Abstract
Effects of small perturbations from a liquid-gas coexistence equilibrium (the Maxwell states) is stud iedfor an isothermal (or isentropic) gas-liquidphase transition in a sealedone- dimensional finite length tube, by using a van per Waals model with a viscous-capillary regular- ization. A matchedasymptotic expansion is usedto d erive formally a linear system satisfiedby lead ing ord er perturbations. The linear system is solvedanalytically andcheckedagainst numerical simulations. Analyses of the linear system suggest the following: (i) A gas-liquidinterface approaches its final destination (determined by mass conservation) in general in a oscillatory manner with fre- quency d eterminedin part by the speed s of soundin gas andliquid ; (ii) Kinetic energies of small initial perturbations will in general be d issipatedin the phase transition process, andthe system approaches steady states; (iii) In some special cases (for example, the time needed for the sound wave to travel in liquidfrom the interface to the tube bound ary 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.
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