Acoustic microstreaming produced by nonspherical oscillations of a gas bubble. I. Case of modes 0 and m.

A theory is developed that allows one to model the velocity field of acoustic microstreaming produced by nonspherical oscillations of an acoustically driven gas bubble. It is assumed that some of the bubble oscillation modes are excited parametrically and hence can oscillate at frequencies different from the driving frequency. Analytical solutions are derived in terms of complex amplitudes of oscillation modes, which means that the mode amplitudes are assumed to be known and serve as input data when the velocity field of acoustic microstreaming is calculated. No restrictions are imposed on the ratio of the bubble radius to the viscous penetration depth. The present paper is the first part of our study in which a general theory is developed and then applied to the case that acoustic microstreaming is generated by the interaction of the breathing mode (mode 0) with a mode of arbitrary order m≥1. Examples of numerical simulations and a comparison with experimental results are provided.