Behavior of a binary asymmetric mixture of interacting particles in the supercritical region

TL;DR

This paper develops a theoretical method to analyze the phase behavior of a binary asymmetric mixture of interacting particles in the supercritical region, deriving equations for critical points, pressure, and the Widom line.

Contribution

It introduces a new approach using the grand partition function in the zero-mode approximation to describe phase behavior of asymmetric binary mixtures.

Findings

Identified a line of critical points for different component proportions.

Derived an explicit pressure expression as a function of temperature and mixing parameter.

Showed that the equations of state reduce to individual species at boundary mixing values.

Abstract

We propose a method for describing a phase behavior of a system consisting of particles of two sorts. The interaction of each species is described by interaction potentials containing the repulsive and attractive components. Asymmetry is ensured by different values of the interaction potentials of each sort. The grand partition function of a binary mixture is calculated in the zero-mode approximation A line of critical points, which correspond to different proportions of the components, is calculated for specific values of parameters of the interaction potential. We have obtained an equation that relates the introduced mixing parameter x with the concentration of the fluid. An explicit expression of the pressure of the binary mixture is derived as a function of relative temperature and mixing parameter x to plot the Widom line. It is established that for boundary values of this parameter (x = 0 and x = 1), the equation of state of a mixture turns into equations of state of its separate species.