Gascushioned droplet impacts with a thin layer of

Authors: Peter D Hicks Richard Purvis

Publish Date: 2015/09/24

Volume: 102, Issue: 1, Pages: 65-87

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Abstract

The preimpact gas cushioning behaviour of a droplet approaching touchdown onto a thin layer of porous substrate is investigated Although the model is applicable to droplet impacts with any porous substrate of limited height a thin layer of porous medium is used as an idealized approximation of a regular array of pillars which are frequently used to produced superhydrophobic and superhydrophilictextured surfaces Bubble entrainment is predicted across a range of permeabilities and substrate heights as a result of a gas pressure buildup in the viscousgas squeeze film decelerating the droplet freesurface immediately below the centre of the droplet For a droplet of water of radius 1 mm and impact approach speed 05 m s1 the change from a flat rigid impermeable plate to a porous substrate of height 5~upmu m and permeability 25~upmu m2 reduces the initial horizontal extent of the trapped air pocket by 48~ as the porous substrate provides additional pathways through which the gas can escape Further increases in either the substrate permeability or substrate height can entirely eliminate the formation of a trapped gas pocket in the initial touchdown phase with the droplet then initially hitting the top surface of the porous media at a single point Droplet impacts with a porous substrate are qualitatively compared to droplet impacts with a rough impermeable surface which provides a second approximation for a textured surface This indicates that only small pillars can be successfully modelled by the porous media approximation The effect of surface tension on gascushioned droplet impacts with porous substrates is also investigated In contrast to the numerical predictions of a droplet freesurface above flat plate when a porous substrate is included the droplet freesurface touches down in finite time Mathematically this is due to the regularization of the parabolic degeneracy associated with the small gasfilmheight limit the gas squeeze film equation by nonzero substrate permeability and height and physically suggests that the level of surface roughness is a critical parameter in determining the initial touchdown characteristicsThe authors are grateful to Dr Manish Tiwari for introducing them to experiments involving droplet impacts with textured substrates PDH is grateful for the use of the Maxwell HighPerformance Computing Cluster of the University of Aberdeen IT Service RP is grateful for the use of the HighPerformance Computing Cluster supported by the Research and Specialist Computing Support service at the University of East AngliaComparative results for these alternative boundary conditions are presented in Figure 9 alongside the full Beavers–Joseph condition for the cases k = 4 and h = 3 The full Beavers–Joseph condition shown in Fig 9a results in a smaller pocket of trapped gas compared to the other two boundary conditions this is because this case has the greatest amount of gas velocity slip at the substrate interface and so the gas is more able to escape from beneath the oncoming droplet The trapped gas pocket in Fig 9c where alpha rightarrow infty delta =0 is the largest gas pocket of the three as this boundary condition corresponds to no slip for the gas on the substrate surface and hence the gas is less able to escape from underneath the oncoming droplet The variations between the different forms of the boundary condition diminish as the value of k falls In cases where the substrate permeability is well known a detailed comparison of the radii of the air pockets both experimentally and using the models described herein would enable an accurate determination of the parameters in the Beavers–Joseph condition

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