On the spreading of impacting drops

Abstract

The energy budget and dissipation mechanisms during droplet impact on solid surfaces are studied numerically and theoretically. We find that for high impact velocities and negligible surface friction at the solid surface (i.e. free slip), approximately one-half of the initial kinetic energy is transformed into surface energy, independent of the impact parameters and the detailed energy loss mechanism(s). We argue that this seemingly universal rule is related to the deformation mode of the droplet and is reminiscent of pipe flow undergoing a sudden expansion, for which the head loss can be calculated by multiplying the kinetic energy of the incoming flow by a geometrical factor. For impacts on a no-slip surface also dissipation in the shear boundary layer at the solid surface is important. In this case the geometric head loss acts as a lower bound on the total dissipation (i.e. the spreading on a no-slip surface approaches that on a free-slip surface when the droplet viscosity is sent to zero). This new view on the impact problem allows for simple analytical estimates of the maximum spreading diameter of impacting drops as a function of the impact parameters and the properties of the solid surface. It bridges the gap between previous momentum balance approaches and energy balance approaches, which hitherto did not give consistent predictions in the low viscosity limit. Good agreement is found between our models and experiments, both for impacts on ‘slippery’ or lubricated surfaces (e.g. Leidenfrost droplet impacts and head-on droplet–droplet collisions) and for impacts on no-slip surfaces.