Acoustic instability in a two-phase mixture with temperature relaxation of particles

Theoretical calculation of acoustic instability in a two-phase mixture with temperature relaxation of particles is performed. Particles are assumed to be spherical and monodisperse, while their mass fraction does not exceed $50\%$. The formula for calculation of the acoustic oscillation frequency and increment, as well as the approximate formula for oscillation-amplitude calculation, are derived in this work. The heat exchange between the particles and the gas mixture is taken into consideration explicitly in these formulas.