WEAK OSCILLATIONS OF A GAS BUBBLE IN A SPHERICAL VOLUME OF COMPRESSIBLE LIQUID

The following spherically symmetric problem is considered: a single ga s bubble at the centre of a spherical flask filled with a compressible liquid is oscillating in response to forced radial excitation of the flask walls. In the long-wave approximation at low Mach numbers, one o btains a system of differential-difference equations generalizing the Rayleigh-Lamb-Plesseth equation. This system takes into account the co mpressibility of the liquid and is suitable for describing both free a nd forced oscillations of the bubble. It includes an ordinary differen tial equation analogous to the Herring-Flinn-Gilmore equation describi ng the evolution of the bubble radius, and a delay equation relating t he pressure at the flask walls to the variation of the bubble radius. The solutions of this system of differential-difference equations are analysed in the linear approximation and numerical analysis is used to study various modes of weak but non-linear oscillations of the bubble , for different laws governing the variation of the pressure or veloci ty of the liquid at the flask wall. These solutions are compared with numerical solutions of the complete system of partial differential equ ations for the radial motion of the compressible liquid around the bub ble. (C) 1998 Elsevier Science Ltd. All rights reserved.