This presentation is for my last Cambridge Rheology course lecture. The presentation links course work with research that had been carried out in the Department. The presentation has been modified a little to aid web clarity.

1. 1
Rheology and Processing. CET3 Lecture 16.
This lecture gave an informal review on examples of work carried out within
the Department where they linked with different parts of the lecture course.
(Presentation has been modified in March 2015 in order to give greater web clarity)
The photo was taken whilst on a lecture tour in Malaysia in the 1980s
At the beginning of each lecture I would give a short slide show usually on
locations I had been to whilst attending conferences throughout the world. I tried to
link each journey with some aspect of rheology.

2. 2
Carbon Black in epoxy
0.1
1
10
100
1000
0.1 1 10 100
Shear Rate (/s)
η
(Pa.s)
0% 1% 2% 4%
Kat Yearsley carried out a PhD in Cambridge and observed “Classic” Cross
equation behaviour for carbon black / epoxy resin suspensions. Just one example
of the many shear thinning fluids.
Graph showing the shear thinning of carbon black suspensions
Section 1.
Shear thinning
The Cross Structure Model

3. 3
Kat Yearsley 2010
Carbon Black has a complex microstructure that can be seen from
the above optical image. The structure model developed in
section 1 of the course can describe the rheology of this type of
system.

4. 4
Section 2
Bingham Plastics
and perfect plastics
Cold Extrusion of Chocolate
The photo was taken during a lecture tour of Australia.
Cottesloe Beach (Perth)
Remarkably; we discovered the cold extrusion of chocolate behaves as a perfect plastic

5. 5
Shear
stress
Shear rate
Bingham Plastic
Perfect Plastic
τyYield stress
Bingham and Perfect Plastic behaviour are classic mathematical models
used in engineering calculations.

6. 6
Temperature
50 100 150 200
C0
∆H
Cold
Extrusion
Normal Melt
ProcessingPolyethylene
Temperature
10 20 30 40
C
0
∆H
Cold
Extrusion
Normal Melt
Processing
Chocolate
Extrusion processing
In the 1980s we developed a low temperature polyethylene ram extrusion process;
however DSM (A Dutch Chemicals Company) had patents in this area for polymers.
So I selected another material which also had a range of melting points and invented
the cold extrusion of chocolate!

7. 7
This laboratory ram extruder was initially designed for polymers and
was the first used to “cold extrude” flexible chocolate.

8. 8
Here are some early cold extruded chocolate samples.

9. 9
This graph shows that the cold extrusion pressure is independent of
piston speed. This, together with a yield stress means that the material
is a perfect plastic.

10. 10
The composition of chocolate varies depending on its type.

11. 11
The microstructure of chocolate is complex. It is a suspension of sugar
crystals and cocoa solids in a matrix of cocoa butter (CB) and the CB
itself contains both solid and liquid fractions at different temperatures.

12. 12
Crucially for the cold extrusion process, Cocoa Butter (CB) melts over a range
of temperatures and at room temperature CB may be 15% liquid and 85%
crystalline.

13. 13
The solid crystalline fraction of CB triglycerides form a
regular crystal lattice as shown schematically above.

14. 14
The non crystalline amorphous fraction of CB are in a random configuration
as shown schematically above.

15. 15
Mechanism 1. The significant amount of work carried out during
cold extrusion heats the chocolate and partially melts some CB.
Rate of doing work = Rate of heat generation
= pressure x area = force
= velocity
= density
= Specific heat
= temperature increase
P A
ρ
Cp
∆ T
∆ T =
P
ρ Cp
∆ T =
100 105
1,200 1,200
= 6.9 0
C
TCxA=xA p ∆ ρP
x
Explanation for Cold Extrusion
Model predicts 7 degree centigrade rise in temperature; but experimentally
we observe an isothermal extrusion with no temperature rise. So Mechanism 1
must be wrong!

16. 16
Mechanism 2 . All the work goes into melting a certain crystal fraction of CB.
Rate of work done/kg =
Work done/kg in melting mass fraction of cocoa butter
= φ λ
φ
λ = latent heat of melting / kg
P
ρ
= φ λ φ =
P
ρ λ
=
107
1,200x150x103
= 5.5%
Equate
ρρ
P
=
xA
xA

P
We believe this unexpected mechanism!

