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

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.

:9 pages, 1 figure, This will appear in J. Stat. Phys. with minor corrections and corresponds to Ref[9] of cond-mat/0507102

References in corpus (2)

• Kinetic Theory of a Dilute Gas System under Steady Heat Conduction
• Extended hydrodynamics from Enskog's equation: The bidimensional case

Cited by in corpus (1)

• Pressure and entropy of hard spheres in the weakly nonequilibrium heat-conduction steady state