Kinetic equation and nonequilibrium entropy for a quasi-two-dimensional gas

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

doi:10.1103/physreve.94.040103

Cited by 14 publications

(43 citation statements)

References 28 publications

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“…The Boltzmann equation, describing the time evolution of the one-particle distribution function, f (r, v, t) for a dilute gas of inelastic hard spheres of mass m and diameter σ, confined between two large hard parallel plates separated a distance h smaller than twice the diameter of a particle, σ < h < 2σ, has the form [21][22][23] ∂f ∂t…”

Section: Description Of the System And Balance Equationsmentioning

confidence: 99%

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Kinetic model for a confined quasi-two-dimensional gas of inelastic hard spheres

Brey¹,

Maynar²,

Soria³

2020

J. Stat. Mech.

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The local balance equations for the density, momentum, and energy of a dilute gas of elastic or inelastic hard spheres, strongly confined between two parallel hard plates are obtained. The starting point is a Boltzmann-like kinetic equation, recently derived for this system. As a consequence of the confinement, the pressure tensor and the heat flux contain, in addition to the terms associated to the motion of the particles, collisional transfer contributions, similar to those that appear beyond the dilute limit. The complexity of these terms, and of the kinetic equation itself, compromise the potential of the equation to describe the rich phenomenology observed in this kind of systems.For this reason, a simpler model equation based on the Boltzmann equation is proposed. The model is formulated to keep the main properties of the underlying equation, and it is expected to provide relevant information in more general states than the original equation. As an illustration, the solution describing a macroscopic state with uniform temperature, but a density gradient perpendicular to the plates is considered. This is the equilibrium state for an elastic system, and the inhomogeneous cooling state for the case of inelastic hard spheres. The results are in good agreement with previous results obtained directly from the Boltzmann equation.PACS numbers:

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Section: Description Of the System And Balance Equationsmentioning

confidence: 99%

“…The equation can be applied, to both elastic [21,22] and inelastic particles [23,24]. The only difference is in the collision rule used to determine the change of the velocities when two particles collide.…”

Section: Introductionmentioning

confidence: 99%

Kinetic model for a confined quasi-two-dimensional gas of inelastic hard spheres

Brey¹,

Maynar²,

Soria³

2020

J. Stat. Mech.

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“…By using a slight modification of the standard way of deriving the usual (bulk) Boltzmann and Enskog kinetic equations [22], it has been shown that the one particle distribution function f (r, v, t) of the confined system of hard spheres in the low density limit satisfies the equation [23] …”

Section: Back To the Origins: Boltzmann-enskog Kinetic Equationmentioning

confidence: 99%

“…It is then proven [23] that in a system with elastic walls, H(t) is bounded from below, and that ∂ t H(t) ≤ 0, the equal sign holding only if…”

Section: Back To the Origins: Boltzmann-enskog Kinetic Equationmentioning

confidence: 99%

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

Brey

Buzón

Soria

et al. 2017

Entropy

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Abstract: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.

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“…The remaining of this paper is organized as follows. In the next section the Boltzmann equation for a strongly confined gas of hard spheres [13,14] is shortly reviewed and extended to the case of smooth inelastic particles. Also, the inhomogeneous cooling state (ICS) is introduced and the condition of isotropic cooling rate is deduced.…”

Section: Introductionmentioning

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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Kinetic equation and nonequilibrium entropy for a quasi-two-dimensional gas

Cited by 14 publications

References 28 publications

Kinetic model for a confined quasi-two-dimensional gas of inelastic hard spheres

Kinetic model for a confined quasi-two-dimensional gas of inelastic hard spheres

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

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

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