17. 17
Do you remember the Coextrusion problem within a capillary that was in the
example sheet?
Chocolate necklace cold extrusion Coextrusion!
Section 2
Engineering flows
Choc composition A
Choc composition B

18. 18
These photos show chocolate that had been crystallised within the extrusion
barrel resulting in a two component semi solid chocolate.

19. 19
R
X.R
Z=0
Z=LB
YB
YB
τx
τx
VB
1 Inner core material flows faster than the
outer material
2 Outer material is under tension and inner is under
compression. Chocolate is weak in tension
3 Eventually, the shear force where the two materials meet will exceed the
tensile force needed to break off the outer
material, forming a new necklace bead. Despite
this, the inner material continues
to flow steadily.
Two materials, two velocities
VA
H Ovaici, M R Mackley, G H McKinley & S J Crook.
Journal of Rheology. 42,1, 125-158 (1998).
When the chocolate was extruded, an “Ovaci Necklace” was observed!
The mechanism by which the Ovaci Necklace
is formed is a bit complex, but explained in the
publication.

20. 20
Section 3
Viscoelasticity.
This photo was taken on a lecture tour of China

21. 21
Processibility
Ink Jet
High
MW
Polymer
melts
10-3
10-1
10 103
105
Viscosity, Pas
“Extreme Rheology”
Viscosity and Processibility
“easy processing”
“easy rheology”
Viscoelasticity is usually important for high viscosity polymer melts; however recent
work in the department has shown that viscoelasticity is important too for low viscosity
printing inks.

22. 22
g η
(τ,γ)
Do you remember the Maxwell Model in section 3 ?
λ
ττγ
+
dt
d
=
dt
d
g
λη=γλ=τ g
relaxation times (s)
λ = η / g
Steady shear Newtonian
Stress relaxation
λ−
τ=τ /t
0e

23. 23
Xaar Drop On Demand DOD Printhead
Platform III : Side shooter
Multipulse grey scale printhead (1001 series)
Ink in
Ink out
30 micron holes
Piezo channels
Ink drops, velocity m/s
Ink jet printing uses low viscosity fluids with viscoelastic additives.
Shear rates are very, very high.

24. 24
Conventional Torsional Rheometer
To transducer
To motor
Sample
Mode 1
Mode 2
Mode 3
To transducer
To motor
Sample
Mode 1
Mode 2
Mode 3
1
10
100
1000
0.1 1 10 100 1000 10000
Frequency (Hz)
Complexviscosity,η*,(mPa.s)
0.1
1
10
100
1000
10000
Elastic(G')andViscous(G")
modulus,(Pa)
G"
G'
η*
linear viscoelastic data of DEP-10% PS210 at 25°C
Conventional oscillatory rheometers usually measure high viscosity fluids and their
frequency range 0.1-50 hz is adequate.

25. 25
Upper lid
Sample
Gap (steel ring foil)
Lower plate with
overflow ditch
Probe head
Piezoelectric (PZT)
elements stuck on a
square copper tube
Section of PAV
Measurement of Linear Viscoelasticity (LVE)
Piezo Axial Vibrator (PAV)
Developed by Prof Wolfgang Pechold
University of Ulm. Germany
Tri Tuladhar, Damien Vadillo and Amit Mulji
Ink jet fluids require higher frequency measurements to follow short timescales and
we bought a PAV that could reach “frequencies other rheometers couldn’t reach”.

26. 26
1
10
100
1000
0.1 1 10 100 1000 10000
Frequency (Hz)
Complexviscosity,η*,(mPa.s)
0.1
1
10
100
1000
10000
Elastic(G')andViscous(G")
modulus,(Pa)
G"
G'
η*
High frequency linear viscoelastic data of DEP-10% PS210 at 25°C
Parallel plate rheometer

27. 27
1
10
100
1000
0.1 1 10 100 1000 10000
Frequency (Hz)
Complexviscosity,η*,(mPa.s)
0.1
1
10
100
1000
10000
Elastic(G')andViscous(G")
modulus,(Pa)
Open: ARES
Close: PAV
G"
G'
η*
High frequency linear viscoelastic data of DEP-10% PS210 at 25°C
Parallel plate rheometer PAV data
The PAV extends the measured frequency domain.

