Radical tessellation of the packing of spheres with a log-normal size distribution.

The packing of particles with a log-normal size distribution is studied by means of the discrete element method. The packing structures are analyzed in terms of the topological properties such as the number of faces per radical polyhedron and the number of edges per face, and the metric properties such as the perimeter and area per face and the perimeter, area, and volume per radical polyhedron, obtained from the radical tessellation. The effect of the geometric standard deviation in the log-normal distribution on these properties is quantified. It is shown that when the size distribution gets wider, the packing becomes denser; thus the radical tessellation of a particle has decreased topological and metric properties. The quantitative relationships obtained should be useful in the modeling and analysis of structural properties such as effective thermal conductivity and permeability.

Characterization of interparticle forces in the packing of cohesive fine particles.

We numerically investigate force structures in the packing of fine cohesive particles using the discrete element method. By changing the particle size and therefore the van der Waals force, the effect of cohesion on the normal contact force and the total normal force, which is the sum of the normal contact forces and the van der Waals forces, is analyzed. It is shown that, with decreasing particle size, the normal contact forces become more uniform and have a narrower and more symmetric distribution, while the distributions of the total normal forces widen. Spatial correlation between the interparticle forces exists for the packing of coarse noncohesive particles. As the particle size decreases, this correlation becomes weaker for the contact forces but stronger for the total normal forces. A comparison between the effective weight of particles and the internal force structure suggests that there are differences between the particle-particle and particle-wall forces. The bimodal distribution of the effective weight indicates that there may exist two phases in the packings when cohesion is present, governed by the compressive and tensile stresses.

Role of interparticle forces in the formation of random loose packing.

We present a physical and numerical study of the settling of uniform spheres in liquids and show that interparticle forces play a critical role in forming the so-called random loose packing (RLP). Different packing conditions give different interparticle forces and, hence, different RLP. Two types of interparticle forces are identified: process dependent and process independent. The van der Waals force, as the major cohesive force in the present study, plays a critical role in effecting the process-dependent forces such as drag and lift forces. An equation is formulated to describe the relationship between the macroscopic packing fraction and microscopic interparticle forces in a packing. We argue there is no lowest packing fraction for a mechanically stable RLP; hence, the packing fractions of RLP can range from 0 to 0.64 depending on the cohesive and frictional conditions between particles.

Pore structure of the packing of fine particles.

This paper presents a numerical study of the pore structure of fine particles. By means of granular dynamics simulation, packings of mono-sized particles ranging from 1 to 1000 microm are constructed. Our results show that packing density varies with particle size due to the effect of the cohesive van der Waals force. Pores and their connectivity are then analysed in terms of Delaunay tessellation. The geometries of the pores are represented by the size and shape of Delaunay cells and quantified as a function of packing density or particle size. It shows that the cell size decreases and the cell shape becomes more spherical with increasing packing density. A general correlation exists between the size and shape of cells: the larger the cell size relative to particle size, the more spherical the cell shape. This correlation, however, becomes weaker as packing density decreases. The connectivity between pores is represented by throat size and channel length. With decreasing packing density, the throat size increases and the channel length decreases. The pore scale information would be useful to understand and model the transport and mechanical properties of porous media.

Self-assembly of particles for densest packing by mechanical vibration.

It is shown that by properly controlling vibrational and charging conditions, the transition from disordered to ordered, densest packing of particles can be obtained consistently. The method applies to both spherical and nonspherical particles. For spheres, face centered cubic packing with different orientations can be achieved by monitoring the vibration amplitude and frequency, and the structure of the bottom layer, in particular. The resultant force structures are ordered but do not necessarily correspond to the packing structures fully. The implications of the findings are also discussed.

Micromechanical simulation and analysis of one-dimensional vibratory sphere packing.

We present a numerical method capable of reproducing the densification process from the so-called random loose to dense packing of uniform spheres under vertical vibration. The effects of vibration amplitude and frequency are quantified, and the random close packing is shown to be achieved only if both parameters are properly controlled. Two densification mechanisms are identified: pushing filling by which the contact between spheres is maintained and jumping filling by which the contact between particles is periodically broken. In general, pushing filling occurs when the vibration intensity is low and jumping filling becomes dominant when the vibration intensity is high.

Packing structure of cohesive spheres.

This paper presents the first set of measured data to probe into the loose packing structure of wet particles featured with large pores, aggregated and chain-connected particles. The structure is also analyzed in terms of radial distribution function and coordination number, and compared with that of the random dense packing.

Voronoi tessellation of the packing of fine uniform spheres.

The packing of uniform fine spherical particles ranging from 1 to 1000 microm has been simulated by means of discrete particle simulation. The packing structure is analyzed, facilitated by the well established Voronoi tessellation. The topological and metric properties of Voronoi polyhedra are quantified as a function of particle size and packing density. The results show that as particle size or packing density decreases, (i) the average face number of Voronoi polyhedra decreases, and the distributions of face number and edge number become broader and more asymmetric; (ii) the average perimeter and area of polyhedra increase, and the distributions of polyhedron surface area and volume become more flat and can be described by the log-normal distribution. The topological and metric properties depicted for the packing of fine particles differ either quantitatively or qualitatively from those reported in the literature although they all can be related to packing density. In particular, our results show that the average sphericity coefficient of Voronoi polyhedra varies with packing density, and although Aboav-Weaire's law is generally applicable, Lewis's law is not valid when packing density is low, which are contrary to the previous findings for other packing systems.