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

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.

Natural oscillation frequencies of a Rayleigh sphere levitated in standing acoustic waves.

Acoustic levitation is an important method of container-free processing, which counteracts gravity through exerting the acoustic radiation force on levitated objects. The Gorkov potential function is used to simplify the calculation of the acoustic radiation force acting on a Rayleigh sphere whose radius is much smaller than the wave length. For the case of a plane standing wave levitation system, a systematic analysis of the sphere dynamics is provided in the axial direction, assuming a small perturbation around the stable equilibrium locations. A generalized extension to an arbitrary standing wave field is provided, which gives formal expressions of the axial and transverse natural oscillation frequencies for the sphere. Particular emphasis is put on the natural oscillation frequencies with and without taking gravity into consideration. The computational results for Gauss and Bessel standing waves are provided as two special cases, which show that the transverse natural oscillation frequency will be overestimated when neglecting gravity, especially for a sphere with a relatively large density. Corresponding experiments are conducted to verify the dependence of the transverse natural oscillation frequency on the sphere density. The results obtained in this work are expected to provide a theoretical guide for enhancing the levitation stability and inversing the physical parameters from the sphere dynamics.