Scattering from a pair of closely spaced bubbles

Acoustic scattering by a single bubble is the most basic problem for bubble detection. For a two-phase flow, the subject of forced oscillations of a pair of bubbles is important because it controls how bubbles interact with each other. Attempts to incorporate interactions between bubbles have traditionally used a multiple scattering methodology. The proposed approach uses a bi-spherical coordinate system and is limited to a description of a sufficiently long-wave acoustical field, so that the bubbles are homobaric, and the medium in the vicinity of the bubbles can be considered incompressible. The choice of a specific coordinate system allows the authors to take into account the internal symmetry inherent in this problem and provides a partial summation on only the most important contributions to the multiple scattering series. A closed form solution was derived for the scattered acoustic field that determines its parametric dependence on bubbles sizes and the separation distance.