Modelling two-dimensional droplet rebound off deep fluid baths

Abstract: In order for a droplet to rebound rather than coalesce with a liquid bath, a layer of gas must persist throughout the impact. This gas, typically an air layer acts as a lubricant to the system and permits a pressure transfer between the two liquid bodies. Through considering separately the bath, air, and drop regions of fluid, we introduce a fully coupled reduced dynamic model of two-dimensional droplets (i.e. cylindrical geometry) rebounding off liquid baths, which incorporates an evolving lubricating air layer. Numerical solutions of the lubrication-mediated model are compared to dedicated direct numerical simulation of the Navier-Stokes equations. The reduced model captures rebounding dynamics well in the regime where it is most relevant: for low-speed impacts of small droplets, where capillary forces are important. Numerically, the reduced model is efficient, allowing for the computation of multiple rebounds and of long time dynamics of droplets rebounding on a vibrating bath. Furthermore, the lubrication-mediated model is able to provide detailed information within the air layer such as pressure and lubrication-layer geometry, which is usually omitted from reduced models.