Splashing of droplets impacting superhydrophobic substrates

A drop of radius R of a liquid of density rho, viscosity mu and interfacial tension coefficient sigma impacting a superhydrophobic substrate at a velocity V keeps its integrity and spreads over the solid for V < V-c or splashes, disintegrating into tiny droplets violently ejected radially outwards for V >= V-c, with V-c the critical velocity for splashing. In contrast with the case of drop impact onto a partially wetting substrate, Riboux & Gordillo (Phys. Rev. Lett., vol. 113, 2014, 024507), our experiments reveal that the critical condition for the splashing of water droplets impacting a superhydrophobic substrate at normal atmospheric conditions is characterized by a value of the critical Weber number, We(c) = rho V-c(2) R/sigma similar to O(100), which hardly depends on the Ohnesorge number Oh = mu/root rho R sigma and is noticeably smaller than the corresponding value for the case of partially wetting substrates. Here we present a self-consistent model, in very good agreement with experiments, capable of predicting Wec as well as the full dynamics of the drop expansion and disintegration for We > Wec. In particular, our model is able to accurately predict the time evolution of the position of the rim bordering the expanding lamella for We greater than or similar to 20 as well as the diameters and velocities of the small and fast droplets ejected when We greater than or similar to We(c).