Kinetic theoretical study of a simply sheared two-dimensional granular gas to Burnett order

Sela, N.; Goldhirsch, I.; Noskowicz, S. H.

doi:10.1063/1.869012

Cited by 114 publications

(100 citation statements)

References 21 publications

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“…The uniform (or simple) shear flow (USF) is perhaps the nonequilibrium state most widely studied, both for granular [6,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40] and conventional [41] gases. In this state the gas is enclosed between two infinite parallel planes located at y = −L/2 and y = +L/2 and in relative motion with velocities −U/2 and +U/2, respectively, along the xdirection.…”

Section: Uniform Shear Flowmentioning

confidence: 99%

Uniform shear flow in dissipative gases: Computer simulations of inelastic hard spheres and frictional elastic hard spheres

Astillero

Santos

2005

Phys. Rev. E

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In the preceding paper (cond-mat/0405252), we have conjectured that the main transport properties of a dilute gas of inelastic hard spheres (IHS) can be satisfactorily captured by an equivalent gas of elastic hard spheres (EHS), provided that the latter are under the action of an effective drag force and their collision rate is reduced by a factor (1 + α)/2 (where α is the constant coefficient of normal restitution). In this paper we test the above expectation in a paradigmatic nonequilibrium state, namely the simple or uniform shear flow, by performing Monte Carlo computer simulations of the Boltzmann equation for both classes of dissipative gases with a dissipation range 0.5 ≤ α ≤ 0.95 and two values of the imposed shear rate a. It is observed that the evolution toward the steady state proceeds in two stages: a short kinetic stage (strongly dependent on the initial preparation of the system) followed by a slower hydrodynamic regime that becomes increasingly less dependent on the initial state. Once conveniently scaled, the intrinsic quantities in the hydrodynamic regime depend on time, at a given value of α, only through the reduced shear rate a * (t) ∝ a/ T (t), until a steady state, independent of the imposed shear rate and of the initial preparation, is reached. The distortion of the steady-state velocity distribution from the local equilibrium state is measured by the shear stress, the normal stress differences, the cooling rate, the fourth and sixth cumulants, and the shape of the distribution itself. In particular, the simulation results seem to be consistent with an exponential overpopulation of the high-velocity tail. These properties are common to both the IHS and EHS systems. In addition, the EHS results are in general hardly distinguishable from the IHS ones if α 0.7, so that the distinct signature of the IHS gas (higher anisotropy and overpopulation) only manifests itself at relatively high dissipations.

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Section: Uniform Shear Flowmentioning

confidence: 99%

Uniform shear flow in dissipative gases: Computer simulations of inelastic hard spheres and frictional elastic hard spheres

Astillero

Santos

2005

Phys. Rev. E

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“…These surprising results provide a partial experimental justification for the theoretical treatment of granular flow by anal-ogy with molecular fluids using standard statistical mechanics and kinetic theory. A large number of kinetic theories of granular flows [7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24] have been produced starting in 1980's. The results of these theories are balance equation analogous to the Navier-Stokes equations for the density, n, the average velocity, v o , and the average kinetic energy per particle or temperature, T , as well as, equations of state and transport coefficients, which are functions of n,v 0 , and T .…”

Section: Introductionmentioning

confidence: 99%

Forcing independent velocity distributions in an experimental granular fluid

2007

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We present experimental results on the velocity statistics of a uniformly heated granular fluid, in a quasi-2D configuration. We find the base state, as measured by the single particle velocity distribution P (c), to be universal over a wide range of filling fractions and only weakly dependent on all other system parameters. There is a consistent overpopulation in the distribution's tails, which scale as P ∝ exp(−A × c −3/2 ). More generally, P (c) deviates from a Maxwell-Boltzmann by a second order Sonine polynomial with a single adjustable parameter, in agreement with recent theoretical analysis of inelastic hard spheres driven by a stochastic thermostat. To our knowledge, this is the first time that Sonine deviations have been measured in an experimental system.

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“…When a shear is applied to the granular system, high-density region, called "shear band", appears [7]. There exist many papers to estimate the transport coefficients by using kinetic theory [8,9,10,11,12,13] and to analyze the pattern dynamics by using continuum mechanics [14,15,16,17,18,19,20,21,22].…”

Section: Introductionmentioning

confidence: 99%

Simulation of pattern dynamics of cohesive granular particles under a plane shear

Takada

Hayakawa

2013

AIP Conference Proceedings

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Abstract.We have performed three-dimensional molecular dynamics simulation of cohesive granular particles under a plane shear. From the simulation, we found the existence of three distinct phases in steady states: (I) a uniform shear phase, (II) a coexistent phase of a shear band and a gas region and (III) a crystal phase. We also found that the critical line between (II) and (III) is approximately represented by ζ ∝ exp(βγL y ), where ζ , β ,γ, L y are the dissipation rate, an unimportant constant, the shear rate and the system size of the velocity gradient direction, respectively.

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Kinetic theoretical study of a simply sheared two-dimensional granular gas to Burnett order

Cited by 114 publications

References 21 publications

Uniform shear flow in dissipative gases: Computer simulations of inelastic hard spheres and frictional elastic hard spheres

Uniform shear flow in dissipative gases: Computer simulations of inelastic hard spheres and frictional elastic hard spheres

Forcing independent velocity distributions in an experimental granular fluid

Simulation of pattern dynamics of cohesive granular particles under a plane shear

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