Radical tessellation of the packing of ternary mixtures of spheres

The packing of ternary mixtures of spheres with size ratios 24.4/11.6/6.4 is simulated by means of the discrete element method. The packing structure is analyzed by the so called radical tessellation which is an extension of the well-established Voronoi tessellation. The topological and metric properties of radical polyhedra are quantified as a function of the volume fractions of this ternary packing system. These properties include the number of edges, area and perimeter per radical polyhedron face, and the number of faces, surface area and volume per radical polyhedron. The properties of each component of a mixture are shown to be strongly dependent on the volume fractions. Their average values can be quantified by a cubic polynomial equation. The results should be useful for understanding the packing structures of multi-sized particles.