Modelling two-dimensional droplet rebound off deep fluid baths

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 (LM) model are compared to dedicated direct numerical simulation (DNS) 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 long-time dynamics of droplets rebounding on a vibrating bath. Furthermore, the LM 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.