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

Brey, J. Javier; Buzón, V.; Soria, M. I. García de; Maynar, P.

doi:10.3390/e19020068

Cited by 4 publications

(3 citation statements)

References 27 publications

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“…The latter limits the possible collision angles, the allowed range being a function of the z coordinate of the considered target particle. The accuracy of the predicted density profile has been checked by means of molecular dynamics simulations [15,20]. Also, other theoretical predictions for the stationary state, like the entropy or some components of the pressure tensor, have been analyzed.…”

Section: The H Theorem and The Equilibrium Distributionmentioning

confidence: 99%

Boltzmann kinetic equation for a strongly confined gas of hard spheres

2017

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A Boltzmann-like kinetic equation for a quasi-two-dimensional gas of hard spheres is derived. The system is confined between two parallel hard plates separated a distance between one and two particle diameters. An entropy Lyapunov function for the equation is identified. In addition to the usual Boltzmann expression, it contains a contribution associated to the confinement of the particles. The steady properties of the system agree with equilibrium statistical mechanics results. Equations describing the energy transfer between the degrees of freedom parallel and perpendicular to the confining plates are obtained for some simple initial configurations. The theoretical predictions are compared with molecular dynamics simulation data and a good agreement is found.

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Section: The H Theorem and The Equilibrium Distributionmentioning

confidence: 99%

Boltzmann kinetic equation for a strongly confined gas of hard spheres

2017

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“…On the basis of the studies of bulk systems of inelastic hard spheres [10][11][12] and of the results for quasi-two-dimensional systems of elastic spheres [14,16], it is assumed that there is a special normal solution of the kinetic equation for which all the time dependence of the distribution function occurs through the granular temperature and all the space dependence takes place through the dependence of the number density on the z coordinate. Moreover, there is no macroscopic velocity flow.…”

Section: Boltzmann Equation and Inhomogeneous Cooling Statementioning

confidence: 99%

Inhomogeneous cooling state of a strongly confined granular gas at low density

2019

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The inhomogeneous cooling state describing the hydrodynamic behavior of a freely evolving granular gas strongly confined between two parallel plates is studied, using a Boltzmann kinetic equation derived recently. By extending the idea of the homogeneous cooling state, we propose a scaling distribution in which all the time dependence occurs through the granular temperature of the system, while there is a dependence on the distance to the confining walls through the density. It is obtained that the velocity distribution is not isotropic, and it has two different granular temperature parameters associated to the motion perpendicular and parallel to the confining plates, respectively, although their cooling rates are the same. Moreover, when approaching the inhomogeneous cooling state, energy is sometimes transferred from degrees of freedom with lower granular temperature to those with a higher one, contrary to what happens in molecular systems.The cooling rate and the two partial granular temperatures are calculated by means of a Gaussian approximation. The theoretical predictions are compared with molecular dynamics simulation results and a good agreement is found.PACS numbers:

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“…A kinetic theory of a confined quasi-two-dimensional gas of hard spheres is presented in the contribution by J.J. Brey, V. Buzón, M.I. García de Soria and P. Maynar [10]. In this paper, a model formulated for granular gases is reviewed and a Boltzmann kinetic equation for elastic hard spheres is introduced in order to obtain a detailed description of the dynamics of the system.…”

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confidence: 99%