Alternative Formulation of the Induced Surface and Curvature Tensions Approach

TL;DR

This paper introduces a new method using Laplace-Fourier transforms to analyze multicomponent hard sphere mixtures, improving the induced surface and curvature tensions model by accounting for particle number fluctuations and higher-order effects.

Contribution

It presents an alternative formulation of the induced surface and curvature tensions approach that incorporates particle number fluctuations and extends to quantum statistics.

Findings

Suppression of tension coefficients is power-like, not exponential.

The method surpasses the Van der Waals approximation at higher packing fractions.

The equation of state is generalized to include higher virial coefficients.

Abstract

We develop a novel method to analyze the excluded volume of the multicomponent mixtures of classical hard spheres in the grand canonical ensemble. The method is based on the Laplace-Fourier transform technique and allows one to account for the fluctuations of the particle number density for the induced surface and curvature tensions equation of state. As a result one can go beyond the Van der Waals approximation by obtaining the suppression of the induced surface and curvature tensions coefficients at moderate and high packing fractions. In contrast to the standard induced surface and curvature tensions equation of state the suppression of these coefficients is not an exponential one, but a power-like one. The obtained alternative equation of state is further generalized to account for higher virial coefficients. This result is straightforwardly generalized to the case of quantum statistics.