# The Enskog Equation for Confined Elastic Hard Spheres

The Enskog Equation for Confined Elastic Hard Spheres A kinetic equation for a system of elastic hard spheres or disks confined by a hard wall of arbitrary shape is derived. It is a generalization of the modified Enskog equation in which the effects of the confinement are taken into account and it is supposed to be valid up to moderate densities. From the equation, balance equations for the hydrodynamic fields are derived, identifying the collisional transfer contributions to the pressure tensor and heat flux. A Lyapunov functional, $${\mathcal {H}}[f]$$ H [ f ] , is identified. For any solution of the kinetic equation, $${\mathcal {H}}$$ H decays monotonically in time until the system reaches the inhomogeneous equilibrium distribution, that is a Maxwellian distribution with a density field consistent with equilibrium statistical mechanics. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Statistical Physics Springer Journals

# The Enskog Equation for Confined Elastic Hard Spheres

, Volume 170 (5) – Jan 30, 2018
20 pages

/lp/springer_journal/the-enskog-equation-for-confined-elastic-hard-spheres-Em0P787NEZ
Publisher
Springer US
Subject
Physics; Statistical Physics and Dynamical Systems; Theoretical, Mathematical and Computational Physics; Physical Chemistry; Quantum Physics
ISSN
0022-4715
eISSN
1572-9613
D.O.I.
10.1007/s10955-018-1971-7
Publisher site
See Article on Publisher Site

### Abstract

A kinetic equation for a system of elastic hard spheres or disks confined by a hard wall of arbitrary shape is derived. It is a generalization of the modified Enskog equation in which the effects of the confinement are taken into account and it is supposed to be valid up to moderate densities. From the equation, balance equations for the hydrodynamic fields are derived, identifying the collisional transfer contributions to the pressure tensor and heat flux. A Lyapunov functional, $${\mathcal {H}}[f]$$ H [ f ] , is identified. For any solution of the kinetic equation, $${\mathcal {H}}$$ H decays monotonically in time until the system reaches the inhomogeneous equilibrium distribution, that is a Maxwellian distribution with a density field consistent with equilibrium statistical mechanics.

### Journal

Journal of Statistical PhysicsSpringer Journals

Published: Jan 30, 2018

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