Acoustic microstreaming produced by nonspherical oscillations of a gas bubble. III. Case of self-interacting modes <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>n</mml:mi><mml:mtext>−</mml:mtext><mml:mi>n</mml:mi></mml:mrow></mml:math>
Claude Inserra, Gabriel Regnault, Sarah Cleve, Cyril Mauger, Alexander A. Doinikov
Abstract
This paper is the continuation of work done in our previous papers [A. A. Doinikov et al., Phys. Rev. E 100, 033104 (2019)2470-004510.1103/PhysRevE.100.033104; Phys. Rev. E 100, 033105 (2019)].2470-004510.1103/PhysRevE.100.033105 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 our previous papers, general equations have been derived to describe the velocity field of acoustic microstreaming produced by modes m and n of bubble oscillations. After solving these general equations for some particular cases of modal interactions (cases 0-n, 1-1, and 1-m), in this paper the general equations are solved analytically for the case that acoustic microstreaming results from the self-interaction of an arbitrary surface mode n≥1. Solutions are expressed in terms of complex mode amplitudes, meaning 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. The self-interaction results in specific streaming patterns: a large-scale cross pattern and small recirculation zones in the vicinity of the bubble interface. Particularly the spatial organization of the recirculation zones is unique for a given surface mode and therefore appears as a signature of the n-n interaction. Experimental streaming patterns related to this interaction are obtained and good agreement is observed with the theoretical model.