Voronoi analysis of the packings of non-spherical particles

Approximate Packing of Binary Mixtures of Cylindrical Particles

Particle packing plays an essential role in industry and chemical engineering. In this work, the discrete element method is used to generate the cylindrical particles and densify the binary cylindrical particle mixtures under the poured packing conditions. The influences of the aspect ratio and volume fraction of particles on the packing structure are measured by planar packing fraction. The Voronoi tessellation is used to quantify the porous structure of packing. The cumulative distribution functions of local packing fractions and the probability distributions of the reduced free volume of Voronoi cells are calculated to describe the local packing characteristics of binary mixtures with different volume fractions. As a result, it is observed that particles with larger aspect ratios in the binary mixture tend to orient randomly, and the particles with smaller aspect ratios have a preferentially horizontal orientation. Results also show that the less dense packings are obtained for mixtures with particles of higher aspect ratios and mixtures with a larger fraction of elongated cylindrical particles.

Porous Structure of Cylindrical Particle Compacts

The porous compacts of non-spherical particles are frequently used in energy storage devices and other advanced applications. In the present work, the microstructures of compacts of monodisperse cylindrical particles are investigated. The cylindrical particles with various aspect ratios are generated using superquadrics, and the discrete element method was adopted to simulate the compacts formed under gravity deposition of randomly oriented particles. The Voronoi tessellation is then used to quantify the porous microstructure of compacts. With one exception, the median reduced free volume of Voronoi cells increases, and the median local packing density decreases for compacts composed of cylinders with a high aspect ratio, indicating a loose packing of long cylinders due to their mechanical interlocking during compaction. The obtained data are needed for further optimization of compact porous microstructure to improve the transport properties of compacts of non-spherical particles.

Analysis of Tortuosity in Compacts of Ternary Mixtures of Spherical Particles

Herein, an approach is proposed to analyze the tortuosity of porous electrodes using the radical Voronoi tessellation. For this purpose, a series of particle compacts geometrically similar to the actual porous electrode were generated using discrete element method; the radical Voronoi tessellation was constructed for each compact to characterize the structural properties; the tortuosity of compact porous structure was simulated by applying the Dijkstra's shortest path algorithm on radical Voronoi tessellation. Finally, the relationships were established between the tortuosity and the composition of the ternary particle mixture, and between the tortuosity and the radical Voronoi cell parameters. The following correlations between tortuosity values and radical Voronoi cell parameters were found: larger faces and longer edges of radical Voronoi cell leads to the increased fraction of larger values of tortuosity in the distribution, while smaller faces and shorter edges of radical Voronoi cell contribute to the increased fraction of smaller tortuosity values, being the tortuosity values more uniform with narrower distribution. Thus, the compacts with enhanced diffusion properties are expected to be obtained by packing particle mixtures with high volume fraction of small and medium particles. These results will help to design the well-packed particle compacts having improved diffusion properties for various applications including porous electrodes.

Evolutions of packing properties of perfect cylinders under densification and crystallization

Cylindrical particles are ubiquitous in nature and industry, and a cylinder is a representative shape of rod-like particles. However, the disordered packing results of cylinders in previous studies are quite inconsistent with each other. In this work, we obtain the MRJ (maximally random jammed) packings and the MDRPs (maximally dense random packings) of perfect cylinders with the aspect ratio (height/diameter) 0.2 ≤ w ≤ 6.0 using the ASC (adaptive shrinking cell) algorithm and the IMC (inverse Monte Carlo) method, respectively. The optimal aspect ratio corresponding to the maximal packing density is w = 0.9 in the MRJ state, while the value is w = 1.2 in the MDRP state. Then we investigate the evolutions of packing properties of perfect cylinders under densification and crystallization. We compare the different final packing states generated via the two methods with different compression rates and order constraints. In the densification procedure, we generate jammed and random packings of cylinders with various compression rates via the ASC and IMC method, respectively. When decreasing the compression rate, we find that the packing density increases but the optimal w remains the same in both methods. In the crystallization procedure, the order constraint in the IMC method is gradually released which means the degree of order in the packings is allowed to increase, and we find that the optimal w shifts from 1.2 to 0.9 while the packing density increases as well. Meanwhile, the random packings evolve into the jammed packings in the crystallization procedure which reflects the competition mechanism between the randomness and jamming. These results also indicate that the optimal w is solely related to the degree of order in the cylinder packings but not determined by the protocol or packing density. Furthermore, a uniform shape elongation effect on the random-packing densities of various shaped particles is found via a new proposed definition of the scaled aspect ratio. Finally, a rough linear relationship between the mean and standard deviation of the reduced Voronoi cell volumes is obtained only for the random packings. Our findings should lead to a better understanding toward the jammed and random packings and are helpful in guiding the granular material design.