Short introduction into rheology
Basics,
testing in rotation, creep and oscillation,
extensional rheology
Contents
• Viscosity
Controlled shear rate (CR), shear stress (CS), deformation (CD)
• Rotational testing
- Newtonian and Non-Newtonian flow behavior
- Yield stress
- Thixotropy
• Viscoelasticity
Structural reasons, modeling
• Creep & recovery testing
- Description with Burgers model
- Elastic and viscous share
• Oscillatory testing
- Time sweep
e.g. relaxation, gelation, sedimentation
- Amplitude sweep
Linear viscoelastic range (LVR), stability
- Frequency sweep
liquid, paste-like or elastic?
- Temperature sweep
e.g. cross-linking
- Cyclic testing
stability
• Extensional Rheology
2
.
Shear stress t, deformation g and shear rate g
Sample height: h
Deflection:
x
Deformation: g
Shear stress t :
force F applied to area A
F
t =
A
x
g =
h
Shear rate = change of
deformation per time unit
. dg
g =
x
A
F
h
dt
Direction of force
3
Typical shear rates
Application
Sedimentation
Phase separation
Leveling, running
Extrusion
Dip Coatings
Chewing
Pumping, stirring
Brushing
Spraying
4
Shear rate (s-1)
10-6 - 10-4
10-6 - 10-4
10-1 - 101
100 - 102
101 - 102
101 - 102
101 - 103
101 - 104
103 - 104
Absolute and relative viscosity
"Resistance to flow"
Viscosity can be determined indirectly:
torque M * A factor
shear stress
t
Viscosity =  = . =
shear rate
g
rotational speed * M factor
Absolute viscosity readings with known measuring geometry only!
5
Relative viscosity
Any scale reading S (time, distance, angular deflection)
is set into ratio with a known viscosity standard
Viscosity of unknown material calculates as follows:
unknown

= Standard
sStandard
 Sunknown
Parameters of testing (rotor, speed, filling …) strictly need to be
kept constant.
Calibration possible for Newtonian Liquids only!
6
Dynamic and kinematic viscosity

(Dynamic) viscosity  [Pas]
t = shear stress [Pa]
.
g = shear rate [1/s]
1 Pas = 1000 mPas
t
= 
g
1 mPas = 1 cP (centi Poise)
Kinematic viscosity n [mm/s2]
 = density [kg/m³]
1 mm/s² = 1 cSt (centi Stokes)
7

n=

Viscosity of fluids: Measured at 20°C
Substance
Water
Milk
Olive oil
Engine oil
Honey
Bitumen
8
Viscosity
1 mPas
5 - 10 mPas
100 mPas
1000 mPas
10 000 mPas
100 000 000 mPas
Measuring flow behaviour
Determination of flow behavior as a function of
varying shear stress or shear rate
Shear Stress t [Pa]
.
Shear Rate g [1/s]
Ramp
(Thixotropy)
Steps
(Steady state)
Time t [s]
9
Newtonian flow behavior
Example: Oil
500
100
Flow curve
450
400
‚ [Pa]
350
300
.
250
10
Viscosity curve
200
150
100
50
0
0
5
10
15
20
25
30
Á [1/s]
10
ƒ [Pa s]
t - Shear
Stress
. - Viscosity

