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UBC Theses and Dissertations

Kinetic equation for a classical gas with a long range attraction. Elliott, Richard Amos


A classical gas whose particles interact through a weak long range attraction and a strong short range repulsion is studied. The Liouville equation is solved as an infinite order perturbation expansion. The terms in this series are classified by Prigogine type diagrams according to their order in the ratio of the range of the interaction to the average interparticle distance. It is shown that., provided the range of the short range force is much less than the average interparticle distance which in turn is much less than the range of the long range forces the terms can be grouped into two classes. The one class, represented by chain diagrams, constitutes the significant contributions of the short range interaction; the other, represented by ring diagrams, makes up, apart from a self-consistent field term, the significant contributions from, the long range force. These contributions are summed to yield a kinetic equation. The orders of magnitude of the terms in this equation are compared for various ranges of the parameters of the system. Retaining only the dominant terms then produces a set of eight kinetic equations each of which is valid for a definite range of the parameters of the system. The short-time stability of the system is examined and a criterion for stability obtained. The equilibrium two-particle correlation function and an equation of state are determined, the latter being compared to the Van de Waals equation of state.

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