Damping efficiency of the void mode in a two-phase gas mixture with a phase transition

We have discussed the wave properties in a two-phase gas mixture, which is composed of a diffuse medium [phase I (PI)] and dense clouds [phase IT (PII )]. Interestingly, there are two wave modes when PII has mobility relative to PI. One is the acoustic mode, and the other is the void mode (or pattern -propagating mode). In this paper, we present a more careful discussion con cerning the restoring force of the void mode. After that, we estimate the d amping rate of the void mode due to the thermal process, which acts as a fr iction effect. We call this thermal friction. For a typical interstellar me dium (ISM), where the cold cloud phase is PEI and the warm phase gas is PI, friction is not so significant within the galaxy evolution timescales. How ever, if the coronal phase is PI, PII of the warm clouds suffers thermal fr iction efficiently. Thus, when the evolution of ISM is described by the cla ssical three-phase model, we can adopt a modified two-phase model within th e context of multi-phase flow; in which PI corresponds to a mixture of the hot and warm phases and PII corresponds to the cold clouds.