The density of random close packing of spheres

Scott, G. D.; Kilgour, D M

doi:10.1088/0022-3727/2/6/311

Cited by 649 publications

(397 citation statements)

References 10 publications

(7 reference statements)

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“…is valid for all friction coefficients and approximates the experimental and numerical estimations [5,6,7,8] which find a close packing limit independent of friction in a narrow range around 0.64. Beyond the fact that 63-64% is commonly quoted as RCP for monodisperse hard spheres, we present a physical interpretation of that value as the ground state of frictional hard spheres characterized by a given interparticle friction coefficient.…”

Section: Phase Diagramsupporting

confidence: 85%

“…(7), are coarse grained from the microscopic states defined by the microscopic Voronoi volume Eq. (6) in the mesoscopic calculations leading to (7) as discussed in Jamming I [49]. This fact has important implications for the present predictions which will be discussed in Section 7.5.…”

Section: Volume Landscape Of Jammed Mattermentioning

confidence: 60%

“…Following the infinite compactivity RLP-line, the volume fraction of the RLP decreases with increasing friction from the frictionless point (φ, Z) = (0.634, 6), towards the limit of infinitely rough hard spheres, Z → 4. Indeed, experiments [6] indicate that lower volume fractions are achieved for larger coefficient of friction. We predict the lowest volume fraction in the limit: µ → ∞, X → ∞ and Z → 4 (and h z → 0) at…”

Section: Phase Diagrammentioning

confidence: 99%

“…A review of the literature indicates that there is no general consensus on the value of RLP as different estimations have been reported ranging from 0.55 to 0.60 [6,9,8], proposing that there is no clear definition of RLP limit. The phase diagram proposes a solution to this problem.…”

Section: Phase Diagrammentioning

confidence: 99%

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Jamming II: Edwards’ statistical mechanics of random packings of hard spheres

Wang

Jin

et al. 2011

Physica A: Statistical Mechanics and its Applications

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The problem of finding the most efficient way to pack spheres has an illustrious history, dating back to the crystalline arrays conjectured by Kepler and the random geometries explored by Bernal in the 60's. This problem finds applications spanning from the mathematician's pencil, the processing of granular materials, the jamming and glass transitions, all the way to fruit packing in every grocery. There are presently numerous experiments showing that the loosest way to pack spheres gives a density of ∼ 55% (named random loose packing, RLP) while filling all the loose voids results in a maximum density of ∼ 63 − 64% (named random close packing, RCP). While those values seem robustly true, to this date there is no well-accepted physical explanation or theoretical prediction for them. Here we develop a common framework for understanding the random packings of monodisperse hard spheres whose limits can be interpreted as the experimentally observed RLP and RCP. The reason for these limits arises from a statistical picture of jammed states in which the RCP can be interpreted as the ground state of the ensemble of jammed matter with zero compactivity, while the RLP arises in the infinite compactivity limit. We combine an extended statistical mechanics approach 'a la Edwards' (where the role traditionally played by the energy and temperature in thermal systems is substituted by the volume and compactivity) with a constraint on mechanical stability imposed by the isostatic condition. We show how such approaches can bring results that can be compared to experiments and allow for an exploitation of the statistical mechanics framework. The key result is the use of a relation between the local Voronoi volumes of the constituent grains (denoted the volume function) and the number of neighbors in contact that permits to simple combine the two approaches to develop a theory of volume fluctuations in jammed * Corresponding author

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Section: Phase Diagramsupporting

confidence: 85%

Section: Volume Landscape Of Jammed Mattermentioning

confidence: 60%

Section: Phase Diagrammentioning

confidence: 99%

Section: Phase Diagrammentioning

confidence: 99%

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Jamming II: Edwards’ statistical mechanics of random packings of hard spheres

Wang

Jin

et al. 2011

Physica A: Statistical Mechanics and its Applications

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“…The model does however not depict the final elastic compact deformation and hence the contact model is not suitable for compressions at high relative densities. Before initiation of compression, the relative density of randomly close packed spheres is approximately 0.64 [22]. At increased compression pressure the interparticle contacts are independent up to relative densities of approximately 0.8.…”

Section: Introductionmentioning

confidence: 97%

An experimental evaluation of the accuracy to simulate granule bed compression using the discrete element method

Persson

Frenning

2012

Powder Technology

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PostprintThis is the accepted version of a paper published in Powder Technology. This paper has been peerreviewed but does not include the final publisher proof-corrections or journal pagination.Citation for the original published paper (version of record):Persson, A., Frenning, G. (2012) An experimental evaluation of the accuracy to simulate granule bed compression using the discrete element method. AbstractIn this work, granule compression is studied both experimentally and numerically with the overall objective of investigating the ability of the discrete element method (DEM) to accurately simulate confined granule bed compression. In the experiments, granules of microcrystalline cellulose (MCC) in the size range 200-710 µm were used as model material. Unconfined uniaxial compression of single granules was performed to determine granule properties such as the yield pressure and elastic modulus and compression profiles of the MCC granules were obtained from granule bed compression experiments. By utilizing the truncated Hertzian contact model for elastic-perfectly plastic materials, the rearrangement and plastic deformation stages of the force displacement curve were found to be in reasonable agreement with experiments. In an attempt to account for the final compression stage, elastic deformation of the compact, a simple modification of the contact model was proposed. This modification amounted to the introduction of a maximal plastic overlap, beyond which elastic deformation was the only deformation mode possible. Our results suggest that the proposed model provides an improved, although not perfect, 2 description of granule bed compression at high relative densities and hence may be used as a basis for future improvements.

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Particle‐Size Statistics

Goldman¹

2004

Encyclopedia of Statistical Sciences

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The density of random close packing of spheres

Cited by 649 publications

References 10 publications

Jamming II: Edwards’ statistical mechanics of random packings of hard spheres

Jamming II: Edwards’ statistical mechanics of random packings of hard spheres

An experimental evaluation of the accuracy to simulate granule bed compression using the discrete element method

Particle‐Size Statistics

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