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)

])([

111

0

T

b

VV

FgpVVt

V

V

0)(

FVt

F

Interface Tracking

Procedure:Surface Reconstruction

Use F-field to determine cell “normal” Determine “case” using normalPosition plane with known slope based upon volume fraction Compute plane area and vertices

Fluid AdvectionCompute flux across cell side (case dependent)Operator Split (i.e. do for x, y and z sweeps)

A sample “F” field

1

1

1 1

1 1

1 1

1

0 0 00

0 00

0

0 0

0

0

0

.85

.92

.68

.35

.09.31

.09

.42Two-fluid VOF method based on Piecewise Linear Interface Calculation (PLIC) algorithm.

Validation: comp. with Fujimoto’s experiments

Non-Dim Time

D/D

0

0 1 2 3 4 50

0.5

1

1.5

2

2.5

3

ExperimentNum. V=2.65Num. V=2.55

Single water droplet impaction on a surface

D=0.56 mm, V=2.65 60,30 era

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

Times: 0, 9, 25, 30, 36, 43, 49, and 60 μs respectively

Coalesc., Δt=30 μs, Δx=57.5 μm

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.

Case 2, Δt=25 μs, Δx=55 μm at times 30, 34, 36, 38, 49, and 60 μs respectively.

Coalescence case 2: effect of timing

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.