The rate of convergence of the virial series in confined systems

We examine cluster-series methods for the behaviour of simple fluids under confinement, applying the Mayer-sampling Monte Carlo method to evaluate the necessary cluster integrals. We examine two series formulations, one based on the density of a bulk phase in equilibrium with the confined phase (effectively specifying the chemical potential), and another based on the density of the confined phase. The theory and methods are used to calculate the structure and properties of hard-sphere fluids confined between parallel planar hard walls. We present the effects of width of the confined region on the inhomogeneous virial coefficients, and through them, on the thermodynamics of the confined system.