UBC Theses and Dissertations
On the condensation of a Van der Waals gas Strickfaden, William Ben
A classical gas whose particles interact through a weak long range attraction and short range repulsion is studied. We study the properties of a non-linear integral equation, previously derived by N.G. Van Kampen, whose solutions give the possible equilibrium density distributions. It is shown that above a critical temperature the solution of the equation is unique, while below the critical temperature multiple solutions exist. The existence of a two phase solution which must satisfy the Maxwell rule is proven by solving the equation exactly for a physically reasonable potential for the long range attraction and a very general form for the short range repulsion. Stability and necessity conditions for the solutions to be extrema of the free energy are given and applied to the various solutions of the integral equation. It is shown that in the limit of large volume the critical point manifests itself as a so-called bifurcation point (point where the number of solutions changes) of the integral equation. Surface tension of simple liquids is calculated from the integral equation and compared to experiment. Agreement is excellent considering the small amount of input data needed and the approximations used. The non-equilibrium properties of the system in the coexistence region are studied by solving a set of hydrodynamic equations numerically. It is shown that the metastable states, at least in the supercooled portion of the isotherm are indeed unstable with respect to large scale pertubations. Growth and decay rates for small droplets of condensing and evaporating liquid are given.
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