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Open AccessArticle

Kinetic Theory of a Confined Quasi-Two-Dimensional Gas of Hard Spheres

Física Teórica, Universidad de Sevilla, Apartado de Correos 1065, 41080 Sevilla, Spain
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Academic Editors: Giancarlo Franzese, Ivan Latella, Miguel Rubi, Antonio M. Scarfone and Kevin H. Knuth
Entropy 2017, 19(2), 68; https://doi.org/10.3390/e19020068
Received: 25 October 2016 / Revised: 14 December 2016 / Accepted: 10 February 2017 / Published: 14 February 2017
(This article belongs to the Special Issue Nonequilibrium Phenomena in Confined Systems)
The dynamics of a system of hard spheres enclosed between two parallel plates separated a distance smaller than two particle diameters is described at the level of kinetic theory. The interest focuses on the behavior of the quasi-two-dimensional fluid seen when looking at the system from above or below. In the first part, a collisional model for the effective two-dimensional dynamics is analyzed. Although it is able to describe quite well the homogeneous evolution observed in the experiments, it is shown that it fails to predict the existence of non-equilibrium phase transitions, and in particular, the bimodal regime exhibited by the real system. A critical revision analysis of the model is presented , and as a starting point to get a more accurate description, the Boltzmann equation for the quasi-two-dimensional gas has been derived. In the elastic case, the solutions of the equation verify an H-theorem implying a monotonic tendency to a non-uniform steady state. As an example of application of the kinetic equation, here the evolution equations for the vertical and horizontal temperatures of the system are derived in the homogeneous approximation, and the results compared with molecular dynamics simulation results. View Full-Text
Keywords: kinetic theory; confined gases; H theorem kinetic theory; confined gases; H theorem
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Brey, J.J.; Buzón, V.; García de Soria, M.I.; Maynar, P. Kinetic Theory of a Confined Quasi-Two-Dimensional Gas of Hard Spheres. Entropy 2017, 19, 68.

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