The effect of diffusion on the acoustic properties of a bubble fluid

Abstract

The problems of wave propagation in bubble media have been of great interest to researchers for almost half a century in connection with the wide distribution of these systems in nature and their intensive use in modern technologies. It is known from the literature that the intensity of attenuation of sound disturbances in the gas-liquid media under consideration is mainly determined by the thermophysical characteristics of the gas in the bubbles. It turns out that these effects are significantly enhanced with increasing vapor concentration due to an increase in the temperature of the system. There are a large number of publications in the literature in which various statements of the wave action on bubble media have been considered. In the present work, the propagation of small perturbations in a liquid with bubbles filled with vapor and a gas insoluble in the liquid phase is considered in the plane one-dimensional and single-velocity approximations. The rate of liquid evaporation (condensation) inside the bubble was determined from the condition of heat balance. To take into account interphase heat and mass transfer, the heat conduction and diffusion equations inside the bubble and the heat conduction equation in the fluid around the bubble are used. From the condition for the existence of a solution in the form of a decaying traveling wave, taking into account the effects of acoustic unloading of bubbles, the dispersion equation is written. From the condition for the existence of a solution in the form of a decaying traveling wave, taking into account the effects of acoustic unloading of bubbles, the dispersion equation is written. Based on the obtained dispersion equation, relations are written for the equilibrium speed of sound depending on the thermophysical parameters of the medium and numerical calculations are performed for water with vapor-gas bubbles. The features of the reflection of harmonic waves from the interface between the “pure” liquid and liquid with vapor-gas bubbles are studied. The influence of the perturbation frequency and the temperature of the medium on the attenuation coefficient of the acoustic wave is studied. The influence of diffusion on the evolution of harmonic waves is analyzed.