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Fluid Kinetic Energy Asymptotic Expansion for Two Variable Radii Moving Spherical Bubbles at Small Separation Distance

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Abstract

Two spherical bubbles with changing radii are considered to be moving in ideal fluid along their center-line. The exact expression for the fluid kinetic energy is obtained. The Stokes stream function is expanded in Gegenbauer polynomials in bispherical coordinates. This expansion is used to obtain the exact series for the fluid kinetic energy quadratic form coefficients. The new series are confirmed to be correct by comparison with the known ones. The main advantage of the new kinetic energy form is the possibility to obtain asymptotic expansions at small separation distance between the bubbles. These expansions are obtained and their convergence is analyzed. The results of this work can be used to describe the bubbles approach before the contact and their coalescence in acoustic field.

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ACKNOWLEDGMENTS

The author thanks A.G. Petrov for his helpful comments and discussion of the paper.

Funding

The present work was supported by the Ministry of Science and Higher Education within the framework of the Russian State Assignment under contract no. AAAA-A20-120011690138-6.

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Authors and Affiliations

  1. Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, 119526, Moscow, Russia

    S. V. Sanduleanu

  2. Moscow Institute of Physics and Technology, 141701, Dolgoprudny, Moscow Region, Russia

    S. V. Sanduleanu

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  1. S. V. Sanduleanu
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Correspondence to S. V. Sanduleanu.

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Translated by A. Ivanov

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Sanduleanu, S.V. Fluid Kinetic Energy Asymptotic Expansion for Two Variable Radii Moving Spherical Bubbles at Small Separation Distance. Fluid Dyn 55, 877–889 (2020). https://doi.org/10.1134/S0015462820070083

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  • DOI: https://doi.org/10.1134/S0015462820070083

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