Abstract

 

Symmetry in Bubble Dynamics

A.O.Maksimov (V.I. Il'ichev Pacific Oceanological Institute Far East Branch, Russian Academy of Sciences, Vladivostok, Russia)

e-mail: pacific@online.marine.su

An investigation on novel lines is made into the problem of nonlinear bubble dynamics. The use of method based on infinitesimal-transformation theory provides a systematic account of symmetries inherent to the problem. The complete symmetry groups are found for the Rayleigh equation. The physical interpretation attaching to these time translation and scaling groups is presented. The detail analysis of nonlinear bubble pulsation under scaling law is given. The domain of attraction of fixed points, its dependence on governing parameters have been determined and the global dynamic portraits of the system has been established. The possible application of the scaling law dynamics to the problem of stable single bubble sonoluminescence is discussed.  Conformal symmetry of Laplace equation provides an approach for finding exact solutions for the pulsation of gas bubble tethered to a rigid wall. An analog of Rayleigh equation has been derived and the dependence of natural frequencies on contact angle has been studied.  The final example illustrating the approach is use of symmetry of .coagulation integral. in the kinetics of interacting bubbles for finding an exact solution for bubble size distribution corresponding constant flow over axis of sizes.

 

Section : 12