Wave Dispersion in a Two-Phase Gas Mixture : Comments on Random Motions and Void Modes

The properties of linear waves in a mixture comprising diffuse and dense phases are discussed using two approaches: (i) In one approach, the repulsive pressure produced in the diffuse phase by ballistically moving dense clouds generates motion of the components when gradients of the volume-filling factor arise; (ii) in the other approach, where this effect is omitted, a mixture is dynamically insensitive to perturbations containing only variations in the volume-filling factor of dense clouds. We show that the wave dynamics in these two approaches is quite different: in the framework of the first approach, the dispersion relation contains two different branches — the acoustic and the void (pattern formation) modes, while in the second approach the void mode disappears. We argue that in most situations for astrophysical gas mixtures, the first approach is more applicable: since effects of repulsive pressure from randomly moving clouds do exist, the void mode must be important in determining the dynamics of small perturbations and the formation of structures.