Kinetic Equation and Non-equilibrium Entropy for a Quasi-two-dimensional Gas

Abstract

A kinetic equation for a dilute gas of hard spheres confined between two parallel plates separated a distance smaller than two particle dimeters is derived. It is a Boltzmann-like equation, which incorporates the effect of the confinement on the particle collisions. A function $S(t)$ is constructed by adding to the Boltzmann expression a confinement contribution. Then it is shown that for the solutions of the kinetic equation, $S(t)$ increases monotonically in time, until the system reaches a stationary inhomogeneous state, when $S$ becomes the equilibrium entropy of the confined system as derived from equilibrium statistical mechanics. From the entropy, other equilibrium properties are obtained, and Molecular Dynamics simulations are used to verify some of the theoretical predictions.

References in corpus (9)

• Caging dynamics in a granular fluid
• Glass Transition in Confined Geometry
• The dynamics of thin vibrated granular layers
• Fluctuations and Criticality of a Granular Solid-Liquid-like Phase Transition
• Sudden chain energy transfer events in vibrated granular media
• Fluids in Extreme Confinement
• Hydrodynamic modes in a confined granular fluid
• Hydrodynamics for a model of a confined quasi-two-dimensional granular gas
• The homogeneous steady state of a confined granular gas

Cited by in corpus (9)

• The Enskog equation for confined elastic hard spheres
• Homogeneous dynamics in a vibrated granular monolayer
• Kinetic theory of a confined quasi-one-dimensional gas of hard disks
• Navier--Stokes transport coefficients for a model of a confined quasi-two-dimensional granular binary mixture
• Dynamics of an inelastic tagged particle under strong confinement
• Confined granular gases under the influence of vibrating walls
• Inhomogeneous cooling state of a strongly confined granular gas at low density
• Self-diffusion in a quasi-two dimensional gas of hard spheres
• Kinetic model for a confined quasi-two-dimensional gas of inelastic hard spheres