An effective equation for plane dispersive waves of very high frequency in compressible liquids containing many micro bubbles

摘要

This study theoretically deals with the propagation of plane waves of very high frequency in a liquid containing many spherical gas bubbles. We focus on a compressibility of liquid phase that has been neglected in many previous works, and treat wave propagation in a mode induced by the liquid compressibility. Waves in this mode propagate with large phase velocity exceeding the sound speed in liquid. We derive the wave equation as a mathematical model for the waves in this mode, i.e., a linear equation with dissipation and dispersion effects can be derived from a set of basic equations in a two-fluid model.