A semi empirical expression of the virial coefficients for hard sphere fluids at all density

TL;DR

This paper introduces a semi-empirical formula for virial coefficients of hard sphere fluids applicable across all densities, improving accuracy over existing models and capturing the singularity at close packing.

Contribution

A new semi-empirical expression for virial coefficients that is valid throughout the entire density range of hard sphere fluids, including near the close packing limit.

Findings

Matches numerical data well across densities

Outperforms Carnahan & Starling equation in validity domain

Captures singularity at close random packing

Abstract

We propose a new semi empirical expression of the virial coefficients for a hard sphere fluid which is valid in the disordered phase over the whole density range. The results are in good agreement with the numerical data and better than those of the well-known Carnahan & Starling equation of state in the domain of validity of the later; moreover this new expression accounts for the singularity which is required for the equation of state at the close random packing limit.