Microstructural characterization of random packings of cubic particles

Abstract

Understanding the properties of random packings of solid objects is of critical importance to a wide variety of fundamental scientific and practical problems. The great majority of the previous works focused, however, on packings of spherical and sphere-like particles. We report the first detailed simulation and characterization of packings of non-overlapping cubic particles. Such packings arise in a variety of problems, ranging from biological materials, to colloids and fabrication of porous scaffolds using salt powders. In addition, packing of cubic salt crystals arise in various problems involving preservation of pavements, paintings, and historical monuments, mineral-fluid interactions, CO2 sequestration in rock, and intrusion of groundwater aquifers by saline water. Not much is known, however, about the structure and statistical descriptors of such packings. We have developed a version of the random sequential addition algorithm to generate such packings, and have computed a variety of microstructural descriptors, including the radial distribution function, two-point probability function, orientational correlation function, specific surface, and mean chord length, and have studied the effect of finite system size and porosity on such characteristics. The results indicate the existence of both spatial and orientational long-range order in the packing, which is more distinctive for higher packing densities. The maximum packing fraction is about 0.57.

Flow, Transport, and Reaction in Porous Media: Percolation Scaling, Critical‐Path Analysis, and Effective Medium Approximation

“…While the great majority of the studies of packings of particles has been devoted to those with spherical grains, packing of nonspherical particles have also been studied. They include elliptical (Feng et al, ; Donev et al, ; Man et al, ; Sherwood, ), disks (Lubachevsky & Stillinger, ; Uche et al, ), Platonic and Archimedean solids (Baker & Kudrolli, ; Torquato & Jiao, ), tetrahedral (Conway & Torquato, ; Haji‐Akbari et al, ; Latham et al, ), spherotetrahedral (Jin et al, ), and cubic particles (Malmir et al, , ). Many of the issues relevant to packings of solid objects have been reviewed by Torquato and Stillinger (), as well as by earlier reviews of Torquato () and Sahimi ().…”

Shape-dependent effective diffusivity in packings of hard cubes and cuboids compared with spheres and ellipsoids

“…Just to give a brief account, studies performed include the random close packing of ellipsoids, 27 monodisperse and polydisperse hard spheres, 28,29 polyhedra including platonic solids, [30][31][32][33] superballs and superellipsoids, [34][35][36] cubes with round edges, 37 and monodisperse and polydisperse cubes and cuboids. [38][39][40][41][42] Hard cubes and cuboids and their packing and phase behavior have been studied both as limiting cases of superballs and superellipsoids, 35,36 and modeled exactly as cubes and cuboids. [39][40][41] The true nature of their behavior is somewhat elusive; as stated by Jiao and Torquato, 31 attempts to create random close packings (or rather maximally random jammed packings) of cubes easily lead to high degrees of order, raising questions concerning the appropriateness of some of the algorithms suggested so far to generate these packings.…”

“…[38][39][40][41][42] Hard cubes and cuboids and their packing and phase behavior have been studied both as limiting cases of superballs and superellipsoids, 35,36 and modeled exactly as cubes and cuboids. [39][40][41] The true nature of their behavior is somewhat elusive; as stated by Jiao and Torquato, 31 attempts to create random close packings (or rather maximally random jammed packings) of cubes easily lead to high degrees of order, raising questions concerning the appropriateness of some of the algorithms suggested so far to generate these packings. Nonetheless, random sequential addition [39][40][41] can produce packings with a high degree of randomness, as can the order-constrained stochastic optimization method described in ref.…”

Image‐based modeling of granular porous media

“…The DEM is, however, accurate if the granular medium consists of particles that are not too complex. Packings with such particle shapes as ellipsoids [Sherwood, 1997;Man et al, 2005;Ng, 2009], cylinders [Pournin et al, 2005], polyhedra [Tillemans and Herrmann, 1995;Lu and McDowell, 2006;Peña et al, 2007;Azéma et al, 2009;Galindo-Torres and Pedroso, 2010;Mollon and Zhao, 2012], polyarcs [Fu and Dafalias, 2011], pentagons [Azéma et al, 2007], rounded rectangles [Boon et al, 2012], and cubes [Malmir et al, 2016a[Malmir et al, , 2016b have been studied.…”