On contact numbers in random rod packings

Random packings of non-spherical granular particles are simulated by combining mechanical contraction and molecular dynamics, to determine contact numbers as a function of density. Particle shapes are varied from spheres to thin rods. The observed contact numbers (and packing densities) agree well with experiments on granular packings. Contact numbers are also compared to caging numbers calculated for sphero-cylinders with arbitrary aspect-ratio. The caging number for rods arrested by uncorrelated point contacts asymptotes towards <γ> = 9 at high aspect ratio, strikingly close to the experimental contact number <C> ≈ 9.8 for thin rods. These and other findings confirm that thin-rod packings are dominated by local arrest in the form of truly random neighbor cages. The ideal packing law derived for random rod–rod contacts, supplemented with a calculation for the average contact number, explains both absolute value and aspect-ratio dependence of the packing density of randomly oriented thin rods

Dense disordered jammed packings of hard spherocylinders with a low aspect ratio: a characterization of their structure

This work numerically investigates dense disordered (maximally random) jammed packings of hard spherocylinders of cylinder length L and diameter D by focusing on L/D ∈ [0,2]. It is within this interval that one expects that the packing fraction of these dense disordered jammed packings ϕMRJ hsc attains a maximum. This work confirms the form of the graph ϕMRJ hsc versus L/D: here, comparably to certain previous investigations, it is found that the maximal ϕMRJ hsc = 0.721 ± 0.001 occurs at L/D = 0.45 ± 0.05. Furthermore, this work meticulously characterizes the structure of these dense disordered jammed packings via the special pair-correlation function of the interparticle distance scaled by the contact distance and the ensuing analysis of the statistics of the hard spherocylinders in contact: here, distinctly from all previous investigations, it is found that the dense disordered jammed packings of hard spherocylinders with 0.45 ≲ L/D ≤ 2 are isostati

Experimental and computational analysis of random cylinder packings with applications

Random cylinder packings are prevalent in chemical engineering applications and they can serve as prototype models of fibrous materials and/or other particulate materials. In this research, comprehensive studies on cylinder packings were carried out by computer simulations and by experiments. The computational studies made use of a collective rearrangement algorithm (based on a Monte Carlo technique) to generate different packing structures. 3D random packing limits were explored, and the packing structures were quantified by their positional ordering, orientational ordering, and the particle-particle contacts. Furthermore, the void space in the packings was expressed as a pore network, which retains topological and geometrical information. The significance of this approach is that any irregular continuous porous space can be approximated as a mathematically tractable pore network, thus allowing for efficient microscale flow simulation. Single-phase flow simulations were conducted, and the results were validated by calculating permeabilities. In the experimental part of the research, a series of densification experiments were conducted on equilateral cylinders. X-ray microtomography was used to image the cylinder packs, and the particle-scale packings were reconstructed from the digital data. This numerical approach makes it possible to study detailed packing structure, packing density, the onset of ordering, and wall effects. Orthogonal ordering and layered structures were found to exist at least two characteristic diameters from the wall in cylinder packings. Important applications for cylinder packings include multiphase flow in catalytic beds, heat transfer, bulk storage and transportation, and manufacturing of fibrous composites

Experimental Study of the Nematic Transition in Granular Spherocylinder Packings under Tapping

Using x-ray tomography, we experimentally investigate the nematic transition in granular spherocylinder packings induced by tapping. Upon the validation of the Edwards ensemble framework in spherocylinders, we introduce an empirical free energy that accounts for the influence of gravity and the mechanical stability requirements specific to granular systems. This free energy can predict not only the correct phase transition behavior of the system from a disordered state to a nematic phase, but also a phase coexistence range and nucleation energy barriers that agree with experimental observations.Comment: 19 pages, 5 figure

