The Enskog Equation for Confined Elastic Hard Spheres

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

doi:10.1007/s10955-018-1971-7

Cited by 15 publications

(20 citation statements)

References 32 publications

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“…Next, two pressure parameters, associated with the separation of the confined walls and with their length, respectively, are defined in terms of the entropy. The expression obtained for the former is consistent with the wall theorem for systems of hard spheres or disks [18][19][20].…”

Section: Introductionsupporting

confidence: 79%

“…The configurational part is due to the confinement of the fluid between the two parallel plates. Its form is consistent with considering a local equilibrium approximation for the N particle distribution function [20][21][22], and also with the expression for the equilibrium entropy of a system of hard disks in the second virial coefficient approximation [19,23]. Our aim is to study the time evolution of H(t) in the confined system.…”

Section: The H Theorem and The Equilibrium Distribution Functionsupporting

confidence: 56%

“…The last result, relating the transversal pressure to the density of the fluid at the walls by means of the ideal gas equation of state, is nothing else but the wall theorem for the pressure tensor [18] applied to the present system. Actually, it has been proven recently that the theorem applies not only in equilibrium situations, but also holds in arbitrary nonequilibrium states [20]. Moreover, a similar wall theorem exists for the heat flux.…”

Section: The Entropy and The Pressure Parametersmentioning

confidence: 88%

See 2 more Smart Citations

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

Mayo,

Brey,

de Soria

et al. 2021

Preprint

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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.

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Section: Introductionsupporting

confidence: 79%

Section: The H Theorem and The Equilibrium Distribution Functionsupporting

confidence: 56%

Section: The Entropy and The Pressure Parametersmentioning

confidence: 88%

See 1 more Smart Citation

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

Mayo,

Brey,

de Soria

et al. 2021

Preprint

Self Cite

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“…and, taking into account that J z vanishes at z = σ/2 and z = h − σ/2 due to the hard walls [16,17], the above equation becomes…”

Section: The Kinetic Equation and The Conservation Lawmentioning

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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“…An analysis of the structure of the collisional transfer contributions leads to a result that generalizes the "contact theorem" of equilibrium statistical mechanics [25] to arbitrary non-equilibrium states and also to inelastic particles for extreme confinement. Actually, this is a particular case of a completely general property following from the dynamics itself of confined hard spheres [26].…”

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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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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The Enskog Equation for Confined Elastic Hard Spheres

Cited by 15 publications

References 32 publications

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

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

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

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

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