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Mathematical modelling for acoustic microstreaming produced by a gas bubble undergoing asymmetric oscillations

Published online by Cambridge University Press:  08 May 2025

Claude Inserra Open the ORCID record for Claude Inserra [Opens in a new window] ,
Cyril Mauger ,
Philippe Blanc-Benon  and
Alexander A. Doinikov
Claude Inserra*
Affiliation:
University of Lyon, Université Claude Bernard Lyon 1, Centre Léon Bérard, INSERM, UMR 1032, LabTAU, Lyon F-69003, France
Cyril Mauger
Affiliation:
INSA Lyon, CNRS, École Centrale de Lyon, Université Claude Bernard Lyon 1, UMR 5509, LMFA, Villeurbanne 69621, France
Philippe Blanc-Benon
Affiliation:
INSA Lyon, CNRS, École Centrale de Lyon, Université Claude Bernard Lyon 1, UMR 5509, LMFA, Villeurbanne 69621, France
Alexander A. Doinikov
Affiliation:
INSA Lyon, CNRS, École Centrale de Lyon, Université Claude Bernard Lyon 1, UMR 5509, LMFA, Villeurbanne 69621, France
*
Corresponding author: Claude Inserra, [email protected]
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Abstract

An exact solution is developed for bubble-induced acoustic microstreaming in the case of a gas bubble undergoing asymmetric oscillations. The modelling is based on the decomposition of the solenoidal, first- and second-order, vorticity fields into poloidal and toroidal components. The result is valid for small-amplitude bubble oscillations without restriction on the size of the viscous boundary layer $(2\nu /\omega )^{1/2}$ in comparison to the bubble radius. The non-spherical distortions of the bubble interface are decomposed over the set of orthonormal spherical harmonics $Y_{n}^{m}(\theta , \phi )$ of degree $n$ and order $m$. The present theory describes the steady flow produced by the non-spherical oscillations $(n,\pm m)$ that occur at a frequency different from that of the spherical oscillation, as in the case of a parametrically excited surface oscillation. The three-dimensional aspect of the streaming pattern is revealed as well as the particular flow signatures associated with different asymmetric oscillations.

JFM classification

Drops and Bubbles: Drops and Bubbles
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1010 , 10 May 2025 , A48
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Copyright
© The Author(s), 2025. Published by Cambridge University Press

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