28. 28
Fit the The single mode Maxwell model to PAV data
( )
2
2
2s
)(1
G
'G
)(1
G
''G
ωλ+
ωλ
=
ωλ+
ωλ
+ωη=
G ηp
ηS is the solvent viscosity
ηp= λ*G is the polymer contribution to the viscosity
G = modulus spring constant
λ is the relaxation time
ω is the frequency in rad/s and ω = 2πf
28
Fit this region to
get λ and G

29. 29
PAV experiments: single Maxwell model relaxation time
29
λLVE is of order of µs and increases with the concentration of polymer
sLVE µ≈λ
LVE
Maxwell
Relaxation
Time
Maxwell model can be used to fit PAV LVE rheology.

30. 30
(a) pure DEP, (b) DEP + 0.2wt% PS110, (c) DEP + 0.5wt% PS110 and (d) DEP
+ 1wt% PS110. Jetting at 6m/s from a Xaar XJ 126-200 printhead.
DOD jetting is very sensitive to polymer content and LVE can discriminate
different ink jet fluid compositions.
Effect of polymer content on ink jet form

31. 31
Viscoelasticity can effect processibility even
for low viscosity fluids.
Message!

32. 32
Section 4
Generalised deformations and
processibility
This photo was taken at Villefranche Sur Mer on the Cotes d’Azur
whilst attending a 1998 Esaform conference on numerical modelling.

33. 33
Examples of comparisons between experimental results and numerical predictions.
There is an optical technique known as flow birefringence where experimental
stress fields for molten polyethylene can be compared with numerically simulated
stress fields. A real test for the modelling.
Exp Integral Wagner simulation
Dr Peter Husband 2001
An early example where numerical simulation can match experimental processing.

34. 34
HDPE, 180°C, Die: L=12.12mm, G=1.2mm
Flowrate = 4.81 g/min
Flow Birefringence of Polyethylene flow within and out of a slit.
Experiment and matching numerical simulation
Dr Peter Husband 2001
Integral Wagner
simulation

35. 35
M.R.Mackley, R.T.J.Marshall and J.B.A.F. Smeulders. The multipass rheometer.
Journal of Rheology. 39(6), 1293- 1309 (1995)
The Cambridge Multipass Rheometer.
A Cambridge developed apparatus for making precise polymer processing measurements.

36. 36
Double-cavity flow birefringence patterns
of a Linear low density polyethylene m-LLDPE
at a temperature, 190°C and flow rate 33.9 mm3s-1,
(apparent wall shear rate in the slit ~ 44 s-1).
Flow is from top to bottom.
Comparison of the overall experimental
flow birefringence pattern with the simulated
PSD (the right hand figure).
As seen, the Wagner model simulations captured
the fringe pattern at cavity 1 (mushroom shape)
and cavity 2 (butterfly shape). The increment of
PSD contour lines is 2.95 × 104 Pa
(SOC, 1.74 × 10-9 Pa-1)
K Lee and M.R.Mackley The application of the Multi-Pass rheometer for precise rheo-optic characterisation of
polyethylene melts. Chemical Engineering Science 56, 5653-5661 (2001)
For further viewing go to http://www.dspace.cam.ac.uk/handle/1810/196406
Experiment and simulation for Double cavity MPR slit geometry

37. 37
Processibility of complex fluids
can now be numerically modelled
for complex flows.
A final grand conclusion
In the 1970s, when I started to be interested in complex fluids and
complex flows the level of understanding and ability to model
processes was relatively poor. That has now changed and engineers
can now, with confidence use numerical models as design tools for
the development of current and next generation processes.

38. 38
Hawkesbill, Antigua, West Indies
Ajax Artemis, Harwich
So finally I sail into the sunset at Hawksbill Hotel in Antigua and with my Ajax
Artemis on the river Orwell at Harwich