Measurements of Grain Motion in a Dense, Three-Dimensional Granular Fluid

Yang, Xiaoyu; Huan, Chao; Candela, D.; Mair, R. W.; Walsworth, Ronald L.

doi:10.1103/physrevlett.88.044301

Cited by 102 publications

(76 citation statements)

References 23 publications

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“…In realistic systems, the energy injected by stirring, shearing, tapping etc. is dissipated by the inelastic collisions among the particles, creating a gradient of granular temperature [46,47,48]. Here we assume that the system is in contact with a thermal bath, a situation which is quite different.…”

Section: Discussionmentioning

confidence: 99%

Slow dynamics under gravity: a nonlinear diffusion model

Arenzon

Levin

Sellitto

2003

Physica A: Statistical Mechanics and its Applications

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We present an analytical and numerical study of a nonlinear diffusion model which describes density relaxation of loosely packed particles under gravity and weak random (thermal) vibration, and compare the results with Monte Carlo simulations of a lattice gas under gravity. The dynamical equation can be thought of as a local density functional theory for a class of lattice gases used to model slow relaxation of glassy and granular materials. The theory predicts a jamming transition line between a low density fluid phase and a high density glassy regime, characterized by diverging relaxation time and logarithmic or power-law compaction according to the specific form of the diffusion coefficient. In particular, we show that the model exhibits history dependent properties, such as quasi reversible-irreversible cycle and memory effects -as observed in recent experiments, and dynamical heterogeneities.

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Section: Discussionmentioning

confidence: 99%

Slow dynamics under gravity: a nonlinear diffusion model

Arenzon

Levin

Sellitto

2003

Physica A: Statistical Mechanics and its Applications

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“…For higher densities the α range is more limited but the Enskog theory still captures the relevant qualitative features. The Enskog transport coefficients for a monocomponent gas [62] have also been tested against NMR experiments of a system of mustard seeds vibrated vertically [43,44]. The average value of the coefficient of restitution of the grains used in this experiment is α = 0.87, which lies outside of the quasielastic limit (α ≈ 0.99).…”

Section: Revised Enskog Kinetic Theorymentioning

confidence: 99%

“…This is so since the reference state is a local HCS whose parameters change throughout the system to match the physical values in each cell. Another examples of good agreement between theory and simulation [42] and experiments [43,44] include the application of the Navier-Stokes hydrodynamics to describe density/temperature profiles in vertical vibrated gases, supersonic flow past at wedge in real experiments [45], and nonequipartition and size segregation in agitated granular mixtures [27,28,46]. In summary, the Navier-Stokes hydrodynamics with the constitutive equations obtained in this paper constitute an important and useful description for many different physical situations, although more limited than for elastic gases.…”

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confidence: 99%

Enskog theory for polydisperse granular mixtures. I. Navier-Stokes order transport

2007

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A hydrodynamic description for an s-component mixture of inelastic, smooth hard disks (two dimensions) or spheres (three dimensions) is derived based on the revised Enskog theory for the single-particle velocity distribution functions. In this first portion of the two-part series, the macroscopic balance equations for mass, momentum, and energy are derived. Constitutive equations are calculated from exact expressions for the fluxes by a Chapman-Enskog expansion carried out to first order in spatial gradients, thereby resulting in a Navier-Stokes order theory. Within this context of small gradients, the theory is applicable to a wide range of restitution coefficients and densities. The resulting integral-differential equations for the zeroth-and first-order approximations of the distribution functions are given in exact form. An approximate solution to these equations is required for practical purposes in order to cast the constitutive quantities as algebraic functions of the macroscopic variables; this task is described in the companion paper.

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“…The analysis for dilute gases has been also extended to finite densities in the context of the revised Enskog kinetic theory (RET) [8]. This hydrodynamic theory succesfully models the density and temperature profiles obtained in a recent experimental study of a three-dimensional system of mustard seeds fluidized by vertical container vibrations [9].…”

Section: Introductionmentioning

confidence: 99%

Shear viscosity for a moderately dense granular binary mixture

Garzó

Montanero

2003

Phys. Rev. E

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The shear viscosity for a moderately dense granular binary mixture of smooth hard spheres undergoing uniform shear flow is determined. The basis for the analysis is the Enskog kinetic equation, solved first analytically by the Chapman-Enskog method up to first order in the shear rate for unforced systems as well as for systems driven by a Gaussian thermostat. As in the elastic case, practical evaluation requires a Sonine polynomial approximation. In the leading order, we determine the shear viscosity in terms of the control parameters of the problem: solid fraction, composition, mass ratio, size ratio and restitution coefficients. Both kinetic and collisional transfer contributions to the shear viscosity are considered. To probe the accuracy of the Chapman-Enskog results, the Enskog equation is then numerically solved for systems driven by a Gaussian thermostat by means of an extension to dense gases of the well-known Direct Simulation Monte Carlo (DSMC) method for dilute gases. The comparison between theory and simulation shows in general an excellent agreement over a wide region of the parameter space.

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Measurements of Grain Motion in a Dense, Three-Dimensional Granular Fluid

Cited by 102 publications

References 23 publications

Slow dynamics under gravity: a nonlinear diffusion model

Slow dynamics under gravity: a nonlinear diffusion model

Enskog theory for polydisperse granular mixtures. I. Navier-Stokes order transport

Shear viscosity for a moderately dense granular binary mixture

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