Abstract
Abstract A system of effective equations for wave propagation in a bubbly liquid with a small gas volume fraction is obtained. The derivation consists of averaging the basic equations of the two-phase flow and then using the method of matched asymptotic expansions in order to define the microscopic problem. The resulting system consists of a continuity equation with a source term and a momentum equation with forcing terms. These terms are coupled to a canonical microscopic problem for the motion of a single bubble. The system accounts for the nonlinear effects of the translation of the bubble centers and the oscillation of the bubble interfaces including the spherically symmetric mode and all the asymmetric modes. The system remains valid regardless of the order of magnitude of the gas volume fraction relative to the reciprocal of the bubble number density.
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