Equation of state of a multicomponent d-dimensional hard-sphere fluid

TL;DR

This paper introduces a new method to derive the compressibility factor for multicomponent d-dimensional hard-sphere mixtures, improving accuracy over existing equations of state by leveraging known conditions and the Percus-Yevick approximation.

Contribution

A novel recipe for calculating the compressibility factor of multicomponent mixtures based on the one-component system and specific boundary conditions.

Findings

The proposed equation matches well with known data for hard discs and spheres.

It outperforms existing equations like Boublik-Mansoori-Carnahan-Starling-Leland in 3D.

The method is validated against simulation data.

Abstract

A simple recipe to derive the compressibility factor of a multicomponent mixture of d-dimensional additive hard spheres in terms of that of the one-component system is proposed. The recipe is based (i) on an exact condition that has to be satisfied in the special limit where one of the components corresponds to point particles; and (ii) on the form of the radial distribution functions at contact as obtained from the Percus-Yevick equation in the three-dimensional system. The proposal is examined for hard discs and hard spheres by comparison with well-known equations of state for these systems and with simulation data. In the special case of d=3, our extension to mixtures of the Carnahan-Starling equation of state yields a better agreement with simulation than the already accurate Boublik-Mansoori-Carnahan-Starling-Leland equation of state.