Inherent rheology of a granular fluid in uniform shear flow

Santos, Andrés; Garzó, Vicente; Dufty, James W.

doi:10.1103/physreve.69.061303

Cited by 109 publications

(207 citation statements)

References 34 publications

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“…Specifically, this is even more necessary if γ ≥ 0 (and this happens when the viscous heating dominates over collisional cooling [32]), since in this case the Knudsen number is always greater than the one for γ < 0 [42]. Such a description of the Couette flow beyond the NS domain was carried out in Ref.…”

Section: Introductionmentioning

confidence: 99%

“…The accuracy of this latter approach has been confirmed by computer simulations in the cases of the diffusion [28,29] and shear viscosity [30,31] coefficients. On the other hand, the practical applicability of the NS equations is limited to small spatial gradients, while many steady granular flows do not fulfill in general this condition, due to the coupling between inelasticity and gradients [1,32].…”

Section: Introductionmentioning

confidence: 99%

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Impurity in a granular gas under nonlinear Couette flow

Reyes¹,

Garzó²,

Santos³

2008

J. Stat. Mech.

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We study in this work the transport properties of an impurity immersed in a granular gas under stationary nonlinear Couette flow. The starting point is a kinetic model for low-density granular mixtures recently proposed by the authors [Vega Reyes F et al. 2007 Phys. Rev. E 75 061306]. Two routes have been considered. First, a hydrodynamic or normal solution is found by exploiting a formal mapping between the kinetic equations for the gas particles and for the impurity. We show that the transport properties of the impurity are characterized by the ratio between the temperatures of the impurity and gas particles and by five generalized transport coefficients: three related to the momentum flux (a nonlinear shear viscosity and two normal stress differences) and two related to the heat flux (a nonlinear thermal conductivity and a cross coefficient measuring a component of the heat flux orthogonal to the thermal gradient). Second, by means of a Monte Carlo simulation method we numerically solve the kinetic equations and show that our hydrodynamic solution is valid in the bulk of the fluid when realistic boundary conditions are used. Furthermore, the hydrodynamic solution applies to arbitrarily (inside the continuum regime) large values of the shear rate, of the inelasticity, and of the rest of parameters of the system. Preliminary simulation results of the true Boltzmann description show the reliability of the nonlinear hydrodynamic solution of the kinetic model. This shows again the validity of a hydrodynamic description for granular flows, even under extreme conditions, beyond the Navier-Stokes domain.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Impurity in a granular gas under nonlinear Couette flow

Reyes¹,

Garzó²,

Santos³

2008

J. Stat. Mech.

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“…This occurs in many important applications for granular fluids [40]. In the limiting case where the low-degree gradients can be controlled by boundary or initial conditions and made small, a further Taylor series expansion can be given…”

Section: Concept Of a Normal Solution And Hydrodynamicsmentioning

confidence: 99%

“…For ordinary (elastic) gases this can be controlled by the initial or boundary conditions. However, in the case of granular fluids the situation is more complicated since in some cases (e.g., steady states such as the simple shear flow problem [40]) the boundary conditions imply a relationship between dissipation and gradients so that both cannot be chosen independently. In these cases, the Navier-Stokes approximation only holds for nearly elastic particles [40].…”

mentioning

confidence: 99%

“…However, in the case of granular fluids the situation is more complicated since in some cases (e.g., steady states such as the simple shear flow problem [40]) the boundary conditions imply a relationship between dissipation and gradients so that both cannot be chosen independently. In these cases, the Navier-Stokes approximation only holds for nearly elastic particles [40]. However, the transport coefficients characterizing the Navier-Stokes hydrodynamic equations are nonlinear functions of the coefficients of restitution, regardless the applicability of those equations.…”

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confidence: 99%

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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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Granular Flows

Dufty

2009

Encyclopedia of Complexity and Systems Science Series

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Inherent rheology of a granular fluid in uniform shear flow

Cited by 109 publications

References 34 publications

Impurity in a granular gas under nonlinear Couette flow

Impurity in a granular gas under nonlinear Couette flow

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

Granular Flows

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