This presentation gives a summary on the development of the Cambridge Trimaster which is an apparatus for studying the fast filament stretching, thinning and break up of low viscosity fluids. The apparatus is particularly relevant to ink jet fluids

1. IFM Cambridge
December 2013
Fast Filament Stretching, Thinning and Breakup
By
Malcolm Mackley, Simon Butler, Damien Vadillo,
Tri Tuladhar, Stephen Hoath and Stewart Huxley
Department of Chemical Engineering and Biotechnology
University of Cambridge
Cambridge, CB2 3RA, UK.
1

2. Tri Tuladhar
Xaar
Steve Hoath
Cam IFM
Stewart Huxley
Huxley Bertram
Damien Vadillo
Akzo
Simon Butler
2
Chem Eng Cam

3. MRM last BSR Presentation
London 2011
“This could be the last time, this could be the last time,
maybe the last time, I don‟t know.”

4. Slow Filament Stretching
On the coefficient of viscous traction and its
relation to that of viscosity
Fred Trouton
Proc. R. Soc. Lond. A 1906
strain rate matrix

0
 ii + P = 2 ii
0


0
0
2
0
0


2
The Trouton Ratio
 11 + P = 2 
 22 + P = - 2
 11 -  22
e


2
= 3  =  e 
= 3
4

5. M1 Fluid Extensional viscosity muddle
David James and Ken Walters,
A.A. Collyer (Ed.), Techniques of
Rheological Measurement,
Elsevier,NewYork, 1994, pp. 33–53.
Chris. Petrie
Extensional viscosity: A critical discussion
J. Non-Newtonian Fluid Mech. 137 (2006) 15–23
5

6. Filament thinning
Newtonian modelling

 zz  P  2 
zz
0

 rr  P  2  rr   2 / D
D

 E   zz   rr  3   2 / D

Mass Balance
D 
1

 D
2
P
D (t )  D 0 

3
t
6

7. Filament thinning
D (t )  D 0 

3
t
7

8. Filament thinning
A.V.Bazilevsky, V.M. Entov and A.N.Rozhkov
3rd European Rheology Conference 1990 Ed D.R.Oliver
The “Russian Rheotester”
C
A
zz
B
E
Top plate
15 cm
D
Bottom plate
8
rr

9. Liang and Mackley (1994)
Extensional Rheotester
S1 fluid
PIB solutions
D (t )  D 0 

3
t
9
R. Liang and M.R. Mackley. Journal of Non-Newtonian Fluid Mech. 52, 387-405 (1994).

10. Liang and Mackley (1994)- Viscoelastic fluids
S1 fluid
First approximation

1
D ( t )  D 0 exp  
 3
R


t


Viscoelastic modelling (John Hinch)
PIB solutions

D / D   g / 3
 g 
D(t)  D 0 exp  
 3η t 



10

11. Multipass Rheometer (MPR) Filament Stretch Rheometer
The MK1 Cambridge Trimaster
Vp
D
R(z,t)
Top Piston
Rmid(t)
Lf
L0
Bottom Piston
Vp
(a) Test fluid positioned
between two pistons.
(b) Test fluid stretched uniaxially (c) Filament thinning and break up
occurrence after pistons has stopped.
at a uniform velocity.
t0
t<0
Tuladhar, T.R. and Mackley, M.R., Journal of Non-Newtonian Fluid Mechanics, 148 97-108. (2008)
11

12. Lodge Commemorative Meeting on Rheometry
Miskin Manor Cardiff 10 -12th April, 2006
Filament profile just before break up
DEP
DEP + 5.0 wt%
1.2 mm
t = 7 ms
t = 2 ms

13. The MK 2 Cambridge Trimaster
A dream turning into a reality
Toothed belt
timing pulley
Linear guide rail
Carrier
Timing belt
Replaceable top and
bottom plate
Stepper motor
attached to a pulley
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Graphics courtesy of James Waldmeyer

14. Drive
belt
Piston
Linear
traverse
Motor
drive
a
b
High speed camera
Fibre optic light
Cambridge Trimaster
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15. Piston response
5000
10 mm/s
100 mm/s
500 mm/s
4000
Top piston
position (mm) 3000
2000
1000
c
0
0
100
200
300
400
500
600
Time (ms)
15

16. The „TriMaster‟ Filament stretch and break up apparatus
piston
sample
belt
pulley
Initial gap ≈ 0.2 mm, Final gap ≈ 1.2 mm
Piston diameter ≈ 1.2 mm, Piston velocity ≈ 100 mm/s16

