Radial and translational motions of a gas bubble in a Gaussian standing wave field

Abstract

Acoustic waves with a finite beam width are widely used in acoustic manipulation and cavitation applications. In view of this, radial oscillation and translational motion of a gas bubble in a Gaussian standing wave field are studied in this work. Dynamic differential equations for the bubble are derived with the axial and transverse motions coupled with each other. A comprehensive numerical study is also carried out in the parameter space of the driving frequency, pressure amplitude, initial coordinate, off-axial distance and beam waist. The results demonstrate that the nonlinear radial oscillation can be intensified by a higher pressure amplitude and a smaller off-axial distance. Whether the driving frequency is much lower than the resonance frequency determines not only the final equilibrium position but also the direction of translational motion for the gas bubble. With the widening of the Gaussian standing wave, the radial oscillation will be weakened and the translational motion will be slowed down due to reduction of the pressure gradient regardless of the driving frequency. The results obtained in this study is of interest for an understanding of the bubble dynamics in non-plane acoustic wave fields.