Two-Parameter Bifurcation Analysis for the Seeking of High Amplitude Oscillation of a Periodically Driven Gas Bubble in Glycerine

Klapcsik, Kálmán and Hegedűs, Ferenc (2015) Two-Parameter Bifurcation Analysis for the Seeking of High Amplitude Oscillation of a Periodically Driven Gas Bubble in Glycerine. In: Proceedings of Conference on Modelling Fluid Flow (CMFF'15). CFD.HU Kft., Budapest, pp. 1-8. ISBN 978-963-313-190-9

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Abstract

The dynamics of a harmonically driven spherical gas/vapour bubble has been studied intensely in the last decades. The collapse of a bubble induce extreme conditions, such as high pressure and temperature or even shock waves. The ultrasonic technology exploit these conditions in various fields of industry, for example, ultrasonic pasteurization, alteration of the viscosity of thixotropic fluids, production of new kind of copolymers, or in cancer therapy. The present study intends to aid the applications through the numerical investigation of a harmonically excited spherical gas bubble placed in the highly viscous glycerine. We seek parameter regions where the bubble wall velocities as high as possible, perhaps even higher than the sound speed in the liquid domain. Such kind of high amplitude, collapse-like radial oscillations are difficult to find due to the very high viscosity, which is approximately three orders of magnitude greater than of water. The two investigated parameters were the pressure amplitude and the frequency of the harmonic forcing. The applied model was the Keller—Miksis equation, which is a second order nonlinear ordinary differential equation, describing the bubble wall motion and taking into account liquid compressibility as a first order approximation.

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