Maximum drop radius and critical Weber number for splashing in the dynamical Leidenfrost regime

At room temperature, when a drop impacts against a smooth solid surface at a velocity above the so-called critical velocity for splashing, the drop loses its integrity and fragments into tiny droplets violently ejected radially outwards. Below this critical velocity, the drop simply spreads over the substrate. Splashing is also reported to occur for solid substrate temperatures above the Leidenfrost temperature, $T_{L}$, for which a vapour layer prevents the drop from touching the solid. In this case, the splashing morphology differs from the one reported at room temperature because, thanks to the presence of the gas layer, the shear stresses acting on the liquid can be neglected. Our purpose here is to predict, for wall temperatures above $T_{L}$, the critical Weber number for splashing as well as the maximum spreading radius. First, making use of boundary integral simulations, we calculate both the time evolution of the liquid velocity as well as the height of the sheet which is ejected tangentially to the substrate. These results are then used as boundary conditions for the one-dimensional mass and momentum equations describing the dynamics of the rim limiting the expanding liquid sheet. Our predictions for both the maximum spreading radius and for the critical Weber number for splashing are in good agreement with experimental observations.