.
Steady-State 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
Visc
osity
Visc
osity
Shear Rate
Visc
osity
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: Rotational Rheometry
R
M
Apply Torque /Measure Torque
Measure Displ.Apply Displacement
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 along the complete gap, easy cleaning, low sample volume, wide viscosity range
• Cone DisAdv: only for homogeneous samples, for disperse samples D90 < 10 x gap, solvent evaporation
• Plate Adv: flexible gap, auto-tension possible, low sample volume, often used for temperature dependent tests, 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 samples showing sedimentation, large surface area, nearly no evaporation effects, good for low viscous samples, less impact of loading errors
• Cup&Bob DisAdv: high moment of inertia limits oscillation and transient steps, high cleaning effort, large sample volumes (ca 2ml – 15ml)
• Double Gap Adv: highest sensitivity for low viscous samples, lower inertia compared to cup&bob, nearly no impact on loading errors
• Double Gap DisAdv: large sample volume (ca. 15ml – 30ml), difficult cleaning
Cup&Bob acc DIN53019
Double Gap
Given quantity: piston speed wall shear rateMeasured quantity: pressure drop wall shear stress
Bore
L
Fully developed flow region
entry
P1
Pw
00 L
Z
P
v
2R
Entrance pressure drop
Shear pressure drop
Full pressure drop
=
+
Principle of Operation: Capillary Rheometer
RH2000
Laminar Pipe Flow
Isothermal, stationary Flow of an incompressible fluid
Newtonian
-R R0
-R 0 R
0
Newtonian
Non-Newtonian
Q = Volume Flux, R= Die Radius, L= Die Length, P=Pressure Drop
3app
Q4R
.
2P. R
Lapp
Choice of Geometry: Capillary Rheometer
2-3 decades of shear rate can be achieved with a capillary die
3app
Q4R×
.
2P× R
×Lapp
Shear Rate Ranges:
2.0mm = ca. 0.1 bis 100 /s1.5mm = ca. 1 bis 1000 /s
1.0mm = ca. 10 bis 10000 /s0.5mm = ca. 100 bis 100.000 /s
0.3mm = ca. 1000 bis 1.000.000 /s
Q = Volume Flux, R= Die Radius, L= Die Length, P=Pressure Drop
Basic Viscometry: How to run a flow curve
CS-Mode: Steady state and non-steady state measurements
Steady state:
non-steady state:
t
t
Table
Ramp
t
.
No Time-Dependency: = ().
t
Time Dependency = (t).
Newton: =.
CR-Mode CS-Mode
. equivalentFlow Curve: = () = ()
. .
equivalentShear ViscosityCurve: = () = ()
.
Steady State Flow Properties
Steady State Condition: Rotational Rheometry
dLnJ/dLnt = 1 for pure viscous flow! Deviations show measurement errors!
Kinexus Rheometer
J
Steady State Condition: Capillary Rheometry
Equilibrium Pressure Drop is needed for Steady State Viscosity.
homogeneous inhomogeneous
Comparison Stress- and Rate Controlled Test
Shower Gel: Comparison CS □ und CR ∆ Shear Viscosity Curve
Normal Stress Difference N1
Fn
Ft
R
FN
Always watch the Normal Stress during a Shear Viscosity Measurement!
Example: Steady State Viscosity Curve
The maximum of relaxation spectrum H() corresponds to reciprocal cross-overFrequency from oscillatory shear experiment.
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% 3
310 h
AR
NM
ckc hsp 2
Mw= 2.400.000 g/mol
Conclusion
• Correct Geometry Choice is key for Viscosity Measurement
• Steady State Condition in both Rotational and Capillary Rheometry
• Monitoring N1
• Interpretation: Correct Stress / Shear Rate Range for Shear Viscosity Curve
