Analytical study on the dynamic characteristics of multiple gas-filled spherical bubbles in typical spatial locations

The dynamic characteristics of multiple gas-filled spherical bubbles in three types of typical spatial locations are investigated analytically through a modified Rayleigh–Plesset equation. In the first type, two bubble centers form a one-dimensional straight line; the second type consists of any number of bubbles whose centers form a regular polygon in a two-dimensional plane; and in the third type, the bubble centers form a regular polyhedron in three-dimensional space. We show that physically these cases correspond qualitatively to periodic oscillations. Analytical expressions are derived for the maximum and minimum radii, based on which the oscillation amplitude and period are studied analytically. Parametric analytical solutions are also obtained. The influences of physical parameters on the multibubble motion are determined with the aid of these analytical results. We also study the limiting behavior of the analytical results for multiple bubbles, with the corresponding results for single bubbles being obtained as the distance between bubble centers approaches infinity.