DYNAMICS OF A CLUSTER OF BUBBLES IN A LIQUID (THEORETICAL-ANALYSIS)

The present work investigates the dynamics of a cluster of bubbles in a liquid by means of a series expansion of spherical harmonics. The go verning equations of three-dimensional motions for an arbitrary config uration of N bubbles are derived by taking account of the translationa l motion and the deformation of each bubble induced by mutual interact ions among the bubbles. These equations are exact to the order of (R(I c)/L(IJ0))5 for inviscid terms, where R(Ic) is the characteristic radi us of a specified bubble I and L(IJ0) the initial distance between the centers of the bubbles I and J. Viscous effects of the liquid are con sidered up to the first order for quantities of the translational moti on and the deformation, on the basis of the potential solution. The eq uations involve previous results for a single and two bubbles as speci al cases. The characteristic equation for oscillations of N spherical bubbles is also obtained, and natural frequencies are calculated for s pecified configurations of the bubbles. It is shown that the lowest na tural frequency of the bubbles is much lower than the frequency of an isolated bubble.