INTERACTION OF TWO SPHERICAL GAS BUBBLES IN A LIQUID IN AN ACOUSTIC FIELD

Abstract: 

A mathematical model and a technique for solving problems of close-range interaction of two spherical gas bubbles in a liquid with allowing for the effects of the liquid viscosity and compressibility, heat trans-fer between the bubbles and liquid are proposed. The model is a system of ordinary second order differen-tial 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 relative to the ratio of sum of the radii of interacting bubbles to the distance between their centers is arbitrary. Some ex-amples of application of the proposed model to describing close-range interaction between the bubbles are presented. 

Key words: 

bubble interaction, acoustic field, velocity potential.

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