Rescaled density expansions and demixing in hard-sphere binary mixtures

TL;DR

This paper investigates the demixing transition in binary hard-sphere mixtures using virial expansions and rescaling techniques, revealing how different theoretical approaches influence the predicted phase behavior.

Contribution

It introduces a detailed analysis of how rescaling the low-density expansion affects the predicted critical points in binary mixtures, highlighting the impact of the Percus-Yevick approximation.

Findings

Virial coefficients shift the critical point to higher pressures and lower compositions.

Rescaling the pressure expansion alters the qualitative behavior of phase separation.

Percus-Yevick factor significantly influences the phase diagram predictions.

Abstract

The demixing transition of a binary fluid mixture of additive hard spheres is analyzed for different size asymmetries by starting from the exact low-density expansion of the pressure. Already within the second virial approximation the fluid separates into two phases of different composition with a lower consolute critical point. By successively incorporating the third, fourth, and fifth virial coefficients, the critical consolute point moves to higher values of the pressure and to lower values of the partial number fraction of the large spheres. When the exact low-density expansion of the pressure is rescaled to higher densities as in the Percus-Yevick theory, by adding more exact virial coefficients a different qualitative movement of the critical consolute point in the phase diagram is found. It is argued that the Percus-Yevick factor appearing in many empirical equations of state for the mixture has a deep influence on the location of the critical consolute point, so that the resulting phase diagram for a prescribed equation has to be taken with caution.