Semiphenomenological model for gas-liquid phase transitions

We examine a rarefied gas with inter-molecular attraction. It is argued that the attraction force amplifies random density fluctuations by pulling molecules from lower-density regions into high-density regions and thus may give rise to an instability. To describe this effect, we use a kinetic equation where the attraction force is taken into account in a way similar to how electromagnetic forces in plasma are treated in the Vlasov model. It is demonstrated that the instability occurs when the temperature T is lower than a certain threshold value T-s depending on the gas density. It is further shown that, even if T is only marginally lower than T-s, the instability generates clusters with density much higher than that of the gas. These results suggest that the instability should be interpreted as a gas-liquid phase transition, with T-s being the temperature of saturated vapor and the high-density clusters representing liquid droplets.