Pre-impact dynamics of a droplet impinging on a deformable surface

Abstract

The nonlinear interaction between air and a water droplet just prior to a high-speed impingement on a surface is a phenomenon that has been researched extensively and occurs in a number of industrial settings. The role that the surface deformation plays in an air cushioned impact of a liquid droplet is considered here. In a two-dimensional framework, assuming small density and viscosity ratios between the air and the liquid, a reduced system of integrodifferential equations is derived governing the liquid droplet free-surface shape, the pressure in the thin air film, and the deformation of the surface, assuming the effects of surface tension, compressibility, and gravity to be negligible. The deformation of the surface is first described in a rather general form, based on previous membrane-type models. The coupled system is then investigated in two cases: a soft viscoelastic case where the surface stiffness and (viscous) damping are considered and a more general flexible surface where all relevant parameters are retained. Numerical solutions are presented, highlighting a number of key consequences of surface deformability on the pre-impact phase of droplet impact, such as reduction in pressure buildup, increased air entrapment, and considerable delay to touchdown. Connections (including subtle dependence of the size of entrapped air on the droplet velocity, reduced pressure peaks, and droplet gliding) with recent experiments and a large deformation analysis are also presented.

Computational study of early-time droplet impact dynamics on textured and lubricant-infused surfaces

“…Time is also scaled such that the time 𝑡 = 0 corresponds to the time that the droplet bottom free-surface would reach 𝑦 = 0 in the absence of air cushioning. The presence of the surrounding air results in the impact being delayed slightly into positive time (Henman et al, 2021;Hicks and Purvis, 2010).…”

The role of body shape and mass in skimming on water

“…The surrounding atmosphere, typically air, is thus treated as a void whose dynamics has a negligible effect during the skim. In practice air cushioning as in [29][30][31][32] could be significant; as yet no rational means of incorporating air cushioning into a skim model has been found but we should mention in passing that research by FTS with Ellen Jolley is underway. In the current model, if x = x 1 (t) is the moving contact point at the front of the wetted underbody at time t then the body motion is described by…”

The Springer Model for Lifetime Prediction of Wind Turbine Blade Leading Edge Protection Systems: A Review and Sensitivity Study

“…An analytical description for low velocity liquid droplet impact on elastic substrates was derived based on a set of integro-differential equations. This approach includes air cushioning [ 54 ] and describes the coupling between the free surfaces of the domains [ 55 ]. This work showed that the dynamic impact pressure highly depends on the impact, material and geometric parameters of the problem.…”