g - Shear
Rate
35
40
45
50
1
Shear thinning flow behavior:
Structural reasons
Orientation
11
Extension
Deformation Dis-aggregation
Flow behavior: Flow curve
Linear plot
Newtonian
Pseudoplastic
(shear thinning)
Dilatant
(shear thickening)
12
Flow behavior: Viscosity curve
Double-logarithmic plot
Newtonian
Pseudoplastic
(shear thinning)
Dilatant
(shear thickening)
13
Yield stress t0 / yield point – a model
The yield stress t0 is the shear stress t required
- to overcome elastic behavior and
- obtain viscoelastic flow behavior
Shear stress t
14
Yield stress t0: Determination
Controlled deformation (CD) mode:
t0: Maximum of the curve shear stress t vs. time t
(linear scaling)
Controlled rate (CR) ramp:
.
t0: Extrapolation of flow curve to shear rate g = 0
(linear scaling)
Controlled stress (CS) ramp:
t0: Intersection of tangents in the change in slope of the curve
log deformation g vs. log shear stress t
15
Yield stress t0: Determination in CD-mode
• Input:
deformation g (constant)
250
• Measurement:
shear stress t
• Result:
shear stress t = f(time t)
Shear Stress ‚ [Pa]
200
150
100
Curve discussion :
Method
• Evaluation:
Determination of the
curve maximum
(= yield stress t0)
16
t [min] t0 [Pa]
---------------------------
50
Maximum 0.3161
224.9
0
0
0.5
1.0
1.5
Time t [min]
2.0
2.5
Yield stress t0: Determination in CR-mode
• Input:
.
shear rate g (varying)
120
• Measurement:
shear stress t
100
• Result:
.
shear stress t = f(shear rate g)
• Evaluation:
yield stress t0
by Extrapolation
of flow curve .
to shear rate g = 0
using a rheological model
17
‚ [Pa]
80
60
Extrapolation
Casson: t0 = 8.808 [Pa]
40
20
0
0
10
20
30
Á [1/s]
40
50
60
Yield stress t0: Determination in CS-mode
• Measurement:
deformation g
• Result:
log deformation g =
f(log shear stress t)
100.000
Deformation  [-]
• Input:
shear stress t
(increase logarithmic)
10.000
1.000
0.100
0.010
• Evaluation :
Transition between the
linear regimes
(= yield stress t0)
18
t0 = 16 Pa
0.001
0.1
1.0
10.0
Shear Stress ‚ [Pa]
100.0
Bingham flow behavior
Example: Tooth paste
100
t - Shear Stress 550
 - Viscosity
500
.
g - Shear Rate
Decrease
in  due to
yield stress
450
400
Flow curve
ƒ [Pa s]
‚ [Pa]
350
.
300
250
200
150
Bingham
100
yield stress: 50
‚¥ = 29 Pa
0
Viscosity curve
10
0
5
10
15
20
25
Á [1/s]
19
30
35
40
45
50
Thixotropy: Structural behavior
Time-dependent
behavior:
Primary particles
Agglomerates
Network
20
Thixotropy: Definition and determination
• Definition of thixotropic flow behaviour:
- Decrease of viscosity as a function of time upon shearing,
- 100% recovery (= regaining the original structures) as a function of time
without shearing.
• Determination
(1) Time Curves
- Base-line of intact structure at low shear rate (e.g. CR mode: 1 1/s)
or in oscillation (e.g. CD mode: 1% deformation)
- Dis-aggregation at constant shear rate (e.g. CR mode: 100 1/s)
- Re-aggregating time at low shear rate (e.g. CR mode: 1 1/s)
or in oscillation (e.g. CD mode: 1% deformation)
(2) Flow Curves
- Ramp up, (peak hold,) ramp down at constant temperature.
- The hysteresis area in this loop is a measure for the thixotropy.
21
Thixotropy: Time curve
Base-line, dis-aggregation, re-aggregating time
22
Thixotropy: Flow curve (thixotropy loop)
• Input:
shear rate .g
- ramp up
- (peak hold)
- ramp down
500
450
400
• Measurement:
shear stress t
Shear Stress ‚ [Pa]
350
Thixotropic
loop area
300
250
200
• Result:
viscosity 
= f(shear rate.g, time t)
150
100
50
• Evaluation:
Determination of
thixotropic loop area
23
0
0
50
100
150
200
250
300
350
Shear Rate Á [1/s]
400
450
500
Viscoelasticity: Structural reasons
Entanglement
in macromolecules
24
Structure/network
of an emulsion
How to model viscoelasticity?
Viscous flow
Viscoelasticity
Elastic deformation
Spring
Dash pot
.
t = g
Voigt/KelvinModel
MaxwellModel
Burgers-Model
25
t = G*g
Testing methods for viscoelasticity
26
Method
Input
Information
Shear stress ramp
Increasing shear stress
Yieldpoint
Creep test
Const. shear stress
Deformation
Time curve
Const. frequency and
const. amplitude
Monitoring of
chemical reaction
Amplitude sweep
Stepwise increasing
amplitude
Network stability
Frequency sweep
Stepwise increasing
frequency
Time
dependence
Temperature curve
const. frequency and
const. amplitude
Temperature
dependence
Signals applied by a rheometer
.
(Stepped) Ramp (g, t)
Rotational Testing
27
.
Jump (g, t)
.
(Co-)Sinus (g, t)
Creep & Recovery
Oscillatory testing
Creep & recovery testing
.
• Shear rate g at low
stress
• Zero shear viscosity 0
• Equilibrium compliance
Je0
• Ratio of viscous and
elastic properties
• Relaxation time l0
• Elastic Modulus G0
28
Mostly elastic sample
Oscillatory testing: Principle
t=0
(change of direction)
t=0
(change of direction)
29
Oscillatory testing: Complex Quantities





