Boltzmann kinetic equation for a strongly confined gas of hard spheres

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

doi:10.1103/physreve.96.042117

Cited by 14 publications

(39 citation statements)

References 20 publications

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“…When considering the expressions of the collisional transfer contributions to the pressure tensor and to the heat flow, Eqs. (22) and (23), it must be kept in mind that that, as already indicated, for physical initial conditions, the one-particle velocity distribution, f (r, v, t) vanishes for positions outside the system, i.e. for both z < σ/2 and z > h − σ/2.…”

Section: Description Of the System And Balance Equationsmentioning

confidence: 93%

“…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%

“…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%

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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: 93%

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 distribution function of labeled particles obeys a modified Boltzmann-Lorentz (BL) equation that follows by reproducing step by step the arguments used in Ref. [6]. Taking into account that labeled particles collide with labeled as well as unlabeled particles and that the total system is at equilibrium, it is readily obtained…”

Section: The Kinetic Equation and The Conservation Lawmentioning

confidence: 99%

“…For this reason, the simplest model of confining walls is considered: elastic hard walls. For this system, a Boltzmann kinetic equation has been derived [5,6]. The equation obeys a modified Htheorem implying the approach to the equilibrium state from any arbitrary initial condition.…”

Section: Introductionmentioning

confidence: 99%

Self-diffusion in a quasi-two-dimensional gas of hard spheres

Brey¹,

Soria²,

Maynar³

2020

Phys. Rev. E

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A quasi-two-dimensional system of hard spheres strongly confined between two parallel plates is considered. The attention is focussed on the macroscopic self-diffusion process observed when the system is looked from above or from below. The transport equation, and the associated selfdiffusion coefficient, are derived from a Boltzmann-Lorentz kinetic equation, valid in the dilute limit. Since the equilibrium state of the system is inhomogeneous, this requires the use of a modified Chapman-Enskog expansion that distinguishes between equilibrium and non-equilibrium gradients of the density of labelled particles. The self-diffusion coefficient is obtained as a function of the separation between the two confining plates. The theoretical predictions are compared with molecular dynamics simulation results and a good agreement is found. PACS numbers:

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The Enskog Equation for Confined Elastic Hard Spheres

2018

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A kinetic equation for a system of elastic hard spheres or disks confined by a hard wall of arbitrary shape is derived. It is a generalization of the modified Enskog equation in which the effects of the confinement are taken into account and it is supposed to be valid up to moderate densities. From the equation, balance equations for the hydrodynamic fields are derived, identifying the collisional transfer contributions to the pressure tensor and heat flux. A Lyapunov functional, H[f ], is identified. For any solution of the kinetic equation, H decays monotonically in time until the system reaches the inhomogeneous equilibrium distribution, that is a Maxwellian distribution with a the density field consistent with equilibrium statistical mechanics.

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Boltzmann kinetic equation for a strongly confined gas of hard spheres

Cited by 14 publications

References 20 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

Self-diffusion in a quasi-two-dimensional gas of hard spheres

The Enskog Equation for Confined Elastic Hard Spheres

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