Part I: Rotational Rheometry How to measure Shear

Brno, 28-29th march 2012 – School of Rheology
Part I: Rotational Rheometry
How to measure Shear Viscosity correctly?
ω
M
Rotation
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
Basic Terms in Shear Rheometry
displacement u
Tangential-force F
s
area = a · b
Gap = s
b
a
u
γ =
s
.
dγ
γ =
dt
Ftan
τ =
A
strain []
Shear rate [1/s]
Shear stress [Pa=N/m2]
Typical Shear Rate Ranges
Sagging,
Levelling
Extrusion, Injection Moulding
Roll Coating, Spraying
Mixing, Blade Coating, Brushing
10-3
10-1
100
101
102
103
104
106
s -1
Rotational-Rheometer
Sample: Water up to solids
Results: Shear-Viscosity, Yield Stesses, Visco-Elasticity, Relaxation...
High Pressure Capillary-Rheometer
Sample: Water up to high viscous
Results: Shear-Viscosity, Elongational-Viscosity, Wall Slip...
Shear Viscosity
Resistance of a sample against the flow
η =
η −
τ −
.
γ −
τ
.
γ
Shear Viscosity
Shear Stress
Shear Rate
Typical Shear Viscosities
Material
Shear-Viscosity (Pas)
10-6
10-4
10-3
10-1
100
103
108
1012
1040
Air
Aceton
Water
Olive Oil
Glycerol
Molten Polymers
Bitumen
Glass at 500°C
Glass at ambient
Units:
Pascal second
Poise
Pas (SI)
P (CGS)
Remember
1 Pas = 10 P
1 mPas = 1 cP
Shear-Viscosity depends on…
.
η (Τ, p, t, γ) =
τ
.
γ
• Physical-chemical structure of the sample
• Temperature (up to 20% / K)
• Pressure
• Time
• Shear Rate
Steady-State Flow Behaviour
Shear Thinning
Shear Rate
Shear Rate
Shear Rate
Shear Rate
Cornflower
.
Shear Rate
Viscosity
Inks, Paints
Viscosity
Viscosity
Silicon Oil, Suspension
Shear Thickening
Stress
Stress
Stress
Newtonian
Shear Rate
Principle of Operation: Rotational Rheometer
Stress- and
Strain Control
possible.
Motor
•
Air bearing
•
Position
sensor
•
Upper Measuring
Plate
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:
Sample
Temperature
Controller
•
•
•
•
Wide Torque Range 10e-9 to 10e-1 Nm
Short Response times
Small inertia design
Direct Stress and Direct Strain
Choice of Geometry: From Fluids to Solids
Apply Torque /
Measure Torque
M
ω
Measure Displ.
Apply Displacement
δ
R
• the higher the viscosity,
the smaller the geometry
Rule of Thumb
for dispersions:
Gap Size > 10 * D90
Parallel Plates
• the higher the shear rate,
the smaller the gap.
Cup&Bob
Solids Fixture
Cone-Plate / Plate-Plate
•
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
0s-1
10s-1
10s-1
10s-1 10s-1
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
Basic Viscometry: How to run a flow curve
CS-Mode: Steady state and non-steady state measurements
Steady state:
τ
.
γ
Table of stresses
t
t
non-steady state: τ
.
γ
Linear ramp
t
t
1. Steady State Flow Properties
η =
Newton:
Flow Curve:
.
τ = τ (γ)
equivalent
CR-Mode
Shear Viscosity
Curve:
.
η = η (γ)
τ
.
γ
.
.
γ = γ (τ)
CS-Mode
equivalent
η = η (τ)
Steady State Condition
Kinexus Rheometer
γ
J=
τ
⇒ dLnJ/dLnt = 1 for pure viscous flow!
⇒ Deviations show measurement errors!
Steady State Calculation
⎛ γ (t ) ⎞
d ln⎜
⎟
d ln J
τ ⎠ d (ln γ (t ) − ln τ ) d ln γ (t ) d ln τ
⎝
=
=
−
=
d ln t
d ln t
d ln t
d ln t
d ln t
τ
η
0
t
Newtons Law : γ = ∫ ⋅ dt =
τ
⋅t
η
η (t ) = const , τ (t ) = const ⇒
⎛τ ⎞
⎛τ ⎞
d ln⎜⎜ ⋅ t ⎟⎟
d ln⎜⎜ ⎟⎟
d ln γ (t ) d ln τ
⎝ η ⎠ + d ln t − d ln τ =
⎝ η ⎠ − d ln τ =
=
−
=
d ln t
d ln t
d ln t
d ln t
d ln t
d ln t d ln t
=
d (ln τ − ln η ) d ln t d ln τ
+
−
d ln t
d ln t d ln t
=
d ln τ d ln η d ln t d ln τ
−
+
−
d ln t d ln t d ln t d ln t
⇒
d ln J
=1
d ln t
for steady state.
Comparison Stress- and Rate Controlled Test
Shower Gel:
Comparison CS □ und CR ∆ Shear Viscosity Curve
Live Measurement on Kinexus:
Shower Gel Flow Curve
Normal Stress Difference N1
Shower Gel
Ft
Fn
Edge failure
⇒ Always watch the Normal Stress during a Shear Viscosity Measurement!
