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

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)

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

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

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)

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

Simulation parameters 20 cells per radius ρ=997 kg/m3 μ=.000891 kg/m.s D=40 μm V=5 m/s σ=0.073 N/m Ө=90º

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

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

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

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

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

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.

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.

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.

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.