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.