Driven Granular Gases

Luding, Stefan; Cafiero, R.; Herrmann, Hans J.

doi:10.1007/978-3-540-39843-1_12

Cited by 12 publications

(23 citation statements)

References 51 publications

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“…(31) also leads to a nonGaussian velocity distribution, which could be predicted analytically [105,145,146]. However, we are not aware that Eq.…”

Section: Energy Input Ratementioning

confidence: 77%

“…As reported in Refs. [105,145,146], and many other papers since then, e.g., for strong dissipation, the driven granular system is sensitive to instabilities and can develop density fluctuations. This issue is not discussed further in this review.…”

Section: Driven Dissipative Hard Sphere Gasmentioning

confidence: 90%

“…For sake of brevity, we do not discuss this problem here in detail. We only present the non-democratic driving mechanism proposed by Cafiero et al [145,146]:…”

Section: Energy Input Ratementioning

confidence: 99%

“…For the analytical treatment and plenty of simulations we refer to the literature [145,146], where also rotational driving is defined [146,147] with the surprising finding that driving the rotational degree of freedom leads to more homogeneous systems even for very strong dissipation [147]. Note that driving can be applied to the whole system, or locally e.g.…”

Section: Energy Input Ratementioning

confidence: 99%

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Towards dense, realistic granular media in 2D

Luding¹

2009

Nonlinearity

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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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“…(31) also leads to a nonGaussian velocity distribution, which could be predicted analytically [105,145,146]. However, we are not aware that Eq.…”

Section: Energy Input Ratementioning

confidence: 77%

Section: Driven Dissipative Hard Sphere Gasmentioning

confidence: 90%

“…For sake of brevity, we do not discuss this problem here in detail. We only present the non-democratic driving mechanism proposed by Cafiero et al [145,146]:…”

Section: Energy Input Ratementioning

confidence: 99%

Section: Energy Input Ratementioning

confidence: 99%

See 2 more Smart Citations

Towards dense, realistic granular media in 2D

Luding¹

2009

Nonlinearity

Self Cite

133

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“…On the microscale, however, the physical quantities are at the individual particle level. Therefore, a so called micro-macro transition (Kirkwood et al, 1949;Luding and Poschel, 2001) needs to be performed to obtain the physical quantities at the macroscale. The framework through which microscale models reduce to macroscale continuum ones includes irreversible thermodynamics (Truesdell, 1984;Beris and Edwards, 1994;Ottinger, 2005), non-equilibrium statistical mechanics (Chapman and Cowling, 1970; Evms and Morriss, 1990), etc.…”

Section: Transition From Microscale To Macroscalementioning

confidence: 99%

Mutiscale Modeling of Segregation in Granular Flows

Sun¹

2007

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Green’s function measurements of force transmission in 2D granular materials

Geng

Reydellet

Clément

et al. 2003

Physica D: Nonlinear Phenomena

157

204

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We describe experiments that probe the response to a point force of 2D granular systems under a variety of conditions. Using photoelastic particles to determine forces at the grain scale, we obtain ensembles of responses for the following particle types, packing geometries and conditions: monodisperse ordered hexagonal packings of disks, bidisperse packings of disks with different amount of disorder, disks packed in a regular rectangular lattice with different frictional properties, packings of pentagonal particles, systems with forces applied at an arbitrary angle at the surface, and systems prepared with shear deformation, hence with texture or anisotropy. We experimentally show that disorder, packing structure, friction and texture significantly affect the average force response in granular systems. For packings with weak disorder, the mean forces propagate primarily along lattice directions. The width of the response along these preferred directions grows with depth, increasingly so as the disorder of the system grows. Also, as the disorder increases, the two propagation directions of the mean force merge into a single direction. The response function for the mean force in the most strongly disordered system is quantitatively consistent with an elastic description for forces applied nearly normally to a surface, but this description is not as good for non-normal applied forces. These observations are consistent with recent predictions of Bouchaud et al. [Bouchaud et al., Euro. Phys. J. E4 451 (2001); Socolar et al., Euro. Phys. J. E7 353 (2002)] and with the anisotropic elasticity models of Goldenberg and Goldhirsch [Goldenberg & Goldhirsch, Phys. Rev. Lett. 89 084302 (2002)]. At this time, it is not possible to distinguish between these two models. The data do not support a diffusive picture, as in the q-model, and they are in conflict with data by Rajchenbach [Da Silva & Rajchenbach, Nature 406 708 (2000)] that indicate a parabolic response for a system consisting of cuboidal blocks. We also explore the spatial properties of force chains in an anisotropic textured system created by a nearly uniform shear. This system is characterized by stress chains that are strongly oriented along an angle of 45 o , corresponding to the compressive direction of the shear deformation. In this case, the spatial correlation function for force has a range of only one particle size in the direction transverse to the chains, and varies as a power law in the direction Preprint submitted to Elsevier Science of the chains, with an exponent of -0.81. The response to forces is strongest along the direction of the force chains, as expected. Forces applied in other directions are effectively refocused towards the strong force chain direction.

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Driven Granular Gases

Cited by 12 publications

References 51 publications

Towards dense, realistic granular media in 2D

Towards dense, realistic granular media in 2D

Mutiscale Modeling of Segregation in Granular Flows

Green’s function measurements of force transmission in 2D granular materials

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