Air cushioning pre-impact dynamics of a wetted body approaching a porous substrate

• Published in: Journal of engineering mathematics Vol. 154; no. 1
• Main Authors: Moreton, Gavin, Cooker, Mark J., Purvis, Richard
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Nature B.V 01.10.2025
• Subjects: Air flow; Cushioning; Deicing; Entrapment; Impact loads; Porosity; Porous media; Shallow water; Substrates; Water film
• ISSN: 0022-0833; 1573-2703
• DOI: 10.1007/s10665-025-10477-0

The impact of liquid-coated solid bodies onto porous substrates, or equivalently the impact of porous bodies onto shallow water layers, is considered. This study investigates the role of air cushioning in the pre-impact dynamics of a wetted particle approaching a dry porous medium. By extending a shallow water air cushioning model, we develop an asymptotic theory that couples flow in a lubricating air layer, with an inviscid shallow water film and with Darcy air flow within the porous substrate. Two distinct regimes are identified, namely shallow- and intermediate-depth substrates. The formulated models are solved numerically to determine the influence of substrates on impact pressure, bubble formation, and air escape mechanisms. Numerical results, up to the instant of liquid–substrate impact, reveal that at high porosity the substrate significantly reduces the impact pressure and can suppress bubble entrapment. Permeability is shown generally to hasten the liquid film’s descent to the top of the substrate (so-called ‘touchdown’) as the air gap is closed but, perhaps most surprisingly, porosity can delay touchdown in the regime of shallow porous layers. These findings enhance our understanding of impact mechanics on porous media and offer insights into practical applications such as de-icing technologies and controlled particle adhesion in manufacturing processes.