Effect of viscosity on motion of splashing crown in high speed drop impact

Abstract

A splashing crown is commonly observed when a high-speed drop impacts a liquid film. The influence of the liquid viscosity on the crown's evolution is not yet clear. We review several existing theories of this problem, and carry out a series of numerical simulations. We find that a three-segment model can describe the crown's motion. In the very early stage when the crown is barely visible, the influence of viscosity is small. Later, a shallow water approach used in most existing models is applicable as long as the initial conditions are formulated properly. They depend on viscous dissipation in the intermediate period. Preliminary estimation based on a dissipation function is proposed to characterize the influence of viscosity in this problem.