Gas-cushioned droplet impacts with a thin layer of porous media

Hicks, Peter and Purvis, Richard (2017) Gas-cushioned droplet impacts with a thin layer of porous media. Journal of Engineering Mathematics, 102 (1). 65–87. ISSN 0022-0833

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Abstract

The pre-impact 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 superhydrophilic-textured surfaces. Bubble entrainment is predicted across a range of permeabilities and substrate heights, as a result of a gas pressure build-up in the viscous-gas squeeze film decelerating the droplet free-surface immediately below the centre of the droplet. For a droplet of water of radius 1 mm and impact approach speed 0.5 m s−1, the change from a flat rigid impermeable plate to a porous substrate of height 5 μm and permeability 2.5 μm2 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 gas-cushioned droplet impacts with porous substrates is also investigated. In contrast to the numerical predictions of a droplet free-surface above flat plate, when a porous substrate is included, the droplet free-surface touches down in finite time. Mathematically, this is due to the regularization of the parabolic degeneracy associated with the small gas-film-height limit the gas squeeze film equation, by non-zero substrate permeability and height, and physically suggests that the level of surface roughness is a critical parameter in determining the initial touchdown characteristics.

Item Type:	Article
Faculty \ School:	Faculty of Science > School of Mathematics
UEA Research Groups:	Faculty of Science > Research Groups > Fluid and Solid Mechanics
Depositing User:	Pure Connector
Date Deposited:	19 Dec 2015 07:12
Last Modified:	21 Oct 2022 01:09
URI:	https://ueaeprints.uea.ac.uk/id/eprint/55769
DOI:	10.1007/s10665-015-9821-y

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