Wave Equation for Bubble Liquid in Lagrangian Variables

Abstract

One-dimensional steady flow of liquid with gas bubbles is considered under the following assumptions: monodisperse mixture; viscosity and thermal conductivity are matter only in the process of interfacial interaction and during bubble pulsations. It was assumed that there is no mass transfer between the phases, and the liquid temperature is constant, unlike the gas temperature in a bubble. The pressure in the bubble was taken uniform, that is true if the radial velocity of the bubble walls is significantly less than the speed of sound in the gas. A polytropic law was taken for the description of gas properties in bubbles. On the basis of one-dimensional stationary equations of fluid flow with gas bubbles, the wave equation for a bubbly fluid in Lagrangian variables is written. For the case of highly viscous liquids a “step” type solution is obtained.