The impact of a drop onto a liquid film with a relatively high impact velocity, leading
to the formation of a crown-like ejection, is studied theoretically. The motion of a
kinematic discontinuity in the liquid film on the wall due to the drop impact, the
formation of the upward jet at this kinematic discontinuity and its elevation are
analysed. Four main regions of the drop and film are considered: the perturbed liquid
film on the wall inside the crown, the unperturbed liquid film on the wall outside
the crown, the upward jet forming a crown, and the free rim bounding this jet. The
theory of Yarin & Weiss (1995) for the propagation of the kinematic discontinuity is
generalized here for the case of arbitrary velocity vectors in the inner and outer liquid
films on the wall. Next, the mass, momentum balance and Bernoulli equations at the
base of the crown are considered in order to obtain the velocity and the thickness
of the jet on the wall. Furthermore, the dynamic equations of motion of the crown
are developed in the Lagrangian form. An analytical solution for the crown shape is
obtained in the asymptotic case of such high impact velocities that the surface tension
and the viscosity effects can be neglected in comparison to inertial effects. The edge
of the crown is described by the motion of a rim, formed due to the surface tension.Three different cases of impact are considered: normal axisymmetric impact of a
single drop, oblique impact of a single drop, and impact and interaction of two drops.
The theoretical predictions of the height of the crown in the axisymmetric case are
compared with experiments. The agreement is quite good in spite of the fact that no
adjustable parameters are used.
Single-drop impingement onto a wavy liquid film and description of the asymmetrical cavity dynamics
