The left-right symmetrical and asymmetrical deformations in a three-bubble system

Abstract

This paper studies the simplest system that can possess left-right symmetrical and asymmetrical surroundings, three bubbles in a line. Assuming that the deformations are small, the surfaces of bubbles are described by a combination of the first three Legendre polynomials, that is, spherical symmetrical mode P0, L-R antisymmetrical mode P1, and symmetrical mode P2. A dynamical model is built to describe aspherical oscillations of central and two side bubbles. It is found that when three identical bubbles are separated uniformly, the central bubble only has a P2 component and P1 component tends to zero, while two side bubbles have both P1 and P2 components. When three identical bubbles are separated by different distances, they can be degenerated into a two-bubble system and a free bubble. The bubble deformations contain both P1 and P2 components in the two-bubble system, while both aspherical components P1 and P2 of the free bubble tend to zero. If side bubbles are different in ambient radii but located symmetrically on the left and right of the central bubble, the side bubble pulsated more strongly plays an important role on the deformation of the central one.