1. Simulation of Droplet Drawback in Inkjet Printing
Ali Jafari and Nasser Ashgriz
Multiphase Flow & Spray Systems Lab (MUSSL)

2. Motivation
Investigate the interaction between two impacting droplets (drawback)
Investigate the effect of different parameters and liquid properties on the final droplet shapes (coalesced or not coalesced drops)

3. Overview Basic assumptions Involved mechanisms
laminar and incompressible fluid flow
density constant
Involved mechanisms
fluid dynamics: viscous and capillary effects
Solidification is not considered

4. Governing Equations Continuity and momentum equations
Volume of Fluid (VOF)

5. Interface Tracking Procedure: Surface Reconstruction Fluid Advection
A sample “F” field 1
.85
.92
.68
.35
.09
.31
.42
Two-fluid VOF method based on Piecewise Linear
Interface Calculation (PLIC) algorithm.
Procedure:
Surface Reconstruction
Use F-field to determine cell “normal”
Determine “case” using normal
Position plane with known slope based upon volume fraction
Compute plane area and vertices
Fluid Advection
Compute flux across cell side (case dependent)
Operator Split (i.e. do for x, y and z sweeps)

6. Validation: comp. with Fujimoto’s experiments
Single water droplet impaction on a surface
D=0.56 mm, V=2.65

7. Simulation parameters
20 cells per radius
ρ=997 kg/m3
μ= kg/m.s
D=40 μm
V=5 m/s
σ=0.073 N/m
Ө=90º

8. Non-coalesc., Δt=30 μs, Δx=58.5 μm
Times: 0, 9, 25, 30, 36, 43, 49, and 60 μs respectively

9. Coalesc., Δt=30 μs, Δx=57.5 μm
Times: 0, 9, 25, 30, 36, 43, 49, and 60 μs respectively

10. Non-coalesc., Δt=25 μs, Δx=56 μm
Times: 0, 9, 25, 30, 36, 43, 49, and 60 μs respectively

11. Coalesc., Δt=25 μs, Δx=55 μm
Times: 0, 9, 25, 30, 36, 43, 49, and 60 μs respectively

12. Velocity field (non-coalescence)
Velocity distribution for case 1, Δt=30 μs, Δx=58 μm at times 36, 40, 43, 45, 49, and 60 μs respectively

13. Velocity field (coalescence)
Velocity distribution for case 1, Δt=30 μs, Δx=57.5 μm at times 36, 40, 43, 45, 49, and 60 μs respectively.

14. Coalescence case 2: effect of timing
Case 2, Δt=25 μs, Δx=55 μm at times 30, 34, 36, 38, 49, and 60 μs respectively.

15. Non-dim. Pressure contours
Δt=30 μs, Δx=57.5 μm at times 43, 45, and 60 μs respectively
Δt=30 μs, Δx=58 μm at times 40, 43, and 60 μs respectively.

16. Conclusions Drawback is sensitive to
Drop spacing
Impact velocity
Contact angle
Inter-drop time
Small changes in any of the above parameters may result in coalescing or non-coalescing drops: e.g. for Δt=25 μs, coalescence at drop spacing of 55 m; no coalescence at 56 m
Further investigation of all important cases and parameters is planned and from these data, theoretical relations for the threshold of coalescence and non-coalescence would be developed.