Inertio-capillary rebound of a droplet impacting a fluid bath

Abstract

The rebound of droplets impacting a deep fluid bath is studied both experimentally and theoretically. Millimetric drops are generated using a piezoelectric droplet-on-demand generator and normally impact a bath of the same fluid. The drop generator can reliably produce droplets with diameters much smaller than the capillary length, and operates efficiently with a variety of low viscosity fluids. Measurements of the droplet trajectory and other rebound metrics are compared directly to the predictions of a linear quasi-potential model, as well as fully resolved direct numerical simulations (DNS) of the unsteady Navier-Stokes equations. Both models resolve the time-dependent bath and droplet shapes in addition to the droplet trajectory. In the quasi-potential model, the droplet and bath shape are decomposed using orthogonal function decompositions leading to two sets of coupled damped linear harmonic oscillator equations solved using an implicit numerical method. The underdamped dynamics of the drop are directly coupled to the response of the bath through a single-point kinematic match condition which we demonstrate to be an effective and efficient model in our parameter regime of interest. Starting from the pure inertio-capillary limit, we document the influence of both weak viscous and gravitational effects on various bouncing metrics. In particular, the quasi-potential model is able to rationalize historical experimental measurements for the coefficient of restitution, presented throughout numerous preceding works on the topic.