17. 17

18. Filament thinning
DEP
DEP
+ 2.5%
PS110
Piston velocity 0.15 m/s
D.C.Vadillo, T.Tuladhar, A.C. Mulji, S. Jung, S.D. Hoath,and M.R. Mackley
Journal of Rheology 54, 2 .261-282 (2010)
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19. Mid filament diameter time evolution
1200
0%
0.50%
1%
2.50%
5%
1000
800
D
(mm )
600
400
200
0
0
10
20
30
40
Time ( ms )
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20. Transient Trouton viscosity ratios
250
DEP-0%PS
DEP-0.5%PS
DEP-1%PS
DEP-2.5%PS
DEP-5%PS
200
Trouton
ratio
E
0
150
100
50
0
0
2
4
Hencky
6
8
10
D 
strain , 2 ln  0 
D 
 t 
20

21. Mk 3 Cambridge Trimaster
Light weight voice coils
The Ideas Studio (Company now dissolved)
a
b
Nearly worked but…..
21

22. Separation velocities
Texture Analyser
Caber
MPR Mk1 Trimaster
Mk2 Trimaster
Mk3 Trimaster
HB4 Trimaster
Ink Jetting velocity
Single
Piston
m/s
0.040
0.075
0.075
0.075
0.2
2.25
Double
Piston
m/s
0.15
0.15
0.4
4.5
6.0
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23. The MK 4 HB4 Cambridge Trimaster
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24. Trimaster development: the HB4
Overhead view of the instrument
Camera
Close up of the pistons
Drive wheel
Top
piston
Bottom
piston
Arms holding Light source
the pistons

25. Trimaster HB4 operation

26. 1600
1400
1200
Piston
separation 1000
/ μm
2.25 m/s
800
2.00 m/s
1.00 m/s
0.50 m/s
600
0.20 m/s
0.10 m/s
400
-2
-1
0
1
2
Time / ms
3
4
5
6
26

27. Speed is of the essence; HB4 vs Mk2 Trimaster
Piston displacement
1.6
Total filament height (mm)
1.4
1.2
1
0.8
MK2-Sample height-150 mm/s
MK4-Sample height- 1m/s
0.6
0.4
0.2
0
0.00
5.00
10.00
Time (s)
15.00
20.00
HB4
27

28. Base case; solvent only
06A-Ink 6-DPM-18k
10000
1.60
During and after stretching
1.20
06A-Ink 6-DPM-18k
1000
1.00
total sample ht
0.80
0.60
100
0.40
Sample height ((mm)
Filament diameter (µm)
1.40
0.20
10
0.00
-2
0
2
4
Time,t, (ms)
Solvent DPM
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29. Polymer additive; does matter
Concentrated Resin solution (Resin 1, Resin 2 and Resin 3)
Filament diameter,D, (µm )
600
After stretching
500
07A-Ink 7-Resin 1-celluose -80kMW-5percent-18K
08A-Ink 8-Resin 2-celluose -370k MW-5percent-18K
09A-Ink 9-Resin 3-acrylic -30kMW-20percent-18K
400
300
200
100
0
0.0
100.0
200.0
300.0
400.0
Time, t, (ms)
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30. Sorting out the good from the bad
Commercial ceramic good and bad inks
Filament diameter,D, (µm )
500
After stretching
450
400
30A-Ink A1-Ceramic Sinker-Good jetting-18K
31A-Ink A2-Ceramic Yellow-Bad jetting-18K
350
300
250
200
150
100
50
0
0.0
1.0
2.0
3.0
4.0
5.0
Time, t, (ms)
“Good ink”
“Bad ink”
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31. The Rheology and Processing Triangle
LVE Rheology
Piezo Axial Vibrator
(PAV)
NLVE Extensional
HB4 Trimaster
1000
G'
Complex viscosity, *, (mPa.s)
eta*
G"
100
10
1
1
10
100
1000
0.1
10000
Elastic (G') & viscous (G") modulus, (Pa)
14A-DPM and 6_6 percent Resin 3
10
Ink Jet Processing
Frequency (Hz)
31

32. Conclusions
HB4 Cambridge Trimaster
Can follow fast filament stretch thinning and breakup
process of low viscosity fluids.
There is a link between ink jet processing and HB4 data.
(See Steve Hoath presentation)
Acknowledgments
EPSRC and industrial partners in
Next Generation Ink Jet Consortium
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