Random packings ofN⩽2000 rigid disks in the plane, subject to periodic boundary conditions on a square primitive cell, have been generated by a concurrent construction which treats all disks on an equal footing, as opposed to previously investigated sequential constructions. The particles start with random positions and velocities, and as they move about they grow uniformly in size, from points to jammed disks. The collection of packings displays several striking geometric features. These include (for largeN) typically polycrystalline textures with irregular grain boundaries and linear shear fractures. The packings occasionally contain monovacancies and trapped but unjammed “rattler” disks. The latter appear to be confined to the grain boundaries. The linear shear fractures preserve bond orientational order, but disrupt translational order, within the crystalline grains. A new efficient event-driven simulation algorithm is employed to generate the histories of colliding and jamming disks. On a computer which can process one million floating-point instructions per second the algorithm processes more than one million pairwise collisions per hour.

/pdf/geometric-properties-of-random-disk-packings-d0qkjrgkab.pdf

Geometric properties of random disk packings

The three-dimensional structure of large packings of monosized spheres with volume fractions ranging between 0.58 and 0.64 has been studied with x-ray computed tomography. We search for signatures of organization, classifying local arrangements and exploring the effects of local geometrical constrains on the global packing. This study is the largest and the most accurate empirical analysis of disordered packings at the grain-scale to date, mapping over 380,000 sphere coordinates with precision within 0.1% of the sphere diameters. We discuss topological and geometrical methods to characterize and classify these systems emphasizing the implications that local geometry can have on the mechanisms of formation of these amorphous structures. Some of the main results are (1) the observation that the average number of contacts increases with the volume fraction; (2) the discovery that these systems have a very compact contact network; (3) the finding that disordered packing can be locally more efficient than crystalline packings; (4) the observation that the peaks of the radial distribution function follow power law divergences; (5) the discovery that geometrical frustration plays no role in the formation of such amorphous packings.

/pdf/geometrical-structure-of-disordered-sphere-packings-4s6mpwsfyt.pdf

Geometrical structure of disordered sphere packings.

Some structural properties of packed bed systems on both the local and overall scales which are available in the literature and of interest in chemical engineering applications are discussed. Regular and random packings of uniformly sized spheres are initially analyzed as a basis for the later examination of the more general case of random packed beds containing particles of various sizes and shapes, with or without restraining surfaces.



On discute, sur une echelle locale et globale, certaines proprietes structurales deg systemes a base de lits garnis qu'on mentionne dans des ecrits et qui sont interessantes a cause de leurs applications en genie chimique. On analyse d'abord des garnitures regulieres et irregulieres de spheres aux dimensions uniformes, et ce comme base d'un examen ulterieur du cas des lits qui sont garnis irregulierement, continnent des particules de dimensions et formes diverses et possedent des surfaces restreintes on non.

Structural properties of packed beds — A review

Local voidage variation in a randomly packed bed of equal-sized spheres

In recent years we have constructed closely packed spheres using the Lubachevsky-Stillinger algorithm to generate morphological models of heterogeneous solid propellants. Improvements to the algorithm now allow us to create large polydisperse packs on a laptop computer, and to create monodisperse packs with packing fractions greater than 70% which display significant crystal order. The use of these models in the physical context motivates efforts to examine in some detail the nature of the packs, including certain statistical properties. We compare packing fractions for binary packs with long-known experimental data. Also, we discuss the near-neighbor number and the radial distribution function (RDF) for monodisperse packs and make comparisons with experimental data. We also briefly discuss the RDF for bidisperse packs. We also consider bounded monodisperse packs, and pay particular attention to the near-wall structure where we identify significant order.

Nature of packs used in propellant modeling.

DURING some work on the tensile strength and cohesion of wet particles, it became necessary to have some knowledge of the number of contacts and near contacts existing in a random packing of equal spheres. The range of centre to centre separations from 1.0 to 1.3 diameters was of particular interest to this work because experimental results had shown that liquid bridges existing between spheres separated by these distances were likely to play a major part in the cohesion of a wet bed of spheres1.

Distribution of Near Neighbours in a Random Packing of Spheres

EARLIER, we reported1 the radial distribution function from a random packing of spheres covering the range of sphere separations from 1.0 to 1.3 diameters. Inspection of the data indicated some possible fine structure in the distribution function. The results supplemented those of Bernal2 and Scott3 which covered a far larger separation range.

/pdf/fine-structure-in-the-radial-distribution-function-from-a-54zyim14a8.pdf

Fine Structure in the Radial Distribution Function from a Random Packing of Spheres

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Distribution of Near Neighbours in a Random Packing of Spheres

Fine Structure in the Radial Distribution Function from a Random Packing of Spheres