Shear thickening of suspensions of dimeric particles

In this article, I study the shear thickening of suspensions of frictional dimers by the mean of numerical simulations. I report the evolution of the main parameters of shear thickening, such as the jamming volume fractions in the unthickened and thickened branches of the flow curves, as a function of the aspect ratio of the dimers. The explored aspect ratios range from $1$ (spheres) to $2$ (dimers made of two kissing spheres). I find a rheology qualitatively similar than the one for suspensions of spheres, except for the first normal stress difference $N_1$, which I systematically find negative for small asphericities. I also investigate the orientational order of the particles under flow. Overall, I find that dense suspensions of dimeric particles share many features with dry granular systems of elongated particles under shear, especially for the frictional state at large applied stresses. For the frictionless state at small stresses, I find that suspensions jam at lower volume fraction than dry systems, and that this difference increases with increasing aspect ratio. Moreover, in this state I find a thus far unobserved alignment of the dimers along the vorticity direction, as opposed to the commonly observed alignment with a direction close to the flow direction.Comment: 27 pages, 13 fig

Packing Characteristics of Different Shaped Proppants for use with Hydrofracing - A Numerical Investigation using 3D FEMDEM

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Basic Understanding of Condensed Phases of Matter via Packing Models

Packing problems have been a source of fascination for millenia and their study has produced a rich literature that spans numerous disciplines. Investigations of hard-particle packing models have provided basic insights into the structure and bulk properties of condensed phases of matter, including low-temperature states (e.g., molecular and colloidal liquids, crystals and glasses), multiphase heterogeneous media, granular media, and biological systems. The densest packings are of great interest in pure mathematics, including discrete geometry and number theory. This perspective reviews pertinent theoretical and computational literature concerning the equilibrium, metastable and nonequilibrium packings of hard-particle packings in various Euclidean space dimensions. In the case of jammed packings, emphasis will be placed on the "geometric-structure" approach, which provides a powerful and unified means to quantitatively characterize individual packings via jamming categories and "order" maps. It incorporates extremal jammed states, including the densest packings, maximally random jammed states, and lowest-density jammed structures. Packings of identical spheres, spheres with a size distribution, and nonspherical particles are also surveyed. We close this review by identifying challenges and open questions for future research.Comment: 33 pages, 20 figures, Invited "Perspective" submitted to the Journal of Chemical Physics. arXiv admin note: text overlap with arXiv:1008.298

Geometrical properties of rigid frictionless granular packings as a function of particle size and shape

Three-dimensional discrete numerical simulation is used to investigate the properties of close-packed frictionless granular assemblies as a function of particle polydispersity and shape. Unlike some experimental results, simulations show that disordered packings of pinacoids (eight-face convex polyhedron) achieve higher solid fraction values than amorphous packings of spherical or rounded particles, thus fulfilling the analogue of Ulam's conjecture stated by Jiao and co-workers for random packings [Y. Jiao and S. Torquato, Phys. Rev. E $\textbf{84}$, $041309$ ($2011$)]. This seeming discrepancy between experimental and numerical results is believed to lie with difficulties in overcoming interparticle friction through experimental densification processes. Moreover, solid fraction is shown to increase further with bidispersity and peak when the volume proportion of small particles reaches $30\%$. Contrarywise, substituting up to $50\%$ of flat pinacoids for isometric ones yields solid fraction decrease, especially when flat particles are also elongated. Nevertheless, particle shape seems to play a minor role on packing solid fraction compared to polydispersity. Additional investigations focused on the packing microstructure confirm that pinacoid packings fulfill the isostatic conjecture and that they are free of order except beyond $30$ to $50\%$ of flat or flat \& elongated polyhedra in the packing. This order increase progressively takes the form of a nematic phase caused by the reorientation of flat or flat \& elongated particles to minimize the packing potential energy. Simultaneously, this reorientation seems to increase the solid fraction value slightly above the maximum achieved by monodisperse isometric pinacoids, as well as the coordination number. Finally, partial substitution of elongated pinacoids for isometric ones has limited effect on packing solid fraction or order.Comment: 12 figures, 12 page