Home – Home – Jornals – Journal of Applied Mechanics and Technical Physics 2025 number 6

We derive a particular solution for a macroscopic model of a two-velocity, two-temperature mixture of gas and suspended particles. The solution to the system of partial differential equations takes the form of a monochromatic sound wave. The mixture is modeled within the interpenetrating continuum approach, incorporating relaxation terms that account for momentum and thermal energy exchange between the carrier and dispersed phases. The particular solution is constructed via the Fourier method and can serve as a verification test for numerical models of gas-particle flows. For arbitrary velocity and thermal relaxation times, the solution is obtained by numerically calculating the complex roots of a sixth-degree polynomial dispersion relation. In the case of infinitely small relaxation times (a state of relaxation equilibrium pertinent to modeling ultra-dispersed mixtures), the reference solution reduces to a traveling wave propagating at the effective speed of sound in the gas-dust medium. We demonstrate the sensitivity of this effective sound speed to the parameters governing the heat transfer processes. The code used to generate the particular solution for arbitrary input parameters is publicly available.