Phase Transition Near a Liquid-Gas Coexistence Equilibrium

Effects of small perturbations from a liquid-gas coexistence equilibrium (the Maxwell states) is studied for an isothermal (or isentropic) gas-liquid phase transition in a sealed onedimensional finite length tube, by using a van per Waals model with a viscous-capillary regularization. A matched asymptotic expansion is used to derive formally a linear system satisfied by leading order perturbations. The linear system is solved analytically and checked against numerical simulations. Analyses of the linear system suggest the following: (i) A gas-liquid interface approaches its final destination (determined by mass conservation) in general in a oscillatory manner with frequency determined in part by the speeds of sound in gas and liquid; (ii) Kinetic energies of small initial perturbations will in general be dissipated in the phase transition process, and the system approaches steady states; (iii) In some special cases (for example, the time needed for the sound wave to travel in liquid from the interface to the tube boundary is a rational multiple of that in gas), kinetic energies of certain small perturbations will not be dissipated (in the leading order expansion); in fact, there are infinitely many linearly independent time periodic solutions to the linear system.