Self-diffusion in freely evolving granular gases

Brey, J. Javier; Ruiz‐Montero, M. J.; Cubero, David; Garcia-Rojo, R.

doi:10.1063/1.870342

Cited by 102 publications

(121 citation statements)

References 21 publications

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“…Although the existence of these correlations restricts the range of validity of the Enskog equation, there is substantial evidence in the literature for the validity of the Enskog theory at moderate densities and higher restitution coefficients especially at the level of macroscopic properties (such as transport coefficients). In the case of molecular dynamics (MD) simulations, the Enskog theory compares quite well with simulations for the radial distribution function [53], the self-diffusion coefficient [57,58], the kinetic temperatures of a binary mixture in homogeneous cooling state [59], and the rheological properties of a mixture under simple shear flow [60,61]. The agreement between MD and Enskog equation is good for moderate densities (solid volume fraction up to 0.15) and even conditions of strong dissipation (restitution coefficients α ij > 0.7).…”

Section: Revised Enskog Kinetic Theorymentioning

confidence: 86%

Enskog theory for polydisperse granular mixtures. I. Navier-Stokes order transport

2007

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A hydrodynamic description for an s-component mixture of inelastic, smooth hard disks (two dimensions) or spheres (three dimensions) is derived based on the revised Enskog theory for the single-particle velocity distribution functions. In this first portion of the two-part series, the macroscopic balance equations for mass, momentum, and energy are derived. Constitutive equations are calculated from exact expressions for the fluxes by a Chapman-Enskog expansion carried out to first order in spatial gradients, thereby resulting in a Navier-Stokes order theory. Within this context of small gradients, the theory is applicable to a wide range of restitution coefficients and densities. The resulting integral-differential equations for the zeroth-and first-order approximations of the distribution functions are given in exact form. An approximate solution to these equations is required for practical purposes in order to cast the constitutive quantities as algebraic functions of the macroscopic variables; this task is described in the companion paper.

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Section: Revised Enskog Kinetic Theorymentioning

confidence: 86%

Enskog theory for polydisperse granular mixtures. I. Navier-Stokes order transport

2007

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“…(27) and (28). This N-particle simulation algorithm is known to be consistent with the Boltzmann equation, in the sense that it provides numerical solutions of the equation.…”

Section: Steady State Representation Of the Hcsmentioning

confidence: 99%

“…Also plotted is the theoretical prediction for D * (α) again in the first Sonine approximation [28],…”

Section: Self-diffusionmentioning

confidence: 99%

“…[28], the expression of the self-diffusion coefficient D of a dilute inelastic gas of hard particles has been derived from the Boltzmann-Lorentz equation by the Chapman-Enskog procedure. In Appendix B it is shown that the results reported in [28] can be expressed in the form…”

Section: Self-diffusionmentioning

confidence: 99%

“…under continuous cooling, in ref. [28], where the diffusion constant was calculated from the mean-square displacement by means of the (inelastic) Einstein relation and also from the linear response of the system to a density perturbation. The comparison between the numerical results obtained there and the theoretical prediction given by Eq.…”

Section: Self-diffusionmentioning

confidence: 99%

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Steady-state representation of the homogeneous cooling state of a granular gas

2004

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The properties of a dilute granular gas in the homogeneous cooling state are mapped to those of a stationary state by means of a change in the time scale that does not involve any internal property of the system. The new representation is closely related with a general property of the granular temperature in the long time limit. The physical and practical implications of the mapping are discussed. In particular, simulation results obtained by the direct simulation Monte Carlo method applied to the scaled dynamics are reported. This includes ensemble averages and also the velocity autocorrelation function, as well as the self-diffusion coefficient obtained from the latter by means of the Green-Kubo representation. In all cases, the obtained results are compared with theoretical predictions.

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Hydrodynamic Transport Coefficients of Granular Gases

Brey

Cubero

2001

Granular Gases

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Abstract. Some transport properties of granular gases are investigated. Starting from a kinetic theory level of description, the hydrodynamic transport equations to Navier-Stokes order are presented. The equations are derived by means of the Chapman-Enskog procedure. To test the existence of a normal solution and the possibility of a hydrodynamic description, the theoretical predictions are compared with numerical simulations of the underlying kinetic equation for small deviations around the reference homogeneous state. An excellent agreement is found for all the range of dissipation in collisions considered. Similar analysis is presented for self-diffusion and Brownian motion. In the former case, also Molecular Dynamics results are shown to agree with the theoretical predictions. Quantitative and also qualitative differences with the elastic limit are discussed.

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Self-diffusion in freely evolving granular gases

Cited by 102 publications

References 21 publications

Enskog theory for polydisperse granular mixtures. I. Navier-Stokes order transport

Enskog theory for polydisperse granular mixtures. I. Navier-Stokes order transport

Steady-state representation of the homogeneous cooling state of a granular gas

Hydrodynamic Transport Coefficients of Granular Gases

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