On the theory of acoustic waves in polydispersed gas–vapor-droplet suspensions

Abstract

A linear theory on the propagation of plane waves in the polydispersed gas-droplets suspensions is presented. The case is considered when the gas carrier phase is a homogeneous mixture of two components. The first one is a vapor, and the second is a neutral gas. Both non-steady and non-equilibrium effects of the phase interaction (mass, momentum, energy interface exchange) are taken into account. A general dispersion equation is obtained. This equation describes the speed of propagation and attenuation of disturbances in the polydispersed gas–vapor-droplets suspensions with arbitrary droplet distribution functions by size. It holds true for a wide range of frequencies complying with the requirement for the medium acoustic homogeneity. An effect of phase transformations (evaporation and condensation) influenced by diffusion of vapor through the neutral gas is studied. Some calculations are done for polydispersed fogs consisting of air and water droplets. High and low frequency asymptotics of the complex wave number that give velocities of the waves and their attenuation are obtained and analyzed. A possibility is shown to describe adequately and simply the attenuation of high and low frequency disturbances in terms of the ‘monodisperse’ models with the use of some averaged droplet radii. A paradoxical effect is found consisting in the non-monotonous dependence of sound attenuation on mass content of droplets, which are the main cause for wave absorbtion.