Kinetic theory of a confined quasi-one-dimensional gas of hard disks

Abstract

A dilute gas of hard disks confined between two straight parallel lines is considered. The distance between the two boundaries is in between one and two particle diameters, so that the system is quasi-one-dimensional. A Boltzmann-like kinetic equation, that takes into account the limitation in the possible scattering angles, is derived. It is shown that the equation verifies an $H$ theorem implying a monotonic approach to equilibrium. The implications of this result are discussed, and the equilibrium properties are derived. Closed equations describing how the kinetic energy is transferred between the degrees of freedom parallel and perpendicular to the boundaries are derived for states that are homogeneous along the direction of the boundaries. The theoretical predictions agree with results obtained by means of molecular dynamics simulations.

References in corpus (10)

• Nanofluidics, from bulk to interfaces
• Kinetic Equations for Diffusion in the Presence of Entropic Barriers
• Hydrodynamic modes in a confined granular fluid
• Green-Kubo Expressions for a Granular Gas
• The homogeneous steady state of a confined granular gas
• Stability analysis of the homogeneous hydrodynamics of a model for a confined granular gas
• Shear viscosity of a model for confined granular media
• Kinetic Equation and Non-equilibrium Entropy for a Quasi-two-dimensional Gas
• Understanding the instability of a vibrated granular monolayer
• The Enskog equation for confined elastic hard spheres

Cited by in corpus (5)

• Equation of state of hard-disk fluids under single-file confinement
• Exact equilibrium properties of square-well and square-shoulder disks in single-file confinement
• Diffusion of impurities in a moderately dense confined granular gas
• Confined granular gases under the influence of vibrating walls
• Transport properties in a model of confined granular mixtures at moderate densities