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 Matem. Mod., 2013, Volume 25, Number 12, Pages 3–18 (Mi mm3425)

Interaction of spherical bubbles with centers located on the same line

A. A. Aganin, A. I. Davletshin

Institute of Mechanics and Engineering, Kazan Science Center, Russian Academy of Sciences

Abstract: A mathematical model and a technique for solving problems of close-range interaction of two and more spherical gas bubbles in a liquid, centers of which are located on the same line, are proposed. In the model, the effects of the liquid viscosity and compressibility, heat transfer between the bubbles and liquid are taken into account. The bubble dynamics is described by a system of the second order ordinary differential equations for the radii of the bubbles and their spatial positions and the first order ones for the gas temperature in each bubble. The equations for the radii of the bubbles and their spatial positions contain coefficients of expansion of the fluid velocity potential in Legendre polynomials, which are determined from a system of linear algebraic equations. The order of accuracy of the proposed model is arbitrary relative to the maximum value, over all pairs of interacting bubbles, of the ratio of sum of the radii of the bubbles in a pair to the distance between their centers. Verification of the proposed model and method of solution is conducted. Some examples of application of the proposed model to describing interaction between the two and three bubbles are presented.

Keywords: interaction of bubbles, acoustic field, fluid velocity potential.

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Bibliographic databases:
UDC: 532.5::534

Citation: A. A. Aganin, A. I. Davletshin, “Interaction of spherical bubbles with centers located on the same line”, Matem. Mod., 25:12 (2013), 3–18

Citation in format AMSBIB
\Bibitem{AgaDav13} \by A.~A.~Aganin, A.~I.~Davletshin \paper Interaction of spherical bubbles with centers located on the same line \jour Matem. Mod. \yr 2013 \vol 25 \issue 12 \pages 3--18 \mathnet{http://mi.mathnet.ru/mm3425} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3221126} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. A. A. Aganin, A. I. Davletshin, “Preobrazovanie neregulyarnykh sharovykh funktsii pri parallelnom perenose sistemy koordinat”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 159, no. 1, Izd-vo Kazanskogo un-ta, Kazan, 2017, 5–12
2. A. A. Aganin, A. I. Davletshin, “Deformatsii vzaimodeistvuyuschikh gazovykh puzyrkov v zhidkosti pri akusticheskom vozdeistvii”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 160, no. 4, Izd-vo Kazanskogo un-ta, Kazan, 2018, 657–669
3. A. I. Davletshin, “Vzaimodeistvie gazovykh puzyrkov v zhidkosti v akusticheskom pole s tsentrami na odnoi ploskosti”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 162, no. 2, Izd-vo Kazanskogo un-ta, Kazan, 2020, 148–159
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