Theoretical analysis for nonlinear pressure waves in bubbly liquids with phase change

Abstract

Weakly nonlinear propagation of pressure waves in initially quiescent liquids containing many spherical microbubbles with phase change is theoretically studied. In particular, we focus on the effect of phase change across the bubble–liquid interface. Gas inside bubbles is composed of air as the non-condensable gas and water vapor as the condensable gas, and the diffusion of gas inside bubble is not considered. The liquid density and temperature are assumed as constants. However thermal boundary layer in liquid phase is considered, and the liquid temperature gradient is treated as a variable. From perturbation analysis using basic equations based on a two-fluid model, the Korteweg–de Vries–Burgers equation is derived. The phase change contributes to the nonlinear, dissipation, dispersion, and advection effects of waves. However, the result of the effect for dissipation effect is different from that in the previous study, and it is considered that treating the liquid temperature as a variable is necessary.