Numerical analysis of the thermal relaxation of the dense gas between two parallel plates: the free energy monotonicity for the Enskog equation

TL;DR

This study analyzes the thermal relaxation of dense gases between parallel plates using the Enskog equation, demonstrating that a modified Enskog factor ensures the free energy decreases monotonically over time, unlike the original version.

Contribution

It introduces and compares two versions of the Enskog equation, showing the modified factor guarantees free energy monotonicity during thermal relaxation.

Findings

Free energy decreases monotonically with the modified Enskog factor.

Original Enskog equation does not guarantee free energy monotonicity.

Differences observed in density profiles and other quantities during evolution.

Abstract

The thermal relaxation problem between two parallel plates with the same temperature is investigated, aiming to study the behavior of the free energy of the dense gas described by the Enskog equation. Two types of Enskog equation have been used: one is the Enskog equation with the original Enskog factor, while the other is that with a modified Enskog factor proposed recently in Takata & Takahashi, Phys. Rev. E 111, 065108 (2025). The evaluated free energy is a natural extension of the thermodynamic free energy to the non-equilibrium state. It is observed that this free energy monotonically decreases in time for the modified factor version, while it is not necessarily the case for the original version. Differences are also observed in other quantities in their time evolutions, most typically in the density profile.