Dynamics of inelastically colliding spheres with Coulomb friction: Relaxation of translational and rotational energy

Herbst, Olaf; Huthmann, Martin; Zippelius, Annette

doi:10.1007/pl00010915

Cited by 69 publications

(74 citation statements)

References 12 publications

(19 reference statements)

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“…The stationary solution (3.13) represents the value of the temperature ratio in the HCS [28,[31][32][33]38]. In such a state the whole time dependence of the distribution function only occurs through the granular temperature T (t), so that the Boltzmann equation (2.12a) becomes 17) where, according to Eq.…”

Section: Homogeneous Cooling Statementioning

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: Homogeneous Cooling Statementioning

confidence: 99%

Transport coefficients of a granular gas of inelastic rough hard spheres

Kremer¹,

Santos

Garzó

2014

Phys. Rev. E

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“…[11,13,29,41,42]. Every simulation is equilibrated without driving with r = 1 and in the smooth surface limit r m t = −1.…”

Section: Simulationsmentioning

confidence: 99%

“…This is the full mean field theory. The calculation is similar to the one for 3D in [13] and is presented in appendix A. We obtain the following coefficients, to be inserted into Eqs.…”

Section: E Model E: Variable (Exact) Tangential Restitution Rt(γ)mentioning

confidence: 99%

“…a non-constant r t ) on different levels of refinement. The most accurate description parallels the three-dimensional (3D) results [13] for freely cooling systems. In addition, we present different levels of approximation to the full model and discuss their shortcomings in MF theory.…”

Section: Introductionmentioning

confidence: 99%

“…Many phenomenona are well reproduced by model granular media, where spheres are used instead of other, possibly more realistic shapes. In order to study such model systems, kinetic theories [4,5,6,7,8,9,10,11,12,13,14,15,16] and numerical simulations [4,15,17,18,19,20,21,22,23] have been applied for special boundary conditions and a variety of interesting experiments have been performed, see for example [24,25,26,27,28]. The dynamics of the system is usually assumed to be dominated by instantaneous two-particle collisions.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A driven two-dimensional granular gas with Coulomb friction

Herbst¹,

Cafiero²,

Zippelius³

et al. 2005

Physics of Fluids

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We study a homogeneously driven granular gas of inelastic hard particles with rough surfaces subject to Coulomb friction. The stationary state as well as the full dynamic evolution of the translational and rotational granular temperatures are investigated as a function of the three parameters of the friction model. Four levels of approximation to the (velocity-dependent) tangential restitution are introduced and used to calculate translational and rotational temperatures in a mean field theory. When comparing these theoretical results to numerical simulations of a randomly driven mono-layer of particles subject to Coulomb friction, we find that already the simplest model leads to qualitative agreement, but only the full Coulomb friction model is able to reproduce/predict the simulation results quantitatively for all magnitudes of friction. In addition, the theory predicts two relaxation times for the decay to the stationary state. One of them corresponds to the equilibration between the translational and rotational degrees of freedom. The other one, which is slower in most cases, is the inverse of the common relaxation rate of translational and rotational temperatures.

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Weakly Frictional Granular Gases

Goldhirsch

Noskowicz

Bar-Lev

Traffic and Granular Flow ’03

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Dynamics of inelastically colliding spheres with Coulomb friction: Relaxation of translational and rotational energy

Cited by 69 publications

References 12 publications

Transport coefficients of a granular gas of inelastic rough hard spheres

Transport coefficients of a granular gas of inelastic rough hard spheres

A driven two-dimensional granular gas with Coulomb friction

Weakly Frictional Granular Gases

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