An equation of state for a fluid of hard disks is proposed: Zϭ͓1Ϫ2ϩ(2 0 Ϫ1)(/ 0) 2 ͔ Ϫ1. The exact fit of the second virial coefficient and the existence of a single pole singularity at the close-packing fraction 0 are the only requirements imposed on its construction. A comparison of the prediction of virial coefficients and of the values of the compressibility factor Z with those stemming out of other known equations of state is made. The overall performance of this very simple equation of state is quite satisfactory.
The Enskog theory for dense multicomponent fluid mixtures is developed. Two versions are considered—the standard theory and the revised theory. Explicit expressions for all the transport coefficients (shear and bulk viscosity, thermal conductivity, mutual and thermal diffusion coefficients) in terms of the sizes, masses, and concentrations of the constituents of the mixture are given in the third Enskog approximation. Applications will be discussed in subsequent papers.
A method to obtain ͑approximate͒ analytical expressions for the radial distribution functions and structure factors in a multi-component mixture of additive hard spheres is introduced. In this method, only contact values of the radial distribution function and the isothermal compressibility are required and thermodynamic consistency is achieved. The approach is simpler than but yields equivalent results to the Generalized Mean Spherical Approximation. Calculations are presented for a binary and a ternary mixture at high density in which the Boublík-Mansoori-Carnahan-Starling-Leland equation of state is used. The results are compared with the Percus-Yevick approximation and the most recent simulation data.
The contact values gij(σij ) of the radial distribution functions of a d-dimensional mixture of (additive) hard spheres are considered. A 'universality' assumption is put forward, according to which gij (σij) = G(η, zij ), where G is a common function for all the mixtures of the same dimensionality, regardless of the number of components, η is the packing fraction of the mixture, and zij = (σiσj/σij ) σ d−1 / σ d is a dimensionless parameter, σ n being the n-th moment of the diameter distribution. For d = 3, this universality assumption holds for the contact values of the Percus-Yevick approximation, the Scaled Particle Theory, and, consequently, the Boublík-GrundkeHenderson-Lee-Levesque approximation. Known exact consistency conditions are used to express G(η, 0), G(η, 1), and G(η, 2) in terms of the radial distribution at contact of the one-component system. Two specific proposals consistent with the above conditions (a quadratic form and a rational form) are made for the z-dependence of G(η, z). For one-dimensional systems, the proposals for the contact values reduce to the exact result. Good agreement between the predictions of the proposals and available numerical results is found for d = 2, 3, 4, and 5.
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