Extended hydrodynamics from Enskog's equation for a two-dimensional system general formalism

TL;DR

This paper derives an extended hydrodynamic model for a two-dimensional dense fluid of hard disks from Enskog's equation, incorporating additional fields like pressure tensor and heat flux, and applies it to a heat conduction problem.

Contribution

It introduces a novel extended hydrodynamics framework for 2D dense fluids based on Enskog's equation, including pressure tensor and heat flux as independent fields.

Findings

The derived hydrodynamic equations are applicable to moderately dense 2D fluids.

The model predicts pressure dependence on density, temperature, and heat flux near equilibrium.

Application to heat conduction shows the pressure's dependence on key thermodynamic variables.

Abstract

Balance equations are derived from Enskog's kinetic equation for a two-dimensional system of hard disks using Grad's moment expansion method. This set of equations constitute an extended hydrodynamics for moderately dense bi-dimensional fluids. The set of independent hydrodynamic fields in the present formulations are: density, velocity, temperature {\em and also}--following Grad's original idea--the symmetric and traceless pressure tensor $p_{ij}$ and the heat flux vector $\mathbf q^{k}$. An approximation scheme similar in spirit to one made by Grad in his original work is made. Once the hydrodynamics is derived it is used to discuss the nature of a simple one-dimensional heat conduction problem. It is shown that, not too far from equilibrium, the nonequilibrium pressure in this case only depends on the density, temperature and heat flux vector.