Collisional Granular Flow as a Micropolar Fluid

Mitarai, Namiko; Hayakawa, Hisao; Nakanishi, Hiizu

doi:10.1103/physrevlett.88.174301

Cited by 96 publications

(67 citation statements)

References 21 publications

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“…e = β 0 = 1 to keep the time reversal symmetry. As will be shown, the result recovers usual Navier-Stokes equation in the dilute limit, but in some situation like in flows on an inclined rough plate the prediction of the dilute gas kinetics seems to be quantitatively useful [11]. The extension of this analysis for dense particles with dissipative collisions will be discussed elsewhere.…”

Section: Kinetic Theory Of Dilute Gasessupporting

confidence: 56%

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Note on a Micropolar Gas-Kinetic Theory

Hayakawa

2003

Traffic and Granular Flow’01

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Abstract. The micropolar fluid mechanics and its transport coefficients are derived from the linearized Boltzmann equation of rotating particles. In the dilute limit, as expected, transport coefficients relating to microrotation are not important, but the results are useful for the description of collisional granular flow on an inclined slope. (This paper will be published in Traffic and Granular Flows 2001 edited by Y. Sugiyama and D. E. Wolf(Springer)).

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Section: Kinetic Theory Of Dilute Gasessupporting

confidence: 56%

“…Therefore, the effect of microrotation is negligible in usual situations of dilute gases. However, as demonstrated by Mitarai et al [11] the shear near the boundary produces the relevant situation for microrotation.…”

Section: Evaluation Of µ Rmentioning

confidence: 92%

Note on a Micropolar Gas-Kinetic Theory

Hayakawa

2003

Traffic and Granular Flow’01

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“…Friction leads to a coupling of rotational and translational degrees of freedom [190][191][192][193][194] and (due to dissipation) to non-equipartition of energies [142,143,157,158,195], and correlations between the different degrees of freedom [166]. The presence of friction and the rotational degrees of freedom has been related to a random restitution coefficient [196,197], however, we disregard here this stochastic approach to a deterministic problem.…”

Section: Frictionmentioning

confidence: 99%

Towards dense, realistic granular media in 2D

Luding¹

2009

Nonlinearity

133

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The development of an applicable theory for granular matter -with both qualitative and quantitative value -is a challenging prospect, given the multitude of states, phases and (industrial) situations it has to cover. Given the general balance equations for mass, momentum, and energy, the limiting case of dilute and almost elastic granular gases, where kinetic theory works perfectly well, is the starting point.In most systems, low density coexists with very high density, where the latter is an open problem for kinetic theory. Furthermore, many additional non-linear phenomena and material properties are important in realistic granular media, involving, e.g.: (i) multi-particle interactions and elasticity (ii) strong dissipation, (iii) friction, (iv) long-range forces and wet contacts (v) wide particle size-distributions, and (vi) various particle shapes. Note that, while some of these issues are more relevant for high density, others are important for both low and high densities; some of them can be dealt with by means of kinetic theory, some can not. This paper is a review of recent progress towards more realistic models for dense granular media in 2D, even though most of the observations, conclusions, and corrections given are qualitatively true also in 3D. Starting from an elastic, frictionless and monodisperse hard sphere gas, the (continuum) balance equations of mass, momentum and energy are given. The equation of state, the (Navier-Stokes level) transport coefficients and the energy-density dissipation rate are considered. Several corrections are applied to those constitutive material laws -one by one -in order to account for the realistic physical effects and properties listed above.

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“…Hence, a more adequate model takes into account the rotational motion of particles and the exchange of rotational and translational energy in collisions [1,6,10,[24][25][26][27][28][29][30][31][32][33][34][35]. Dissipative frictional gases exhibit additional unusual features which are not present in molecular gases.…”

Section: The European Physical Journal Special Topicsmentioning

confidence: 99%

Correlation of spin and velocity in the homogeneous cooling state of a granular gas of rough particles

Kranz

Brilliantov

Pöschel

et al. 2009

Eur. Phys. J. Spec. Top.

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Abstract. In a granular gas of rough particles the spin of a grain is correlated with its linear velocity. We develop an analytical theory to account for these correlations and compare its predictions to numerical simulations, using Direct Simulation Monte Carlo as well as Molecular Dynamics. The system is shown to relax from an arbitrary initial state to a steady-state, which is characterized by time-independent, finite correlations of spin and linear velocity. The latter are analyzed systematically for a wide range of system parameters, including the coefficients of tangential and normal restitution as well as the moment of inertia of the particles. For most parameter values the axis of rotation and the direction of linear momentum are perpendicular like in a sliced tennis ball, while parallel orientation, like in a rifled bullet, occurs only for a small range of parameters. The limit of smooth spheres is singular: any arbitrarily small roughness unavoidably causes significant translation-rotation correlations, whereas for perfectly smooth spheres the rotational degrees of freedom are completely decoupled from the dynamic evolution of the gas.

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Collisional Granular Flow as a Micropolar Fluid

Cited by 96 publications

References 21 publications

Note on a Micropolar Gas-Kinetic Theory

Note on a Micropolar Gas-Kinetic Theory

Towards dense, realistic granular media in 2D

Correlation of spin and velocity in the homogeneous cooling state of a granular gas of rough particles

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