Splash of Solid Particles as a Stochastic Point Process

Abstract

A splash experiment was carried out on a model soil–glass beads with a diameter of 425–600 μm using high‐speed cameras and sticky paper. Two different types of particles were involved in the process: droplets of water and glass beads. We argue that the result of splash of solid particles is best modeled as a stochastic point process, that is, a random number of randomly distributed points (beads) on a plane, and provide basic physical and statistical evidence that, in medium distance range (i.e., for our experiment, in the ranges of 29–64 mm), the splash may be modeled as the Poisson point process. We also argue that, in the range between 15 and 29 mm, a distribution different than Poisson is closer to reality. These two radically different types of distributions of numbers of beads in two regions reflect the fact that the solid phase of the splash involves two types of beads: those ejected in the early stage, traveling larger distances, and those ejected later, traveling shorter distances. Information on the distributions of and relations between the numbers of splashed particles in different regions may be instrumental in understanding mechanics and scale of the spread of pollutants/pathogens and plant diseases as a result of splash. Meanwhile, we describe the distributions of the total number of beads, the maximum range, and the average distance beads particles travel in a single experiment and discuss effectiveness of detection of beads by the cameras.