Weak oscillations of a gas bubble in a spherical volume of compressible liquid

I. Sh Akhatov, N. K. Vakhitova, G. Ya Galeyeva, R. I. Nigmatulin, D. B. Khismatullin

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


The following spherically symmetric problem is considered: a single gas bubble at the centre of a spherical flask filled with a compressible liquid is oscillating in response to forced radial excitation of the flask walk. In the long-wave approximation at low Mach numbers, one obtains a system of differential-difference equations generalizing the Rayleigh-Lamb-Plesseth equation. This system takes into account the compressibility of the liquid and is suitable for describing both free and forced oscillations of the bubble. It includes an ordinary differential equation analogous to the Herring-Flinn-Gilmore equation describing the evolution of the bubble radius, and a delay equation relating the 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 velocity of the liquid at the flask wall These solutions are compared with numerical solutions of the complete system of partial differential equations for the radial motion of the compressible liquid around the bubble.

Original languageEnglish
Pages (from-to)921-930
Number of pages10
JournalJournal of Applied Mathematics and Mechanics
Issue number6
Publication statusPublished - 1997
Externally publishedYes


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