Real gas effects in sound wave propagation through two-phase systems

Abstract

We study sound wave propagation through a two-phase system of gas with dispersed liquid droplets. The key element of the study is a combination of real gas effects, entering the model via a suitable equation of state, with steady and unsteady contributions to the drag force and heat transfer. This feature makes the model applicable for arbitrary pressures and temperatures. In the cases of low and high wave frequencies, ω, analytical solution is derived. At low ω, the model yields a generalization of the homogenous flow approximation to real gases. At high ω, the speed of sound tends to its value in the real gas in the absence of droplets while the attenuation coefficient diverges as [Formula: see text]. The model predicts the phenomenon of resonant attenuation demonstrated by the maximum of the growth rate of attenuation coefficient when ω is close to the eigen frequency of particle relaxation. In the absence of droplets (single-phase limit) for the gas satisfying the van der Waals equation of state, the model yields the corresponding states principle for the speed of sound: The ratio of the actual speed of sound to its ideal-gas value is the universal function of reduced density and temperature. This ratio demonstrates a nonmonotonous behavior of the speed of sound as a function of density reflecting the competition between the repulsive and attractive terms in the intermolecular interaction potential.