Coupled oscillations of a pair of closely spaced bubbles

The interaction of closely spaced bubbles is relevant for a variety of geophysical, industrial, and medical applications. The present study fills a research gap in that it is concerned theoretically with the volume pulsations of bubbles at small distances compared with their sizes. It was shown that the bi-spherical coordinates provide separation of variables and are more suitable for analysis of this problem. A coupled oscillator method is used to describe collective acoustic resonances from closely spaced bubbles in water. Explicit formulas have been derived that describe the dependence of the bubbles natural frequencies and damping coefficients on their sizes and the separation distance.