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

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

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

Section 2

Bingham Plasticsand 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

Shearstress

Shear rate

Bingham Plastic

Perfect PlasticτyYield stress

Bingham and Perfect Plastic behaviour are classic mathematical modelsused in engineering calculations.

6

Temperature

50 100 150 200

C0

∆ H

Cold Extrusion

Normal Melt ProcessingPolyethylene

Temperature

10 20 30 40

C0

∆ 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

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

8Here are some early cold extruded chocolate samples.

9

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

10

The composition of chocolate varies depending on its type.

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

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

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

14

The non crystalline amorphous fraction of CB are in a random configurationas shown schematically above.

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

ρCp

∆ T

∆ T = P

ρ Cp∆ T =

100 105

1,200 1,200 = 6.9 0C

T C x A = x A 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 1must be wrong!

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 / kgPρ

= φ λ φ = Pρ λ

= 107

1,200x150x103 = 5.5%Equate

ρρP

= x Ax A

P

We believe this unexpected mechanism!

17

Do you remember the Coextrusion problem within a capillary that was in the example sheet?

Chocolate necklace cold extrusion Coextrusion!

Section 2Engineering flows

Choc composition A

Choc composition B

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

19

RX.R

Z=0

Z=LB

YB

YBτx

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 Necklaceis formed is a bit complex, but explained in the publication.

20

Section 3Viscoelasticity.

This photo was taken on a lecture tour of China

21

Processibility

Ink Jet

High MWPolymermelts

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 recentwork in the department has shown that viscoelasticity is important too for low viscosity printing inks.

22

g η

(τ, γ)

Do you remember the Maxwell Model in section 3 ?

λττγ

+ dt

d =

dt

dg

λη=γλ=τ g

relaxation times (s)λ = η / g

Steady shear Newtonian

Stress relaxation λ−τ=τ /t

0e

23

Xaar Drop On Demand DOD Printhead

Platform III : Side shooterMultipulse 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

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)

Co

mp

lex

visc

osi

ty, η

*, (

mP

a.s

)

0.1

1

10

100

1000

10000

Ela

stic

(G

') a

nd

Vis

cou

s (G

")

mo

du

lus,

(P

a)

G"

G'

η*

linear viscoelastic data of DEP-10% PS210 at 25°C

Conventional oscillatory rheometers usually measure high viscosity fluids and theirfrequency range 0.1-50 hz is adequate.

25

Upper lidSample

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 PecholdUniversity 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

1

10

100

1000

0.1 1 10 100 1000 10000

Frequency (Hz)

Co

mp

lex

visc

osi

ty, η

*, (

mP

a.s

)

0.1

1

10

100

1000

10000

Ela

stic

(G

') a

nd

Vis

cou

s (G

")

mo

du

lus,

(P

a)

G"

G'

η*

High frequency linear viscoelastic data of DEP-10% PS210 at 25°C

Parallel plate rheometer

27

1

10

100

1000

0.1 1 10 100 1000 10000

Frequency (Hz)

Co

mp

lex

visc

osi

ty, η

*, (

mP

a.s

)

0.1

1

10

100

1000

10000

Ela

stic

(G

') a

nd

Vis

cou

s (G

")

mo

du

lus,

(P

a)

Open: ARESClose: 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

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

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

(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 discriminatedifferent ink jet fluid compositions.

Effect of polymer content on ink jet form

31

Viscoelasticity can effect processibility evenfor low viscosity fluids.

Message!

32

Section 4Generalised deformations and

processibility

This photo was taken at Villefranche Sur Mer on the Cotes d’Azurwhilst attending a 1998 Esaform conference on numerical modelling.

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

HDPE, 180°C, Die: L=12.12mm, G=1.2mmFlowrate = 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 Wagnersimulation

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

Double-cavity flow birefringence patternsof 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 experimentalflow 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

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

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