Crater evolution after the impact of a drop onto a semi-infinite liquid target

This paper is devoted to an experimental and theoretical investigation of the crater formed by the impact of a single drop onto a semi-infinite target of the same liquid. The shape of the crater at various time instances after impact has been observed using a high-speed video system and then accurately characterized. A theoretical model for the crater expansion has been developed, which is able to predict the temporal variation of the crater depth for sufficiently high Weber, Froude, and Reynolds numbers. The flow around the crater is approximated by an irrotational velocity field past a moving and expanding sphere. The equations describing the propagation of the surface of the crater have been obtained from the balance of stresses at the crater interface, accounting for inertia, gravity, and surface tension. The temporal evolution of the crater depth has been calculated by numerical solution of the equations of motion. The agreement between the theoretical predictions and experimental data are rather good.