The document discusses the rheology and microstructure of structured fluids at high shear rates, focusing on three case studies: alkyd resin suspension, ice cream, and carbon nanotubes. It examines shear thinning mechanisms using various equations and models, highlighting experimental results and viscosity behavior under different conditions. Key findings include high shear viscosity reduction due to drop deformation in suspensions and the complex interactions within ice cream and carbon nanotube composites.

1. CEMEF. Sophia Antipolis, April 2005
“The rheology and microstructure of structured fluids
at high shear rate.”
( Shear thinning and shear thinning mechanisms)
By
Malcolm Mackley
Department of Chemical Engineering
University of Cambridge
With acknowledgment to;
Members of Polymer Fluids Group.
Case study 1
Alkyd Resin suspension. Dr Martin Thompson
Case study 2
Ice Cream. Dr Karine Odic
Case study 3
Carbon Nanotubes. Prof Alan Windle, Dr Simon Butler
Sameer Rahatekar

2. Non Newtonian flow; Shear thinning equations
Power law fluid. Carreau Equation. Cross equation.
(ηo - η ∞ )
[ ]
⋅
n −1 2 −p
ηa = k γ η a = η 0 1 + ( λγ ) ηa = η∞ +
 ⋅n
1 + α γ 
 
 
10000
Power Law S1
S2
1000 S3
Apparent S4
Carreau S5
viscosity S6
S7
ηa Pas 100 S8
S9
S10
Cross
S11
S12
10 S13
S14
S15
S16
S17
1 S18
1 10 100 1000 10000 100000 1000000
Shear rate γ s -1

3. The Mechanisms for shear thinning
Molten Polymers.
10000
Chain orientation Doi and Edwards 1978
1000
Apparent100
Entanglement
Carreau S7
S8 Chain stretch Mcleish and Larson 1987
S9
viscosity S10
of chains S11
S12
10
Chain disentanglement ?
1
1 10 100 1000 10000 100000 1000000
Shear rate
Particle suspensions.
1000
Cross Effect of shear on number of interactions
100
Moore and Chen 1967
C1
C2
Apparent Interactions C3
dm
C4
Viscosity contribution due to interactions
= - k 1m γ n + k 2 [ m 0 - m ]
viscosity of particle C5
C6
10
dt
1 Matrix viscosity
ηi m
1 10 100 1000 10000 100000 1000000
=
Shear rate ηi o
mo

4. Viscosity modification in a simple shear flow
due to presence of particles, drops or voidage
Spheres.
η r = η 0 ( 1 + 2.5 φ ) Einstein
Flow 1911
− [ η ] φm
 φ  Krieger Dougherty
ηr =  1 -
 φ   1959
 m
Flow
Cylinders
Flow
?????????
Flow

5. Cambridge Multi-Pass Rheometer

6. Multi-Pass Rheometer (MPR)
top piston
heating jacket
pressure transducer
slit die or
capillary inserts
bottom piston

7. Data from MPR
Pressure difference vs time Flow curve
10000
differential pressure
1000
time Predicted
η * (Pa.s)
RDS
MPR2, L/D=2.5
MPR2, L/D=5
MPR2, L/D=20
MPR4, L/D=2.5
MPR4, L/D=4
MPR4, L/D=5
100
0.01 0.1 1 -1 10 100 1000 10000
shear rate (s )
FLOW

8. Case Study 1. Martin Thompson
Alkyd resin suspension. Water drops in polymer resin matrix.
Visualisation; Linkam CSS (Cambridge Shear System)
M.J.Thompson, J.R.A Pearson and M.R.Mackley Journal of Rheology. 45(6) 1341-1358 (2001)

9. Bohlin concentric cylinder rheometer and MPR capillary data
25
φ = 0.000
φ = 0.020
20
φ = 0.048
Apparent viscosity Pas
φ = 0.091
15
φ = 0.167
φ = 0.286
10
Concentric
5 cylinders MPR
0
10 100 1000 10000 100000
Shear stress Pa
Remarkably; High shear viscosity of deformed drop suspension is lower than the base viscosity of matrix

10. MPR slit flow optical scattering data
Flow
(a)
CCD camera
670nm
laser
focussable Translucent
paper
(b)
At rest before shear 4kPa during shear 19kPa during shear
60kPa during shear 144kPa during shear Repeat of 4kPa after
144kPa experiment
Results show that drops are deformed at high shear

11. Modelling high shear viscosity reduction
(a) (b)
Flow
r
d
θ
b
Filament
Flow Cell boundary
at r = d
(c) (d)
Flow 1.20
5 Experiment, and empirical
r/b 1.00 fit to ηe = (1 − φ )
water
Relative viscosity
4
3
0.80
resin 2
d
1 0.60
b
water -5 -4 -3 -2 -1
0
0 1 2 3 4 5
0.40
-1 (1 − φ )
u z / Gb Model ηe =
resin -2
0.20 (1 + φ )
-3
water -4 0
0 0.05 0.10 0.15 0.20 0.25 0.30
-5
Flow Volume fraction
2π d  2
Ratio of perturbed 1 − b 
∫ ∫ηm ( ∇uz ) rdrdθ
2
ηe η e  d 2  (1 − φ )
To unperturbed = 20 d
b = =
( ) ηm 
π 2  (1 + φ )
ηm
dissipation 0 2
∫ ∫ηm ∇uz rdrdθ 1 + b 
 d2 
0 0  
M.J.Thompson, J.R.A Pearson and M.R.Mackley Journal of Rheology. 45(6) 1341-1358 (2001)