Complex modulus
Storage modulus
Loss modulus
Loss angle
Loss factor
 Complex Viscosity
 Angular frequency
30
G* = G’ + i G’’
(i2 = -1)
G’ (elastic properties)
G’’ (viscous/damping properties )
d
G*
tand = G’’/G’
*= G* / i w
w = 2p f
d
G’
G”
Amplitude Sweep
Example: Delicate gel
Material Stability
Gel strength correlates
with the gel's yield point
The critical stress
from the stress sweep
is used as
characteristic value.
Remember the test is
frequency dependent,
therefore it is a
relative result!
31
LVR
Amplitude Sweep
Example: Gels with different carbopol (hydro colloid) content
32
Frequency Sweep:
Frequency and temperature dependence
122°C
180°C
250°C
elastic
paste
flowing
33
Frequency Sweep
Material Characterization
Paste - Entangled
solution (circles)
Gel - 3D network
(triangles)
Note:
A Gel is not necessarily
“stronger” than a Paste
34
Cross-over
Time Sweep: Gelation
Verlustanteile G"
CrossOver
Parameters:
f = 0.5 Hz
g=1%
T = 35°C
35
Curing
Pwd-cure
G' = f (T)
G" = f (T)
10000000
Curing of powder coating
1000000
G' [Pa],G" [Pa]
100000
Storage modulus G’
Loss modulus G”
10000
1000
100
10
1
80
100
120
140
T
HAAKE RheoWin Pro 2.6
36
[°C]
160
180
200
Test for prediction of temperature stability Brummer et al
• Oscillation (g , w = const.)
• Cyclic temperature ramps (-10 ... 50°C, 20 min each)
• Indicators: G' und G":
37
- G' and G" not affected
sample is stable
- Changes in G' and G"
sample not stable
Test for prediction of temperature stability Brummer et al
G´´ [Pa]
Temp. T [°C]
G´ [Pa]
Example: Cosmetics
w = konstant
Time t [min]
Cyclic testing  stable sample
38
Test for prediction of temperature stability Brummer et al
G´´ [Pa]
Temp. T [°C]
G´ [Pa]
Example: Cosmetics
w = konstant
Time t [min]
Cyclic testing  sample not stable
39
Extensional Rheology
• HAAKE CaBER 1
- Capillary Breakup Extensional Rheometer
- Designed for fluids
• Extensional behaviour ist relevant for
- Processability
- Strand formation / stringiness
- Time to breakup
- Relaxation time
- Filling of bottels etc.
40
Sample
Laser micrometer
Apparent viscosity
Extensional Rheology:
HAAKE CaBER 1 - how it works
Calculations
Result:
Measurement
D=f(t)
41
Apparent extensional
viscosity vs.
Hencky strain
Extensional Rheology: Bottle Filling
• Subtle changes in shampoo formulation caused difference
in strand detachment during bottle filling
• Up-line characterization would prevent costly external
washing of poorly-filled bottles
42
Further Reading
• A handbook of elementary rheology.
H.A. Barnes, University of Wales, Aberystwyth, Dyfed, U.K., 2000
• Non-Newtonian flow in the process industries - fundamentals and
engineering applications.
Chhabra RP, Richardson JF, Butterworth Heinemann, Oxford, 1999
• A practical approach to rheology und rheometry
G. Schramm, Thermo Haake GmbH, Karlsruhe, 1995
• Engineering rheology - Oxford engineering science series vol 52.
R.I. Tanner, Oxford University Press, Oxford, 2000
43
Questions ?
44