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

Content Provider	Springer Nature Link
Author	Hicks, Peter D. Purvis, Richard
Copyright Year	2015
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 $$5~μ $$ m and permeability $$2.5~μ $$ m $$^2$$ 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.
Ending Page	87
Page Count	23
Starting Page	65
File Format	PDF
ISSN	00220833
e-ISSN	15732703
Journal	Journal of Engineering Mathematics
Issue Number	1
Volume Number	102
Language	English
Publisher	Springer Netherlands
Publisher Date	2015-09-24
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Porous media Liquid-gas two-phase flows, bubbly flows Viscous-inviscid interaction Gas entrainment Analysis Classical Mechanics Capillarity (surface tension) Applications of Mathematics Mathematical Modeling and Industrial Mathematics Droplet impacts
Content Type	Text
Resource Type	Article
Subject	Mathematics Engineering

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