A quasi-static model of drop impact

Abstract

We develop a conceptually simple theoretical model of non-wetting drop impact on a rigid surface at small Weber numbers. Flat and curved impactor surfaces are considered, and the influence of surface curvature is elucidated. Particular attention is given to characterizing the contact time of the impact and the coefficient of restitution, the goal being to provide a reasonable estimate for these two parameters with the simplest model possible. Approximating the shape of the drop during impact as quasi-static allows us to derive the governing differential equation for the droplet motion from a Lagrangian. Predictions of the resulting model are shown to compare favorably with previously reported experimental results.