12. 25
φ = 0.000
φ = 0.020
20
φ = 0.048
Apparent viscosity Pas
φ = 0.091
15
φ = 0.167
φ = 0.286
10
Concentric
5 cylinders MPR
0
10 100 1000 10000 100000
Shear stress Pa
High shear viscosity reduction is result of drop deformation

13. Case Study 2 Karine Odic
Ice cream
a complex composite material:
Ice cream is a 3 phase material: diameter range -5°c
–ice crystals 25µm to 40 µm 15%
–air bubbles 20µm to 60 µm 50%
–matrix 35%
Conventional ice cream microstructure:
Air cells
Ice Crystals
Matrix
100µm x300

14. The ice cream manufacturing process
Rheology at this stage

15. Ice cream matrix, Bohlin rheometer data

16. Air cells
Ice Crystals
Matrix
100µm x300

17. Ice cream matrix and ballotini glass spheres!
100000
τc1 +, + φ = 0.6
×, × φ = 0.5
10000 τc1 ∗, ∗ φ = 0.4
Apparent Viscosity (Pa.s)
τc1 ,  φ = 0.3
τc1  ,  φ = 0.2
1000
,  φ = 0.1
,  φ = 0.0
100
τc2
τc2
10 τc2 τc2
1
Parallel Plates MPR-3
0.1
0.01 0.1 1 10 100 1000 10000 100000
Shear Stress (Pa)

18. Ice Cream matrix and hard spheres. Low shear viscosity enhancement
100
Experiments
Thomas
Kitano
Relative Viscosity
Krieger-Dougherty
10
1
0 0.2 0.4 0.6 0.8
Volume Fraction

19. Ice cream matrix with foam inclusion
100000
10000 φ = 0.6
Apparent viscosity (Pa.s)

 φ = 0.5
1000  φ = 0.4
φ = 0.0
100
10
1
Parallel Plates MPR-3
0
0.01 0.1 1 10 100 1000 10000 100000
Shear stress (Pa)

20. Ice cream matrix and foam inclusion
Visualisation; Linkam CSS (Cambridge Shear System)

21. Ice cream matrix and foam inclusion
100000
Foam
10000
Apparent Viscosity (Pa.s)
1000
100
Matrix
continuous phase
10
1
0
0.01 0.1 1 10 100 1000 10000 100000
Shear Stress (Pa)

22. Model fluids vs the real thing!

23. Case Study 3 Sameer Rahatekar
Carbon Nanotubes
Multi-walled carbon nanotubes

24. Nanotube loading, Ares parallel plate rheometer.
1000
S 0.5 %
old
S1 %
0.35
S2 %
0.15
S3 %
0.07
Apparent viscosity /Pa.s
100 S6
0.009%
Epoxy
10
1
0.1 1 10 100 1000
-1
Shear rate / s

25. Effect of Temperature
1000
Epoxy 25C
CNT/Epoxy 25C
Epoxy 80C
100 CNT/Epoxy 80C
Apparent viscosity / Pa.s
10
1
0.1
0.01
0.1 1 10 100 1000
Shear rate / s-1

26. Low concentration alignment
Visualisation; Linkam CSS (Cambridge Shear System)
40 μm 40 μm
Volume % = 0.02 Volume % = 0.02
Shear = 0 s-1 Shear = 20 s-1

27. Nanotube loading, Ares parallel plate rheometer.
1000
S 0.5 %
old
S1 %
0.35
S2 %
0.15
S3 %
0.07
Apparent viscosity /Pa.s
100 S6
0.009%
Epoxy
10
1
0.1 1 10 100 1000
-1
Shear rate / s

28. High concentration aggregation
200 μm 200 μm
Volume % of CNTs = 0.02 Volume % CNTs = 0.04
200 μm
Volume % CNTs = 0.2

30. Nanotube loading, Ares parallel plate rheometer.
1000
S 0.5 %
old
S1 %
0.35
S2 %
0.15
S3 %
0.07
Apparent viscosity /Pa.s
100 S6
0.009%
Epoxy
10
1
0.1 1 10 100 1000
-1
Shear rate / s

31. Conclusions
Material Low shear High shear rate
enhancement. thinning.
Alkyd resin Water drops. Deformed
water filaments of
suspension. water.
Ice cream. Polymer matrix. Polymer.
Ice crystals. Foam filaments.
Foam inclusion.
Carbon Nanotube cluster Nanotube cluster
nanotubes. interaction. break up.