Weak Shock Waves in a Liquid Containing Gas Bubbles

Abstract

By making use of the Crespo model of two-phase flow, the structure of a steady weak plane shock wave is investigated analytically. Provided that the Reynolds number based on the bubble radius is of O (1), the thickness of a shock wave is proportional to ε⁻², where ε is a measure of the shock strength, and decreases in proportion to the sum of the reciprocals of two parameters, which express the effects of viscosity and heat transfer between two phases, respectively. The formation of a shock wave by an impulsive motion of a piston is also considered. A transition solution for the initial value problem is obtained by making use of a matching procedure. When the piston speed is small, the solution for large values of the time is governed by Burgers’ equation as in ordinary gas dynamics.