Numerical analysis of the total scattering cross section on a set of sound-permeable spheres

Abstract

One of the most important subtasks of the problem of acoustic wave scattering on a set of small spherical obstacles is to determine the main characteristic of the scattering phenomenon, namely, the total scattering cross section. Its solution will make it possible to establish at what system parameters the interaction between particles is insignificant and can be neglected (in this case, the problem can be simplified and reduced to the many single particles case), and at what parameters this interaction cannot be neglected. In present work a numerical parametric analysis of the total scattering cross section on a spheres system under the influence of a spherical wave from a monopole radiation source is carried out on the base on an explicit formula for the total scattering cross section on a set of interacting sound-permeable spheres. In order to determine the ratio of the physical parameters of the sphere and the environment, under which the effects of multiple scattering are significant for given types of system configuration, a series of computational experiments was carried out to calculate the main scattering characteristic taking into account multiple scattering, as well as the sums of characteristics for single sound-permeable spheres. It is shown that in all cases considered, the effects of multiple scattering cannot be neglected when determining the total scattering cross section. In the case of air bubbles in water, the type of configuration of the system is an essential factor; for water droplets in the air, both the type of configuration and the number of spheres in it are essential; and for dichloroethane droplets in water, the type of configuration and the number of spheres in it are insignificant factors.