Abstract
An arbitrary irrotational flow of perfect incompressible liquid containing a considerable number of spherical gas bubbles is considered. Two methods of averaging exact characteristics of the motion of bubbles in the liquid, viz. by volume and by bubble centers, are introduced. Formulas relating the average quantities of two different kinds are derived. The boundary value problem for the mean potential is formulated on the basis of the exact boundary value problem for the velocity potential. The obtained equation for the potential in the particular case of unbounded liquid with low concentration of bubbles coincides with that derived in /1/. It is shown that dynamic equations for the average characteristics of moving bubbles accurate to within the product of volume concentration by the velocity of bubbles cannot be derived without considering the pattern of disposition of bubbles relative to the medium microstructure. Closed equations of motion are derived for a liquid with bubbles, and conditions of the applicability of the model of liquid with “frozen in” bubbles are obtained. A comprehensive survey of publications on the subject of equations of motion of liquid with bubbles appears in /1/.
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