This presentation gives a summary of work carried out in the Chemical Engineering Department at Cambridge on the rheology and processing of ink jet fluids. The linear viscoelastic properties are captured using a PAV rheometer and the non linear extensional behaviour using a "Cambridge Trimaster".

1. Seminar Monash University
11th March 2009
The rheology and processing of ink jet fluids.
by
Malcolm Mackley,
With acknowledgement to
Damien Vadillo, and Tri Tuladhar*
Department of Chemical Engineering, Cambridge
*Xaar plc
mrm5@cam.ac.uk
Department of Chemical Engineering
University of Cambridge
Cambridge, CB2 3RA, UK.
1

2. CIJ Printhead
Nozzle
Charge electrode
Deflector & Phase
plates
Gutter
2

3. Xaar DOD Printhead
Platform III : Side shooter
Multipulse grey scale printhead (1001 series)
3

4. The Cambridge MultiPass Rheometer (MPR)
Pressure variation Rheology flow Cross-slot Filament stretch
mode mode flow mode mode
4

5. The Cambridge Multipass Rheometer (MPR)
Top
section
Test
section
Bottom
section
5

6. MPR as capillary rheometer
Diethyl phthalate (DEP) Supplier: Sigma Aldrich
BP = 294-296°C; ρ = 1118 kg/m3 ;
σ 20°C = 36 mN/m; η25°C = 10 mPa.s
Polystyrene: Supplier: BASF – Polystyrol VPT granule
M.W ~ 195000
100
ARES data MPR data
90
Apparent viscosity, η (mPa.s)
80
70 DEP
DEP + 1.0 wt% PS
60
DEP + 2.5 wt% Ps
50 DEP + 5.0 wt% PS
40
30
20
10
0
1 10 100 1000 10000 100000 1000000
Shear rate (/s)
6

7. 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
B
E
15 cm
D
7

8. Liang and Mackley (1994)- Extensional Rheotester
Newtonian modelling
•
τzz τ zz = − p 0 + 2η γ zz = 0 (11)
•
τrr
Top plate
τ rr = − p 0 + 2η γ rr = −2σ / D (12)
•1•
D= εD (13)
Bottom plate
2
•
Extensional rheotester τ E = τ zz − τ rr = 3η ε = 2σ / D (14)
• 2σ
ε= (15)
3ηD
•
η E = τ E / ε = 3η (16)
σ
D(t ) = D0 − t (17)
3η
8

9. Liang and Mackley (1994)- Viscoelastic fluid
S1 fluid First approximation
 1  (18)
D (t ) = D0 exp −
 3λ t

 R 
Viscoelastic modelling
•
τ E = 3η ε d = 2σ / D (19)
• • •
τ E = g ε s = −2σ D/ D 2 (20)
• •
PIB solutions
εd = εs (21)
•
D/ D = − g / 3η (22)
 g 
D (t ) = D0 exp − t 
 3η  (23)
 
9

10. MPR Filament stretch Rheometer
Vp
D
R(z,t)
Top Piston
Lf Rmid(t)
L0
Bottom Piston
Vp
(a) Test fluid positioned (b) Test fluid stretched uniaxially (c) Filament thinning and break up
between two pistons. at a uniform velocity. occurrence after pistons has stopped.
t<0 t≥0
10

11. MPR Filament stretching and thinning of DEP solution
DEP
DEP + 5.0 wt% PS
1.2 mm
Piston diameter = 1.2 mm
Initial stretch velocity = 200 mm/s
Initial sample height = 0.35 mm
Final sample height = 1.35 mm
(piston displaced by 0.5 mm each side)
11

12. The CambridgeTrimaster
A dream turning into a reality
Toothed belt Linear guide rail
timing pulley
Carrier
Timing belt
Replaceable top and
bottom plate
Stepper motor
attached to a pulley
12
Graphics courtesy of James Waldmeyer

13. Drive
belt
Piston
Linear
traverse
Motor
drive
a b
High speed camera
Fibre optic light
Cambridge Trimaster
13

14. Piston response
5000
4000 10 mm/s
100 mm/s
Top piston 500 mm/s
position (µm) 3000
2000
1000
c
0
0 100 200 300 400 500 600
Time (ms)
14

