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## Simulation of Droplet Drawback in Inkjet Printing

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**Simulation of Droplet Drawback in Inkjet Printing**Multiphase Flow & Spray Systems Lab (MUSSL) Ali Jafari and Nasser Ashgriz**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 • 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)**Two-fluid VOF method based on Piecewise Linear**Interface Calculation (PLIC) algorithm. 1 1 1 .68 0 1 1 1 .42 0 A sample “F” field .92 .09 1 1 0 1 0 0 .85 .35 .09 0 0 0 .31 0 0 0 0 0 Interface Tracking • 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.