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Ink jet rheology and processing-Monash 2009

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".

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Ink jet rheology and processing-Monash 2009

  1. 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.ukDepartment of Chemical EngineeringUniversity of CambridgeCambridge, CB2 3RA, UK. 1
  2. 2. CIJ Printhead Nozzle Charge electrode Deflector & Phase plates Gutter 2
  3. 3. Xaar DOD PrintheadPlatform III : Side shooterMultipulse grey scale printhead (1001 series) 3
  4. 4. The Cambridge MultiPass Rheometer (MPR)Pressure variation Rheology flow Cross-slot Filament stretchmode mode flow mode mode 4
  5. 5. The Cambridge Multipass Rheometer (MPR) Top section Test section Bottom section 5
  6. 6. MPR as capillary rheometerDiethyl phthalate (DEP) Supplier: Sigma Aldrich BP = 294-296°C; ρ = 1118 kg/m3 ; σ 20°C = 36 mN/m; η25°C = 10 mPa.sPolystyrene: 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. 7. Filament thinningA.V.Bazilevsky, V.M. Entov and A.N.Rozhkov3rd European Rheology Conference 1990 Ed D.R.Oliver The “Russian Rheotester” C A B E 15 cm D 7
  8. 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. 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. 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 upbetween two pistons. at a uniform velocity. occurrence after pistons has stopped. t<0 t≥0 10
  11. 11. MPR Filament stretching and thinning of DEP solution DEP DEP + 5.0 wt% PS 1.2 mmPiston diameter = 1.2 mmInitial stretch velocity = 200 mm/sInitial sample height = 0.35 mmFinal sample height = 1.35 mm (piston displaced by 0.5 mm each side) 11
  12. 12. The CambridgeTrimaster A dream turning into a reality Toothed belt Linear guide rail timing pulley Carrier Timing belt Replaceable top and bottom plateStepper motorattached to a pulley 12 Graphics courtesy of James Waldmeyer
  13. 13. Drive belt Piston Linear traverseMotordrive a b High speed camera Fibre optic light Cambridge Trimaster 13
  14. 14. Piston response 5000 4000 10 mm/s 100 mm/s Top piston 500 mm/sposition (µm) 3000 2000 1000 c 0 0 100 200 300 400 500 600 Time (ms) 14
  15. 15. The ‘TriMaster’ Filament stretch and break up apparatuspistonsamplebeltpulley Initial gap ≈ 0.2 mm, Final gap ≈ 1.2 mm 15 Piston diameter ≈ 1.2 mm, Piston velocity ≈ 1 m/s
  16. 16. 16
  17. 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 cInitial gap size: 0.6mm,Stretching distance:0.8mm, 5.3ms 6.15 7 7.5 7.65 7.8 8Stretching 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. 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. 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 strainfor 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. 20. Breakup a 0ms 4 5.5 6.2 6.35 6.5 7 DEP, b DEP + 0.5% PS110, 0ms 5 6.5DEP + 1% PS110, 7.7 8.2 8.35DEP + 2.5% PS110, 8.5DEP + 5% PS110.tial gap size: 0.6mm, cetching 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. 21. Drop on demand ink jet process (d) (e) 1(a) (b) (c) (f) (g) 2 3 (h) (i) 21
  22. 22. 1 Tail Filament a Main drop 2 3Ligament Drop thread bNewtonian “Optimum” Viscoelastic Viscoelastic a b c 22
  23. 23. Measurement of Linear Viscoelasticity (LVE) Piezo Axial Vibrator (PAV) Developed by Prof Wolfgang Pechold University of Ulm. Germany Upper lidSampleGap (steel ring foil)Lower plate withoverflow ditchProbe headPiezoelectric (PZT)elements stuck on asquare copper tube Section of PAV 23
  24. 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 eiδK1 K1   02 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"2Mechanical representation G * (ω ) = G (ω ) + iG" (ω ) η* = 24 ωwith springs.
  25. 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. 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. 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. 28. 1% PS70 Eff: 1.08Photo, courtesy of Dr Steve Routh 28
  29. 29. The effect of polymer addition Polystyrene MW = 210k in Diethyl phthalate solvent PAV Trimaster 1000Elastic 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. 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%ModulusRatioG’/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. 31. The “Ulm” Torsion ResonatorThe 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. 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. 33. Conclusions Piezo Axial Vibrator (PAV)Can quantify LVE response of low viscosity viscoelastic fluids Cambridge TrimasterCan follow filament break up process of low viscosity fluids Acknowledgments EPSRC and industrial partners in Next Generation Ink Jet Consortium 33

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