Backward Formalism to Derive the Size of Secondary Ejected Droplets Produced by Crown Splashing of Drops Impinging on a Solid Wall

Abstract

Crown splashing, produced by high speed impact of a droplet on a rough or wet wall, is physically very complicated. It is impossible to determine the size of secoundary ejected droplets by literally solving the full set of nonlinear Navier-Stokes equations supplemented by complex initial and boundary conditions. In order to get useful impact laws and, most importantly, to propose a genearl concept of deriving useful results without going through the complex mathematical details, we propose a backward formalism in which we determine the size of the secoundary ejected droplets by tracking the past event whenever it is required and just what is required. This procedure allows us to discard those complex details of negligible importance. Such a formalism, conceptually very simple and possibly meaningful for other complex problems, leads to a reasonably correct formula for the most probable diameter of secondary ejected droplets, compared to know experimental data.