Nearly Smooth Granular Gases

Goldhirsch, I.; Noskowicz, S. H.; Bar-Lev, O.

doi:10.1103/physrevlett.95.068002

Cited by 62 publications

(60 citation statements)

References 21 publications

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“…Next, multiplication of Eq. (4.20) by V i V j − 1 3 δ ij V 2 and integration over velocity yields 20) where…”

Section: Navier-stokes-fourier Transport Coefficients a Exact Formentioning

confidence: 99%

“…Previous attempts have been restricted to nearly elastic collisions (α 1) and either nearly smooth particles (β −1) [17,20,21] or nearly perfectly rough particles (β 1) [17,24]. The goal of this paper is to uncover the whole range of values of the two coefficients of restitution α and β and derive explicit expressions for the NSF transport coefficients of a dilute granular gas beyond the above limiting situations.…”

Section: Introductionmentioning

confidence: 99%

“…For nearly smooth spheres (β −1), some authors [17,20,21] have chosen (in addition to n and u) the two partial contributions T t and …”

Section: Introductionmentioning

confidence: 99%

“…This parameter ranges from −1 (perfectly smooth spheres) to 1 (perfectly rough spheres). A more sophisticated model incorporates the Coulomb friction coefficient as a third collision constant, so that collisions become sliding beyond a certain impact parameter [18][19][20][21]. On the other hand, this three-parameter model significantly complicates the kinetic description, while the simpler two-parameter (α, β) model captures the essential features of granular flows when particle rotations are relevant.…”

Section: Introductionmentioning

confidence: 99%

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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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“…Next, multiplication of Eq. (4.20) by V i V j − 1 3 δ ij V 2 and integration over velocity yields 20) where…”

Section: Navier-stokes-fourier Transport Coefficients a Exact Formentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…For nearly smooth spheres (β −1), some authors [17,20,21] have chosen (in addition to n and u) the two partial contributions T t and …”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Transport coefficients of a granular gas of inelastic rough hard spheres

Kremer¹,

Santos

Garzó

2014

Phys. Rev. E

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“…Obviously, the model can be made closer to reality by introducing extra ingredients. In particular, polydispersity and roughness are especially relevant because they unveil an inherent breakdown of energy equipartition in granular fluids, even in homogeneous and isotropic states [2,3,4,5,6,7].…”

Section: Introductionmentioning

confidence: 99%

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

Santos¹

2011

AIP Conference Proceedings

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Abstract. In a recent paper [A. Santos, G. M. Kremer, and V. Garzó, Prog. Theor. Phys. Suppl. 184, 31-48 (2010)] the collisional energy production rates associated with the translational and rotational granular temperatures in a granular fluid mixture of inelastic rough hard spheres have been derived. In the present paper the energy production rates are explicitly decomposed into equipartition rates (tending to make all the temperatures equal) plus genuine cooling rates (reflecting the collisional dissipation of energy). Next the homogeneous free cooling state of a binary mixture is analyzed, with special emphasis on the quasi-smooth limit. A previously reported singular behavior (according to which a vanishingly small amount of roughness has a finite effect, with respect to the perfectly smooth case, on the asymptotic long-time translational/translational temperature ratio) is further elaborated. Moreover, the study of the time evolution of the temperature ratios shows that this dramatic influence of roughness already appears in the transient regime for times comparable to the relaxation time of perfectly smooth spheres.

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Electrophoresis analysis of a hydrophobic spherical particle in a micropolar electrolyte solution

Faltas,

Sherief,

Ismail

2024

Z Angew Math Mech

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The general expression for the time‐independent electrophoretic velocity of a spherical colloidal particle with a slippage surface in a microstructure electrolyte solution is derived. The two extreme cases of nonconducting and perfect conducting particles are investigated. The derived expression is valid for arbitrary Debye length and low particle zeta potentials. The concept of velocity spin slip is incorporated with the usual velocity slip at the particle's surface. The effect of the microstructure of fluid particles on the electrophoresis phenomena is discussed based on a micropolar fluid model. The influences of velocity slip and velocity spin slip are shown through various plots of electrophoretic velocity. The limiting case of electrolyte viscous solution is recovered. The principal findings of this research can be summarized as follows: As the micropolarity parameter increases, the normalized electrophoretic velocity decreases and reaches its peak in the case of Newtonian fluids. Additionally, the velocity slip acts as a counteracting factor that promotes an increase in the electrophoretic velocity. In the context of nonconducting particles, the normalized electrophoretic velocity rises as the spin slip parameter and Debye length decrease. Conversely, for perfectly conducting particles, it increases as the spin slip parameter and Debye length increase.

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Nearly Smooth Granular Gases

Cited by 62 publications

References 21 publications

Transport coefficients of a granular gas of inelastic rough hard spheres

Transport coefficients of a granular gas of inelastic rough hard spheres

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

Electrophoresis analysis of a hydrophobic spherical particle in a micropolar electrolyte solution

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