Transport coefficients for granular media from molecular dynamics simulations

Bizon, C.; Shattuck, Mark D.; Swift, J. B.; Swinney, Harry L.

doi:10.1103/physreve.60.4340

Cited by 104 publications

(98 citation statements)

References 42 publications

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“…A granular gas of this kind is different from an equilibrium gas in that a continuous supply of energy from an external source is necessary to maintain a steady state and balance dissipation due to inelastic collisions between particles. The energy source determines typical scales of the dynamics in the system, but is presumed not to affect the microscopic constitutive laws such as the equation of state or expressions for transport coefficients [1]. In this Letter we study an externally fluidised granular gas and find that the details of the energising mechanism affect relations between intensive quantities even in the bulk of the system.…”

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confidence: 99%

Heating Mechanism Affects Equipartition in a Binary Granular System

Wang

Menon

2008

Phys. Rev. Lett.

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Two species of particles in a binary granular system typically do not have the same mean kinetic energy, in contrast to the equipartition of energy required in equilibrium. We investigate the role of the heating mechanism in determining the extent of non-equipartition of kinetic energy. In most experiments, different species are unequally heated at the boundaries. We show by event-driven simulations that differential boundary heating affects non-equipartition even in the bulk of the system. This conclusion is fortified by studying numerical and solvable stochastic models without spatial degrees of freedom. In both cases, even in the limit where heating events are rare compared to collisions, the effect of the heating mechanism persists.An issue of broad generality for nonequilibrium physics is the assignment of intensive temperature variables to steady states of driven systems. A widely-studied example of practical importance is a dilute system of macroscopic grains. A granular gas of this kind is different from an equilibrium gas in that a continuous supply of energy from an external source is necessary to maintain a steady state and balance dissipation due to inelastic collisions between particles. The energy source determines typical scales of the dynamics in the system, but is presumed not to affect the microscopic constitutive laws such as the equation of state or expressions for transport coefficients [1]. In this Letter we study an externally fluidised granular gas and find that the details of the energising mechanism affect relations between intensive quantities even in the bulk of the system.In a typical real-world situation, energy is delivered at the boundaries of a granular system by vibration, shear or other mechanical means. In equilibrium, a gas placed in contact with a heat bath acquires a uniform temperature and density. However, in the case of a granular system, there are gradients in density and particle motions as a function of distance from the energizing boundary. For dilute gases of inelastic particles there has been considerable progress [2]in describing this inhomogeneous steady state in terms of density and"temperature" fields, where the temperature is a purely kinetic construct, defined as the mean kinetic energy per degree of freedom, by analogy to kinetic theory of a molecular gas.An important conceptual tool in validating the use of nonequilibrium temperatures involves thermal contact between systems [3,4]. One can ask whether a candidate definition for the temperature governs the direction of energy flow and whether the temperatures equalise or evolve to bear a fixed relationship. In this spirit, we consider a granular system with two species of particles. There is no requirement that the species acquire the same kinetic temperature; indeed, experiments [5,6,7] document a violation of equipartition. It is observed that two species a and b acquire temperatures whose ratio γ ≡ T a /T b is affected strongly by the ratio of particle masses, m a /m b , and weakly by their inelasticity. ...

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confidence: 99%

Heating Mechanism Affects Equipartition in a Binary Granular System

Wang

Menon

2008

Phys. Rev. Lett.

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“…The advantages of this model for the coefficient of restitution are discussed and demonstrated in Refs. [15,18,19,20,21,22]. We have set ǫ = 0.6, because this value gives the best agreement in terms of particle compaction observed in similarly agitated states in experiments with nylon balls and in our simulations.…”

Section: B System Parametersmentioning

confidence: 99%

Granular circulation in a cylindrical pan: Simulations of reversing radial and tangential flows

et al. 2007

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Granular flows due to simultaneous vertical and horizontal excitations of a flat-bottomed cylindrical pan are investigated using event-driven molecular dynamics simulations. In agreement with recent experimental results, we observe a transition from a solid-like state, to a fluidized state in which circulatory flow occurs simultaneously in the radial and tangential directions. By going beyond the range of conditions explored experimentally, we find that each of these circulations reverse their direction as a function of the control parameters of the motion. We numerically evaluate the dynamical phase diagram for this system and show, using a simple model, that the solid-fluid transition can be understood in terms of a critical value of the radial acceleration of the pan bottom; and that the circulation reversals are controlled by the phase shift relating the horizontal and vertical components of the vibrations. We also discuss the crucial role played by the geometry of the boundary conditions, and point out a relationship of the circulation observed here and the flows generated in vibratory conveyors.

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“…The coefficient of restitution e, in principle, is not a constant and usually depends on impact velocity (Bizon et al 1999;Brilliantov & Pöschel 2004). Nevertheless, for simplicity, we assume that e is constant with 0 e 1 in this work.…”

Section: Short Review Of Kinetic Theorymentioning

confidence: 99%

Higher-order moment theories for dilute granular gases of smooth hard spheres

2017

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Grad's method of moments is employed to develop higher-order Grad moment equations-up to first 26-moments-for dilute granular gases within the framework of the (inelastic) Boltzmann equation. The homogeneous cooling state of a freely cooling granular gas is investigated with the Grad 26-moment equations in a semi-linearized setting and it is shown that the granular temperature in the homogeneous cooling state still decays according to Haff's law while the other higher-order moments decay on a faster time scale. The nonlinear terms of fully contracted fourth moment are also considered and, by exploiting the stability analysis of fixed points, it is shown that these nonlinear terms have negligible effect on Haff's law. Furthermore, an even larger Grad moment system which includes the fully contracted sixth moment is also scrutinized and the stability analysis of fixed points is again exploited to conclude that even the inclusion of scalar sixth order moment into the Grad moment system has negligible effect on Haff's law. The constitutive relations for the stress and heat flux (i.e., the Navier-Stokes and Fourier relations) are derived through the Grad 26-moment equations and compared with those obtained via CE expansion and via computer simulations. The linear stability of the homogeneous cooling state is analyzed through the Grad 26-moment system and various sub-systems by decomposing them into longitudinal and transverse systems. It is found that one eigenmode in both longitudinal and transverse systems in the case of inelastic gases is unstable. By comparing the eigenmodes from various theories, it is established that the 13-moment eigenmode theory predicts that the unstable heat mode of the longitudinal system remains unstable for all wavenumbers below a certain coefficient of restitution while any other higher-order moment theory shows that this mode becomes stable above some critical wavenumber for all values of the coefficient of restitution. In particular, the Grad 26-moment theory leads to a smooth profile for the critical wavenumber in contrast to the other considered theories. Furthermore, the critical system size obtained through the Grad 26-moment and existing theories are also in excellent agreement.

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Transport coefficients for granular media from molecular dynamics simulations

Cited by 104 publications

References 42 publications

Heating Mechanism Affects Equipartition in a Binary Granular System

Heating Mechanism Affects Equipartition in a Binary Granular System

Granular circulation in a cylindrical pan: Simulations of reversing radial and tangential flows

Higher-order moment theories for dilute granular gases of smooth hard spheres

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