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

Abstract

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.