液体中での気泡群の力学 : 第1報, 理論解析

The present work investigates the dynamics of a cluster of bubbles in a liquid by means of a series expansion of spherical harmonics. The governing equations of three-dimensional motions for arbitrary configurations of N bubbles are derived by taking account of translational motions and deformations induced by mutual interactions among the bubbles. These equations are exact to the order (RIC/LIJO)5 for inviscid terms, where RIC is the characteristic radius of a specified bubble I and LIJO the initial distance between the centers of the bubbles I and J. Viscous effect of the liquid is considered up to the first order in perturbation of spherical symmetry on the basis of the potential solution. The equations involve previous results for a single and two bubbles as special cases. Characteristic equations for oscillations of N spherical bubbles are also obtained and natural frequencies are calculated for specified configurations of the bubbles. It is shown that the lowest frequency of the bubbles is much lower than that of an isolated bubble.