Lubrication layer driven capillary-scale rebound dynamics: A pesudo-spectral approach
Date:
A droplet about to impact a free surface must first make its way through a layer of air acting as a barrier preventing coalescence. In a millimetric regime, the capillary action of the free surface may dominate the dynamics of the interaction and is able to provide an upward kick to rebound the droplet prior the full evacuation of the air layer, which would have allowed coalescence. In such a regime, the trapped air acts as a lubrication layer between the impactor and the free surface. To leading order, such a millimetric droplet acts as a rigid sphere, allowing developments of numerical models for solid-liquid impacts to be a reasonable approximation of droplet dynamics. In this talk, we present the development of a 2D model of a millimetric solid sphere impacting on a free surface. We take a multi-scale approach to include the air layer as a dynamical component in the system by coupling an asymptotic derivation of the leading order problem, with psuedo-spectral methods to model the behaviour of the free surface, and smaller scale lubrication regime for the dynamics of the cushioning layer.