Asymptotic expansion based equation of state for hard-disk fluids offering accurate virial coefficients

TL;DR

This paper develops a new asymptotic expansion-based equation of state for hard-disk fluids that accurately reproduces the first eighteen virial coefficients and aligns well with simulation data, improving understanding of fluid behavior.

Contribution

A novel equation of state derived from asymptotic expansion that accurately matches the first eighteen virial coefficients of hard-disk fluids.

Findings

Accurately reproduces the first eighteen virial coefficients.

Matches simulation data for the compressibility factor.

Identifies configurations with potential for future higher virial coefficient calculations.

Abstract

Despite the fact that more that more than 30 analytical expressions for the equation of state of hard-disk fluids have been proposed in the literature, none of them is capable of reproducing the currently accepted numeric or estimated values for the first eighteen virial coefficients. Using the asymptotic expansion method, extended to the first ten virial coefficients for hard-disk fluids, fifty-seven new expressions for the equation of state have been studied. Of these, a new equation of state is selected which reproduces accurately all the first eighteen virial coefficients. Comparisons for the compressibility factor with computer simulations show that this new equation is as accurate as other similar expressions with the same number of parameters. Finally, the location of the poles of the 57 new equations shows that there are some particular configurations which could give both the accurate virial coefficients and the correct closest packing fraction in the future when higher virial coefficients than the tenth are numerically calculated.