Equations of Interaction of Weakly Non-Spherical Gas Bubbles in Liquid

被引：13

作者：

Aganin A.A. ^{[1
]}

Davletshin A.I. ^{[1
]}

机构：

[1] Institute of Mechanics and Engineering—Subdivision of Kazan Scientific Center of the Russian Academy of Sciences, ul. Lobachevskogo 2/31, Kazan, Tatarstan

来源：

Lobachevskii Journal of Mathematics | 2018年 / 39卷 / 8期

基金：

俄罗斯科学基金会;

关键词：

hydrodynamic interaction of bubbles; method of spherical functions; small deformations of bubbles; Weakly non-spherical bubbles;

D O I：

10.1134/S1995080218080024

中图分类号：

学科分类号：

摘要：

Equations of spatial hydrodynamic interaction of gas bubbles in an ideal incompressible liquid are derived with allowing for small deformations of their surfaces. The derivation is carried out by the method of spherical functions using the Bernulli integral, the kinematic and dynamic boundary conditions on the bubble surfaces. At that, an original expression of transformation of irregular solid spherical harmonics at parallel translation of the coordinate system is applied. The result of the derivation is a system of ordinary differential equations of the second order in the radii of the bubbles, the position-vectors of their centers and the vectors characterizing small deviations of the bubble surfaces from the spherical one. Due to their compactness, these equations are much more convenient for analysis and numerical solution than their known analogs. © 2018, Pleiades Publishing, Ltd.

引用

页码：1047 / 1052

页数：5

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