Departure from Fourier's Law for Fluidized Granular Media

We consider a dilute gas of hard spheres in dimension d ≥ 2 that upon collision either annihilate with probability p or undergo an elastic scattering with probability 1 − p. For such a system neither mass, momentum, nor kinetic energy are conserved quantities. We establish the hydrodynamic equations from the Boltzmann equation description. Within the Chapman-Enskog scheme, we determine the transport coefficients up to Navier-Stokes order, and give the closed set of equations for the hydrodynamic fields chosen for the above coarse grained description (density, momentum and kinetic temperature). Linear stability analysis is performed, and the conditions of stability for the local fields are discussed.

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“…A similar quantity appears for granular gases, which again is non-vanishing in the inelastic case only [26,37]. The identification of Eq.…”

Section: Navier-stokes Transport Coefficientsmentioning

confidence: 86%

Hydrodynamics of probabilistic ballistic annihilation

2004

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“…This implies the introduction of a new coefficient, the diffusive heat conductivity µ, that vanishes in the elastic limit. This coupling has been derived by kinetic theory methods [1,2,3], and its consequences confirmed in computer simulations [4,5,6]. For the particular case of a vibrated granular gas in the presence of gravity, this term implies a peculiar behavior of the temperature profile, that increases with height after a minimum.…”

Section: Introductionmentioning

confidence: 99%

Heat flux in a vibrated granular gas: the diffusive heat conductivity coefficient

Brey¹,

Ruiz‐Montero²

2005

AIP Conference Proceedings

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Abstract. The transport coefficient coupling heat flux and density gradient in a granular gas is measured by taking advantage of the existence of a minimum in the temperature profile of an open vibrated granular medium. This temperature inversion is closely related to the existence of the new transport coefficient. Particle simulations using the Direct Simulation Monte Carlo method will be used to compute the transport coefficient, and the results will be compared with theoretical predictions derived from the Boltzmann equation. Finally, the accuracy of a boundary condition requiring the hydrodynamic heat flux to vanish for infinite heights will be discussed.

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“…Soto et al [29] also has studied the heat conduction between two parallel plates by molecular dynamics simulation of the IHS model.…”

Section: D Model Heated From the Boundaries Without Gravitymentioning

confidence: 99%

Bifurcations of a Driven Granular System under Gravity

Isobe¹

2003

Traffic and Granular Flow’01

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Molecular dynamics study on the granular bifurcation in a simple model is presented. The model consists of hard disks, which undergo inelastic collisions; the system is under the uniform external gravity and is driven by the heat bath. The competition between the two effects, namely, the gravitational force and the heat bath, is carefully studied. We found that the system shows three phases, namely, the condensed phase, locally fluidized phase, and granular turbulent phase, upon increasing the external control parameter. We conclude that the transition from the condensed phase to the locally fluidized phase is distinguished by the existence of fluidized holes, and the transition from the locally fluidized phase to the granular turbulent phase is understood by the destabilization transition of the fluidized holes due to mutual interference.

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Departure from Fourier's Law for Fluidized Granular Media

Cited by 81 publications

References 25 publications

Hydrodynamics of probabilistic ballistic annihilation

Hydrodynamics of probabilistic ballistic annihilation

Heat flux in a vibrated granular gas: the diffusive heat conductivity coefficient

Bifurcations of a Driven Granular System under Gravity

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