15. The ‘TriMaster’ Filament stretch and break up apparatus
piston
sample
belt
pulley
Initial gap ≈ 0.2 mm, Final gap ≈ 1.2 mm
15
Piston diameter ≈ 1.2 mm, Piston velocity ≈ 1 m/s

16. 16

17. Filament thinning
a
5.3ms 5.8 6.3
6.8 7
7.2 7.7
(a) DEP,
b
(b) DEP + 0.2% PS110,
(c) DEP + 0.5% PS110,
(d) DEP + 1% PS110, 5.3ms 6 6.7
7 7.15
(e) DEP + 2.5% PS110. 7.3 7.6
c
Initial gap size: 0.6mm,
Stretching distance:0.8mm, 5.3ms 6.15 7
7.5 7.65
7.8 8
Stretching velocity:150mm/s
d
5.3ms 7 7.85
8.7 9.6
10.4 10.6
e
5.3ms 8.2 10.2 13.5
15.2
17
16.8 17

18. Mid filament diameter time evolution
1200
1000 0%
0.50%
800 1%
2.50%
D 5%
600
(µ m )
400
200
0
0 10 20 30 40
Time (ms )
18

19. 250
DEP-0%PS
DEP-0.5%PS
200
DEP-1%PS
Trouton ratio DEP-2.5%PS
150 DEP-5%PS
ηE
η0 100
50
0
0 2 4 6 8 10
D 
Hencky strain, 2 ln 0 
D 
 t
The transient extensional rheology of DEP solutions as a function of relaxation Hencky strain
for different PS concentrations.
Initial distance 0.6mm, final distance: 1.4mm.
The line represent are obtained from the exponential fitting of the evolution of the thinning of the diameter.
The geometrical factor “X” is fitted using the experimental data at low Hencky strain.
19

20. Breakup a
0ms 4 5.5
6.2 6.35 6.5
7
DEP, b
DEP + 0.5% PS110,
0ms 5 6.5
DEP + 1% PS110, 7.7 8.2 8.35
DEP + 2.5% PS110, 8.5
DEP + 5% PS110.
tial gap size: 0.6mm, c
etching distance: 1.6mm,
etching velocity: 150mm/s
0ms 6.7 8
9.35 9.85 10.15
10.35
d
0ms 7.5 10.65 14.15 17
17.15 17.35
e
0ms
38
10.7
39.15
22.35 31
39.35
20

21. Drop on demand ink jet process
(d) (e)
1
(a) (b) (c)
(f) (g)
2
3
(h) (i)
21

22. 1
Tail Filament a
Main drop
2 3
Ligament
Drop thread b
Newtonian “Optimum”
Viscoelastic
Viscoelastic
a b c
22

23. Measurement of Linear Viscoelasticity (LVE)
Piezo Axial Vibrator (PAV)
Developed by Prof Wolfgang Pechold
University of Ulm. Germany
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
23

24. Mechanical equivalent model of PAV
2R The lower plate oscillates with constant force F (∝
m1
x1
excitation volt Uref) for a given frequency.
K* Sample d
With blank test: Dynamic compliance of the
m0
x0 lower plate is measured.  ∆x  ~ U eiδ
K1 K1
  0
2 2
 F 0 U ref
K01 F
With sample: Modulated compliance of the
x2 *
K02 m2 sample is measured  ∆x  U iδ
  ~ e
 F  U ref
Mechanical equivalent
model of the PAV. Complex squeeze stiffness K* of the material can
be calculated from the ratio of ∆x0 and ∆x*.
K02 K01 K* K1
m2 m0 m1
For linear viscoelasticity
2 d3  ρω 2 d 2 
F G* = K * 1 +
 + ....

x2 x0 x1 3π R 4  10G * 
G '2 +G"2
Mechanical representation G * (ω ) = G ' (ω ) + iG" (ω ) η* =
24 ω
with springs.

