Acoustic microstreaming produced by nonspherical oscillations of a gas bubble. II. Case of modes 1 and m.

Abstract

This paper continues a study that was started in our previous paper [A. A. Doinikov etal., Phys. Rev. E 100, 033104 (2019)10.1103/PhysRevE.100.033104]. The overall aim of the study is to develop a theory for modeling the velocity field of acoustic microstreaming produced by nonspherical oscillations of an acoustically driven gas bubble. In the previous paper, general equations were derived that describe the velocity field of acoustic microstreaming produced by modes n and m of bubble oscillations. In the present paper, the above equations are solved analytically in the case that acoustic microstreaming is the result of the interaction of the translational mode (mode 1) with a mode of arbitrary order m≥1. Solutions are expressed in terms of complex mode amplitudes, which means that the mode amplitudes are assumed to be known and serve as input data for the calculation of the velocity field of acoustic microstreaming. No restrictions are imposed on the ratio of the bubble radius to the viscous penetration depth. Analytical results are illustrated by numerical examples.