Linear hydrodynamics for driven granular gases

Soria, M. I. García de; Maynar, P.; Trizac, Emmanuel

doi:10.1103/physreve.87.022201

Cited by 28 publications

(43 citation statements)

References 45 publications

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“…Given that most of the experimental setups consider granular systems confined in two dimensions, we intend to determine the NSF transport coefficients for systems of inelastic rough hard disks by using a methodology similar to the one followed here. Moreover, the structure of the collisional frequencies derived in the Appendix can be exploited to obtain the NSF transport coefficients of driven granular gases, in analogy to the case of smooth spheres [63][64][65]. Finally, we will test the transport coefficients obtained from the first Sonine approximation against DSMC numerical solutions of the Boltzmann equation by methods similar to those employed for smooth spheres [63,[66][67][68][69][70][71].…”

Section: Discussionmentioning

confidence: 99%

Transport coefficients of a granular gas of inelastic rough hard spheres

Kremer¹,

Santos

Garzó

2014

Phys. Rev. E

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The Boltzmann equation for inelastic and rough hard spheres is considered as a model of a dilute granular gas. In this model, the collisions are characterized by constant coefficients of normal and tangential restitution and hence the translational and rotational degrees of freedom are coupled. A normal solution to the Boltzmann equation is obtained by means of the Chapman-Enskog method for states near the homogeneous cooling state. The analysis is carried out to first order in the spatial gradients of the number density, the flow velocity, and the granular temperature. The constitutive equations for the momentum and heat fluxes and for the cooling rate are derived, and the associated transport coefficients are expressed in terms of the solutions of linear integral equations. For practical purposes, a first Sonine approximation is used to obtain explicit expressions of the transport coefficients as nonlinear functions of both coefficients of restitution and the moment of inertia. Known results for purely smooth inelastic spheres and perfectly elastic and rough spheres are recovered in the appropriate limits.

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Section: Discussionmentioning

confidence: 99%

Transport coefficients of a granular gas of inelastic rough hard spheres

Kremer¹,

Santos

Garzó

2014

Phys. Rev. E

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“…In the stochastic model, the evolution equation for the temperature in the hydrodynamic regime and for d = 2 is [48] …”

Section: Appendix B: the Kovacs-like Effect In The Stochastic Thermosmentioning

confidence: 99%

Memory effects in the relaxation of a confined granular gas

et al. 2014

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The accuracy of a model to describe the horizontal dynamics of a confined quasi-two-dimensional system of inelastic hard spheres is discussed by comparing its predictions for the relaxation of the temperature in a homogenous system with molecular dynamics simulation results for the original system. A reasonably good agreement is found. Next the model is used to investigate the peculiarities of the nonlinear evolution of the temperature when the parameter controlling the energy injection is instantaneously changed while the system was relaxing. This can be considered as a nonequilibrium generalization of the Kovacs effect. It is shown that, in the low-density limit, the effect can be accurately described by using a simple kinetic theory based on the first Sonine approximation for the one-particle distribution function. Some possible experimental implications are indicated.

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“…Moreover, the dependence of the viscosity on the coefficient of normal restitution is clearly nonlinear, again in agreement with the simulations for dilute systems. It is worth to remind that in (non-confined) dilute granular gases of smooth inelastic hard spheres [5,6] the viscosity decreases as the coefficient of normal restitution increases, and that in a stochastic thermostat model it has been found to be a non-monotonic function of the inelasticity [31,32]. On the other hand, the dependence on the restitution coefficients of the two transport coefficients associated with the heat flux is not monotonic in the homogeneous steady state of the model discussed here, exhibiting both a minimum.…”

Section: Transport Coefficients In the Homogeneous Steady Statementioning

confidence: 99%

Hydrodynamics for a model of a confined quasi-two-dimensional granular gas

et al. 2015

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The hydrodynamic equations for a model of a confined quasi-two-dimensional gas of smooth inelastic hard spheres are derived from the Boltzmann equation for the model, using a generalization of the Chapman-Enskog method. The heat and momentum fluxes are calculated to Navier-Stokes order, and the associated transport coefficients are explicitly determined as functions of the coefficient of normal restitution and the velocity parameter involved in the definition of the model. Also an Euler transport term contributing to the energy transport equation is considered. This term arises from the gradient expansion of the rate of change of the temperature due to the inelasticity of collisions, and vanishes for elastic systems. The hydrodynamic equations are particularized for the relevant case of a system in the homogeneous steady state. The relationship with previous works is analyzed.

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Linear hydrodynamics for driven granular gases

Cited by 28 publications

References 45 publications

Transport coefficients of a granular gas of inelastic rough hard spheres

Transport coefficients of a granular gas of inelastic rough hard spheres

Memory effects in the relaxation of a confined granular gas

Hydrodynamics for a model of a confined quasi-two-dimensional granular gas

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