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

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

doi:10.1103/physreve.100.052901

Cited by 4 publications

(9 citation statements)

References 26 publications

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“…Let us mention that the inhomogeneity of the density field in the direction perpendicular to the confining plates, and the quantitative accuracy of the theoretical predictions based on the Boltzmann equation have been verified both for elastic [21] and inelastic [24] hard spheres by means of molecular dynamics simulations.…”

Section: The Inhomogeneous Cooling Statementioning

confidence: 79%

“…A special idealized state of the confined system we are considering here is that of inhomogeneous cooling state (ICS), for which all the time dependence of the macroscopic dynamics occurs through the time dependence of the granular temperature, while there is a spatial dependence through the density, that is a function of the distance to the confining walls [24]. The ICS occurs in freely evolving systems, i.e.…”

Section: The Inhomogeneous Cooling Statementioning

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%

“…On the other hand, as in the equilibrium state, the density is not uniform along the direction perpendicular to the plates. For this reasons, this state has been referred to as the inhomogeneous cooling state [24] In this work, balance equations for the density, momentum, and energy are derived from the Boltzmann equation for the confined system. This is done in the more general case of inelastic hard spheres, but the results for the elastic case are easily obtained by taking the appropriate limit.…”

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: The Inhomogeneous Cooling Statementioning

confidence: 79%

Section: The Inhomogeneous Cooling Statementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Brey¹,

Maynar²,

Soria³

2020

J. Stat. Mech.

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“…For this reason, modified Boltzmann kinetic equations for this special quasi-two-dimensional confinement have been proposed 30,81 and the inhomogeneous cooling state has been widely analyzed. 29,82,83 On the other hand, there are still some interesting open problems in the ∆-model. Among them, the evaluation of the heat flux transport coefficients by considering the second Sonine approximation is a challenging issue.…”

Section: Discussionmentioning

confidence: 99%

Navier–Stokes transport coefficients for a model of a confined quasi-two-dimensional granular binary mixture

2021

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The Navier-Stokes transport coefficients for a model of a confined quasi-two-dimensional granular binary mixture of inelastic hard spheres are determined from the Boltzmann kinetic equation. A normal or hydrodynamic solution to the Boltzmann equation is obtained via the Chapman-Enskog method for states near the local version of the homogeneous time-dependent state. The mass, momentum, and heat fluxes are determined to first order in the spatial gradients of the hydrodynamic fields, and the associated transport coefficients are identified. They are given in terms of the solutions of a set of coupled linear integral equations. In addition, in contrast to previous results obtained for low-density granular mixtures, there are also nonzero contributions to the first-order approximations to the partial temperatures T(1) i and the cooling rate ζ (1) . Explicit forms for the diffusion transport coefficients, the shear viscosity coefficient, and the quantities T(1) i and ζ (1) are obtained by assuming steady-state conditions and by considering the leading terms in a Sonine polynomial expansion. The above transport coefficients are given in terms of the coefficients of restitution, concentration, and the masses and diameters of the components of the mixture. The results apply in principle for arbitrary degree of inelasticity and are not limited to specific values of concentration, mass and/or size ratios. As a simple application of these results, the violation of the Onsager reciprocal relations for a confined granular mixture is quantified in terms of the parameter space of the problem.

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Granular dynamics and gravity

Sánchez

2020

Soft Matter

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

Cited by 4 publications

References 26 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

Navier–Stokes transport coefficients for a model of a confined quasi-two-dimensional granular binary mixture

Granular dynamics and gravity

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