Steady State Flow Curves: Impact of Particle Size
η (Pa.s)
102
101
175 µm
100
ƒ Increase the size of latex
particles in a pressure sensitive
adhesive from D50=175µm to
D50=750mm
ƒ Polydispersity and Volume
Fraction similar
10-1
750 µm
10-2
10-1
100
101
102 103
.
γ (s-1)
104
105
106
ƒ 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 Dependency
Log η
Entanglement Network / Particle-Particle-Interaction
.
Log γ
Equilibrium
Destruction >
Recovery
No Entanglements
Molecules / Particles
Entanglements / Particle Interaction
Steady State Flow Curves: Impact of Particle Loading
Changing the Volume Fraction of Particles…
Newtonian
φm
< 0.1
0.1 < φ
φm
< 0.5
Log Zero Shear Viscosity
φ
Shear Thinning
Shear Thickening
φ
φm
> 0.5
Krieger-Dougherty:
η
η medium
Volume Fraction
⎛
φ
= ⎜⎜1 −
⎝ φm
⎞
⎟⎟
⎠
− [η ]φ m
Shear Thickening of concentrated dispersions
Kinexus Rheometer
⇒ those shear thickening effects can have negative impact on processability –
see section capillary rheometry
Steady State Flow Curves: Impact of Polydispersity
We keep the volume fraction (φ) constant
But changing polydispersity…
Particle Size Distribution
Volume (%)
20
15
10
5
0
0.1
1
10
Particle Size (µm)
What happens to the viscosity?
100
1000
3000
Impact of Polydispersity on Flow Behaviour
Zero Shear Viscosity
Fine talc of different D50, mixed into an epoxy resin
100%
175 µm
100%
750 µm
Krieger-Dougherty
0%
Increasing amount of 175 µm particles 100%
η
100%
Increasing amount of 750µm particles
0%
η medium
⎛
φ
= ⎜⎜1 −
⎝ φm
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.
⎞
⎟⎟
⎠
− [η ]φ m
Steady State Flow Curves: Impact of Matrix Additives
Xanthan Solution - measured with Cone Plate and Double Gap
1000
η sp
Mw= 2.400.000 g/mol
1%
c
100
M =
Shear viscosity[Pas].
0.5%
= [η ] + k h [η ] c
2
10 π
⋅N
3
A
⋅
R h3
[η ]
10
1%
0.3%
0.5%
1
0.3%
0.1% CP
0.1%
0,1
0.1% DG
0,01
0,001
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]
==> the higher the concentration of Xanthan, the higher the zero shear viscosity.
Further Factors Influencing Dispersion Rheology
Spray Particle
Analyzer
Laser Diffraction
volume fraction, φ
Particle size
Particle size distribution
Digital Microscopy
Vs
Light Scattering
Size and Zeta
Electrostatic interactions
Steric Hindrance
Particle shape
Dry
+
+
+
+
+
+
+
+
------
Wet
Polymer Melt Rheology: Determination of Mw from Flow Curves
.
γ
Polymer Melt Rheology: Effect of Molecular Weight Distribution
Log Viscosity (Pa.s)
ÂA Polymer with a broad MWD exhibits nonNewtonian flow at a lower rate of shear than a
polymer with the same η0 but has a narrow MWD
Narrow MWD
Broad MWD
Log Shear Rate (1/s)
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.
Shear rate
Thixotropic Example
Two samples… one very thixotropic, one not so
thixotropic.
Viscosity
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.
Time
Thixotropy 3- Step-Shear profile
Thixotropy: Decrease of viscosity vs. time at
constant shear + complete recovery under rest
1 2
3
1 = Initial Viscosity at low shear
2 = 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.
Relation to Flow Curves
“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
Log Viscosity
The viscosity plateau’s as the shear rate
approaches zero, i.e. flows / liquid like
when stationary.
THIXOTROPIC
Both materials can be, and tend to be
“thixotropic” – viscosity depends on time.
Rheometer measurement range
Viscometer
Measurement range
10-6
Studying weaker
interactions
Log Shear Rate
106
Studying stronger
interactions
Yield Stress Determination by Stress Ramp and
Creep Tests
Viskoses Fleßen
Schubspannung
3Pa
Schubspannungen
1Pa, 1.5Pa, 2Pa, 2.5Pa
Fließgrenze = 3Pa
Linear or logarithmic Stress Ramp
Energy absorbed - strong association - no flow
Mutliple Creep Tests at different
Stresses
Usually Stress Ramp is used as a pre-test, whereas Multiple Creep
gives precise Yield Stress
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 gravity
on 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
Log Viscosity
Suspension with micron particles
and zeta potential -> 0mV
Associated structure
strong enough to induce
a yield stress.
Suspension with
sub-micron particles
and high zeta potential
Log Shear Stress
At isoelectric point the zero shear viscosity gets infinite
Stronger associated structures which resist even
high shear stresses.
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
pH3.97
pH3.52
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.
Any Questions? torsten.remmler@malvern.de