Effect of vortex fluid motion on nonspherical oscillations of a gas bubble

Abstract

This paper studies the effect of the vortex fluid motion produced by periodic radial oscillations of a weakly nonspherical gas bubble on the variation in the small initial deviation from the spherical shape of this bubble. It is shown that the most intense vortex motion of the fluid occurs in the boundary layer (near field ), and in the far field, the vortex fluid motion rapidly transforms to potential motion. The ranges of problem parameters in which vortex motion in the far field flow does not affect bubble oscillations and the ranges in which accounting for this motion is necessary for a qualitatively correct description of the oscillations are determined.Key words: periodic action, stability of spherical bubble shape, deviation, effect of vortex motion, vorticity.Introduction. Bubble dynamics research has been stimulated by the discovery of stable periodic singlebubble sonoluminescence, by which is meant the periodic emission of short light pulses by a small gas bubble which oscillates at the antinode of an ultrasonic standing pressure wave [1,2]. In addition, there has been increased interest in the variation in the deviation of the bubble shape from a sphere during periodic oscillations. Until recently, the ranges of stable oscillations have been primarily determined [3,4].In this paper, we study the effect of the vortex fluid motion caused by periodic radial oscillations of a weakly nonspherical bubble on the variation in the small initial deviation of the bubble shape from a sphere. Emphasis is placed on the effect of vortex motion in the far (relative to the bubble) flow field. As is known, if a body placed in a weakly viscous fluid performs high-frequency oscillations whose amplitude is small compared to the body size, the most intense vortex motion of the fluid occurs in the boundary layer (near field) of thickness δ c ∼ 2ν/ω c , where ω c is the oscillation frequency and ν is the kinematic viscosity [5]. At distances larger than δ c (in the far field), the fluid motion rapidly becomes potential; therefore, in many cases, the vortex motion in the far field can be neglected. This assumption is made in most of the well-known approximate methods of taking into account the effect of viscosity on the dynamics of gas bubbles (see, for example, [6]). If the frequency and amplitude of nonspherical oscillations vary widely, the intensity ratio of the vortex motion in the near and far (in the region r > R + δ c ) fields can vary. In the present work, we use a model in which the evolution of the deviation of the bubble shape from sphericity is described by an equation [7] which takes into account vortex fluid motion in both the near and far field.It is shown that during stable radial oscillations, the variation in the deviation from period to period can be not only exponential (as is the case under the effect of the near vorticity field) but much slower (power-law) due to the effect of vortex fluid motion in the far field. In addition, the deviation value can alternatively decrease and increase from period to per...