The Enskog equation for confined elastic hard spheres

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, $\mathcal{H}[f]$, is identified. For any solution of the kinetic equation, $\mathcal{H}$ decays monotonically in time until the system reaches the inhomogeneous equilibrium distribution, that is a Maxwellian distribution with a the density field consistent with equilibrium statistical mechanics.

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• The dynamics of thin vibrated granular layers
• Fluctuations and Criticality of a Granular Solid-Liquid-like Phase Transition
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Cited by in corpus (6)

• Homogeneous dynamics in a vibrated granular monolayer
• Kinetic theory of a confined quasi-one-dimensional gas of hard disks
• Confined granular gases under the influence of vibrating walls
• Self-diffusion in a quasi-two dimensional gas of hard spheres
• Mesoscopic description of the adiabatic piston: kinetic equations and $\mathcal{H}$-theorem
• Kinetic model for a confined quasi-two-dimensional gas of inelastic hard spheres