Modeling crown formation due to the splashing of a droplet

Abstract

The typical crown formation created by the impact of a single drop on a slightly wetted target surface is treated as a series of two surfaces of discontinuity from which the jump momentum and mass equations are developed along with the governing equation for crown radius. The crown radius equation is solved in conjunction with the governing equations of the flow emanating from drop/wall impact. This flow is modeled initially as a cylindrical region of prescribed height and velocity. Both viscid and inviscid situations are treated. For the inviscid case of a crown moving through a motionless film, analytical solutions are found for the evolution of film height and velocity. For the viscid situation, a numerical scheme based on the discretization of the governing equations along the characteristic directions is employed. The results are validated by comparing with experimental and computational results from the literature. The effects of target surface film height, velocity, and wall friction on the crown dynamics are investigated.

Three-dimensional numerical investigation of a droplet impinging normally onto a wall film

“…Viscous effects seem to play an important role, some time after crown formation and not in the early stages, as also reported by Nikolopoulos et al [10]. This indicates that in the case of high impact velocities the main influencing factor on the formation of the crown is the inertia of the liquid, while film thickness is more important for the crown radius evolution, as reported by Roisman and Tropea [8] and Trujillo and Lee [9].…”

“…The dynamic equations of motion of the crown are determined following a Lagrangian approach; therefore an analytical solution for the crown shape is formulated, in the asymptotic case that the surface tension and viscosity effects are negligible in comparison with inertial effects. Trujillo and Lee [9] extended Yarin and Weiss concept [2] for the propagation of kinematic discontinuity, including viscosity effects on the flow resulting from impact, i.e. the internal flow that moves liquid into the crown.…”

Crown behavior and bubble entrainment during a drop impact on a liquid film

“…Later, Trujillo and Lee [28] modified this theory and considered influence of the film thickness. Roisman and Tropea [29] further generalized the kinematic discontinuity, taking into account inertial effect, neglecting surface tension and viscous forces in the crown.…”

A linear stability theory on time-invariant and time-dependent spatial domains with symmetry: the drop splash problem

“…The analogous geometric considerations were used in the work of Macklin and Metaxas [41], who neglected the crown rim thickness as well. Conservation laws were also utilized in the recent works by Trujillo and Lee [63] and Roisman and Tropea [53], which were concerned with late stages of the crown formation. Here we deal with the early stages of the crown formation, i.e.…”