Shock wave formation in droplet impact on a rigid surface: lateral liquid motion and multiple wave structure in the contact line region

The early phase of high-speed liquid droplet impact on a rigid wall is characterized by compressibility effects through the creation of a shock wave attached to the contact area periphery. Initially, the area of compressed liquid is assumed to be bounded by the shock envelope, which propagates both laterally and upwardly into the bulk of the liquid. In this paper, an analytical model accounting for the lateral liquid motion in the compressed area is developed and compared to the axisymmetric numerical solution of the inviscid (Euler) flow equations. It is shown that the often employed assumption that the compressed area is separated from the liquid bulk by a single shock wave attached to the contact line breaks down and results in an anomaly. This anomaly emerges prior to the time when the shock wave departs from the contact line, initiating lateral liquid jetting. In order to remove this anomaly, the analytical model presented in this paper proposes the transition from a single to a multiple wave structure in the contact line region, prior to jetting eruption. The occurrence of this more complex multiple wave structure is also supported by the numerical results.