For a macroscopic model of a two-velocity two-temperature mixture of gas and dispersed particles, we have obtained a partial solution to a system of partial differential equations in the form of a monochromatic acoustic wave. The mixture has been modeled as interpenetrating continua with relaxation terms describing momentum and thermal energy transfer between the dispersed and carrier phases. The partial solution has been found by the Fourier method and can be used as a verification test for numerical models of gas dispersion media. At arbitrary velocity and thermal relaxation times, to generate a solution one should numerically find complex roots of the dispersion relation, a sixth-degree polynomial. In the case of infinitely short velocity and thermal relaxation times (relaxation equilibrium that is obtained in simulation of ultrafine mixtures), a reference solution has the form of a traveling wave whose velocity is equal to the effective speed of sound in the gas–dust medium. The effective speed of sound has been shown to be sensitive to parameters determining heat transfer processes. We have presented a publicly available code that generates a partial solution for arbitrary problem parameters.
Markelova et al. (Mon,) studied this question.