Weakly nonlinear propagation of pressure waves in liquids containing translational bubbles acting a drag force

Abstract

Weakly nonlinear (i.e., finite but small amplitude) propagation of plane pressure waves in liquids uniformly containing many spherical microbubbles is theoretically investigated. Although the effects of a translation of bubbles and a drag force acting on bubbles are incorporated, the creation, extinction, coalescence, break up, and polydispersity of bubbles are not considered. From the second order of approximation based on the method of multiple scales, the KdV–Burgers equation for a low frequency long wave is derived from the basic equations for bubbly flows composed of the conservation equations in a two-fluid model installing a virtual mass force and the bubble-dynamics equation for spherical symmetric oscillating translational bubbles. As a result, the translation of bubbles increased an effect of wave nonlinearity in a far field.