Acoustics of a Polydisperse Vapor–Gas Bubbles-Laden Liquid

Abstract

A mathematical model is presented that determines the propagation of acoustic waves in a liquid containing polydisperse vapor–gas bubbles with account for mass transfer processes. A system of integrodifferential equations of a disturbed motion of a two-phase mixture is written, and a dispersion relation is obtained. A general expression for the equilibrium velocity of sound has been found for a vapor–gas liquid mixture, and the influence of vapor concentration and of the volume content of bubbles on the value of the equilibrium velocity of sound has been analyzed. In particular cases, expressions of the equilibrium velocity of sound are presented for gas–liquid and vapor–liquid mixtures, and satisfactory agreement of the obtained values with the familiar experimental data has been obtained. The results of comparison of the dispersion curves of phase velocity and of the attenuation coefficient for a mixture of water with vapor–air bubbles at different values of the initial concentration of vapor in bubbles are given.