Heat exchange between a gas bubble and a liquid

Abstract

The nonlinear problem of thermal and dynamic interaction between a single gas bubble and surrounding liquid is considered. This problem is met in studies of gas-liquid mixture flows, in particular, in Shockwave propagation in such media. A numerical solution is presented for various modes of bubble surface radial motion. The modes correspond to bubble behavior directly beyond a shock-wave front, where the latter enters the bubble screen, and to the behavior of a bubble located in the depths of the bubble curtain, where the wave becomes diffuse. Analytic solutions of the linearized problem of thermal conductivity for free and constrained small harmonic oscillations of a gas bubble in a liquid were obtained in [1, 2]. Cooling of a hot gas bubble was considered in [3], that study, however, contains inaccuracies. In particular, it was assumed in the solution that the gas density in the bubble was homogeneous. The equation for heat flux in dimensionless variables was written inaccurately. However, in the examples considered in [3] these inaccuracies do not lead to significant errors in the numerical results.