Homogeneous Free Cooling State in Binary Granular Fluids of Inelastic Rough Hard Spheres

Santos, Andrés

doi:10.1063/1.3562637

Cited by 12 publications

(13 citation statements)

References 8 publications

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“…This singular effect of a 20 is analogous to the one observed for the ratio ͗͑c · w͒ 2 ͘ / ͗c 2 w 2 ͘, 32,33 as well as in the case of the translational/translational temperature ratio in mixtures. 34,35 The explanation of this interesting phenomenon is similar in all these situations. While for smooth particles ͑␤ =−1͒ the rotational temperature is totally isolated from the translational one ͑so that the dotted arrows in Fig.…”

Section: ͑45͒mentioning

confidence: 74%

“…The equipartition terms, which exist even when energy is conserved by collisions ͑␣ = 1 and ␤ = Ϯ 1͒, tend to make temperatures equal. 35,37 Therefore, they can be positive or negative depending essentially on the sign of the temperature difference T tr − T rot . On the other hand, the genuine cooling terms reflect the collisional energy dissipation and thus they are positive if ␣ Ͻ 1 and/or ͉␤͉ Ͻ 1, vanishing otherwise.…”

Section: ͑11͒mentioning

confidence: 98%

“…They can be decomposed into two classes of terms: 35 equipartition rates and cooling rates ͑see Fig. 1͒.…”

Section: ͑11͒mentioning

confidence: 99%

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Sonine approximation for collisional moments of granular gases of inelastic rough spheres

2011

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We consider a dilute granular gas of hard spheres colliding inelastically with coefficients of normal and tangential restitution ␣ and ␤, respectively. The basic quantities characterizing the distribution function f͑v , ͒ of linear ͑v͒ and angular ͑͒ velocities are the second-degree moments defining the translational ͑T tr ͒ and rotational ͑T rot ͒ temperatures. The deviation of f from the Maxwellian distribution parameterized by T tr and T rot can be measured by the cumulants associated with the fourth-degree velocity moments. The main objective of this paper is the evaluation of the collisional rates of change of these second-and fourth-degree moments by means of a Sonine approximation. The results are subsequently applied to the computation of the temperature ratio T rot / T tr and the cumulants of two paradigmatic states: the homogeneous cooling state and the homogeneous steady state driven by a white-noise stochastic thermostat. It is found in both cases that the Maxwellian approximation for the temperature ratio does not deviate much from the Sonine prediction. On the other hand, non-Maxwellian properties measured by the cumulants cannot be ignored, especially in the homogeneous cooling state for medium and small roughness. In that state, moreover, the cumulant directly related to the translational velocity differs in the quasi-smooth limit ␤ → −1 from that of pure smooth spheres ͑␤ =−1͒. This singular behavior is directly related to the unsteady character of the homogeneous cooling state and thus it is absent in the stochastic thermostat case.

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Section: ͑45͒mentioning

confidence: 74%

Section: ͑11͒mentioning

confidence: 98%

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Sonine approximation for collisional moments of granular gases of inelastic rough spheres

2011

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“…After a certain transient period, the gas reaches a long-time asymptotic regime where all temperatures decay with a common rate [3,46,59,61], so that the temperature ratios are obtained from the conditions ξ tr 1 = ξ tr 2 = · · · = ξ rot 1 = ξ rot 2 = · · · . Our goal now is to compare those ratios in the cases of hard disks and hard spheres.…”

Section: Undriven Gas: Homogeneous Cooling Statementioning

confidence: 99%

Driven and undriven states of multicomponent granular gases of inelastic and rough hard disks or spheres

Megías

Santos

2019

Granular Matter

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Starting from a recent derivation of the energy production rates in terms of the number of translational and rotational degrees of freedom, a comparative study on different granular temperatures in gas mixtures of inelastic and rough disks or spheres is carried out. Both the homogeneous freely cooling state and the state driven by a stochastic thermostat are considered. It is found that the relaxation number of collisions per particle is generally smaller for disks than for spheres, the mean angular velocity relaxing more rapidly than the temperature ratios. In the asymptotic regime of the undriven system, the rotational-translational nonequipartition is stronger in disks than in spheres, while it is hardly dependent on the class of particles in the driven system. On the other hand, the degree of component-component nonequipartition is higher for spheres than for disks, both for driven and undriven systems. A study of the mimicry effect (whereby a multicomponent gas mimics the rotational-translational temperature ratio of a monocomponent gas) is also undertaken.

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“…In particular, there exists a vast literature about polydisperse systems of smooth disks or spheres [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27], as well as about friction (or roughness) in monodisperse systems [10,. On the other hand, much fewer works have dealt with multicomponent gases of rough spheres [66][67][68][69][70][71][72]. This class of systems is especially relevant because of an inherent breakdown of energy equipartition, even in homogeneous and isotropic states (driven or undriven), as characterized by independent translational (T tr i ) and rotational (T rot i ) temperatures associated with each component i.…”

Section: Introductionmentioning

confidence: 99%

Interplay between polydispersity, inelasticity, and roughness in the freely cooling regime of hard-disk granular gases

Santos

2018

Phys. Rev. E

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A polydisperse granular gas made of inelastic and rough hard disks is considered. Focus is laid on the kinetic-theory derivation of the partial energy production rates and the total cooling rate as functions of the partial densities and temperatures (both translational and rotational) and of the parameters of the mixture (masses, diameters, moments of inertia, and mutual coefficients of normal and tangential restitution). The results are applied to the homogeneous cooling state of the system and the associated nonequipartition of energy among the different components and degrees of freedom. It is found that disks typically present a stronger rotational-translational nonequipartition but a weaker component-component nonequipartition than spheres. A noteworthy "mimicry" effect is unveiled, according to which a polydisperse gas of disks having common values of the coefficient of restitution and of the reduced moment of inertia can be made indistinguishable from a monodisperse gas in what concerns the degree of rotational-translational energy nonequipartition. This effect requires the mass of a disk of component i to be approximately proportional to 2σ_{i}+〈σ〉, where σ_{i} is the diameter of the disk and 〈σ〉 is the mean diameter.

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Homogeneous Free Cooling State in Binary Granular Fluids of Inelastic Rough Hard Spheres

Cited by 12 publications

References 8 publications

Sonine approximation for collisional moments of granular gases of inelastic rough spheres

Sonine approximation for collisional moments of granular gases of inelastic rough spheres

Driven and undriven states of multicomponent granular gases of inelastic and rough hard disks or spheres

Interplay between polydispersity, inelasticity, and roughness in the freely cooling regime of hard-disk granular gases

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