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

26. High frequency linear viscoelastic data of DEP-10% PS210 at 25°C
Parallel plate rheometer PAV data
1000 10000
η*
Complex viscosity, η*, (mPa.s)
Elastic (G') and Viscous (G")
1000
Open: ARES
100 Close: PAV
modulus, (Pa)
100
10
10 G"
1
G'
1 0.1
0.1 1 10 100 1000 10000
Frequency (Hz)
26

27. Effect of Polymer on the Linear Viscoelastic response of ‘model’
fluid containing different polymer concentration
Polystyrene MW = 210k in Diethyl phthalate solvent
1000 1000
0.1%
100 100 0.2%
Loss Modulus
G’’ 0% Elastic Modulus 0.4% C%
10 G’ 10 1%
Pa 0.1% 0%
0.2% Pa
1 1
0.4%
1%
0.1 0.1
1 10 100 1000 10000 100 1000 10000
Frequency (Hz) Frequency (Hz)
2.00E-02 1
0%
0.1% 0%
Complex 1.75E-02 0.2% Modulus ratio 0.1%
viscosity 0.4%
1%
G’/ G* 0.2%
0.4%
C%
η∗ 1.50E-02 0.1
Pa.s 1%
1.25E-02
1.00E-02 0.01
1 10 100 1000 10000 100 1000 10000
Frequency (Hz) Frequency (Hz)
27
27

28. 1% PS70
Eff: 1.08
Photo, courtesy of Dr Steve Routh
28

29. The effect of polymer addition
Polystyrene MW = 210k in Diethyl phthalate solvent
PAV Trimaster
1000
Elastic Modulus C%
G’ 100
Pa
10 1%
0.4%
1 0.2%
0.1%
0.1
100 1000 10000
Frequency (Hz)
No Polymer With Polymer
Development of the elasticity
as function of polymer Development of a long ligament
molecular weight for same
complex viscosity
29

30. Link between inkjet rheology and printability for printing inks
Work carried out in conjunction with IFM
G'/G* at 5 kHz frequency and 25°C
30%
Satellite Single drop Filaments / beads
No release
Dimensionless elastic modulus, G'/G*, (-)
25%
20%
Modulus
Ratio
G’/G* 15%
10%
5%
0%
DEP PS20- LB016- PS70- JSB1-B- PS110- JSB1-A- PS210- LB016- PS488-
5.0% 47 2.7% jetting 2.0wt% Non 1.7% 48 1.0%
30 jetting 30

31. The “Ulm” Torsion Resonator
The non linear viscoelastic behaviour (NLVE)
The piezoelectric sensor oscillates at its
two resonance frequencies, 26kHz and
77kHz respectively.
With blank test: Determination of the
apparatus constant K for each frequency
Piezoelectric
sensor With sample: Measure of the resonance
frequency shift Df and the damping shift
Sample
DD at each resonance frequency.
K  ∆D  2 
 − ( ∆f ) 
2
Fluid vessel G =
'

ρ sample  2 
 

with
Temperature K
control vessel G '' = ∆D.∆f
ρ sample
31
31

32. The Torsion Resonator
Proof of concept (DEP + 2.5%wt PS110)
G’’(77 kHz) G’’(25 kHz) PAV TR
10000 10000
1000 G’’
G’ and G’’
100
G’ and G’’
(Pa) 1000
(Pa)
10
G’(77 kHz)
1
G’(77 kHz) G’’
100 0.1
10 20 30 40 50 10 100 1000 10000 100000
Experiment number
Frequency (Hz)
PAV TR
0.1 0.1
η1 (25 kHz) η1 (77 kHz)
η1 and η2 0.01 η2 (25 kHz) η2 (77 kHz) η* (Pa.s)
(Pa.s)
0.001 G’(7 kHz) 0.01
10 20 30 40 50 10 100 1000 10000 100000
Frequency (Hz)
32
Experiment number
32

33. Conclusions
Piezo Axial Vibrator (PAV)
Can quantify LVE response of low viscosity viscoelastic fluids
Cambridge Trimaster
Can follow filament break up process of low viscosity fluids
Acknowledgments
EPSRC and industrial partners in
Next Generation Ink Jet Consortium
33