Insights on the impact of a plane drop on a thin liquid film

Abstract

Numerical simulations of early and intermediate instants of a plane two-dimensional drop impact on a preexisting thin film of the same liquid are performed. The evolution of the phenomenon is analyzed by solving the free-surface Navier–Stokes equations by means of a volume of fluid (VOF) method. Viscous, inertial and surface tension forces are taken into account; gravity is neglected. The so-called splashing regime is emphasized, where the emergence of an initial horizontal ejecta sheet is followed by the formation of an almost vertical lamella sheet, which is the planar counterpart of the well known splashing-crown of spherical geometry. Overall velocity and pressure fields as well as detailed interface shapes are presented, and several insights on the relevant scaling laws are furnished. In the ejecta sheet (jet) regime a major result is the finding of a deviation from the standard square root behavior for the dependence on time of the contact length of sheet first emergence, which is proved to be crucial in the subsequent original application of the potential theory of Howison et al. [J. Fluid Mech. 542, 1 (2005)]. In the lamella sheet regime, the outwards expansion of its base is discussed in connection with the theory of the formation of a kinematic discontinuity within the underneath film of Yarin and Weiss [J. Fluid Mech. 283, 141 (1995)]. Analogies between planar and axysymmetric configurations are discussed.