Application of the Voronoï tessellation to study transport and segregation of grains inside 2D and 3D packings of spheres

Abstract

This article provides a simple method to simulate the transport of a small bead through a static granular medium as a random walk on a network. This kind of displacement is strongly related to the geometry of the porous structure. A way to map the interparticle space is to calculate the Voronoi tessellation of the packing whose edges describe the network of pores of the medium. Then, the calculation of the probabilities to use each bond and a Monte-Carlo method for the choice of them, can simulate the displacement of the sphere. We introduce this technique for the inter-particle percolation of a fine particle through a packing of monosize spheres. We compare our numerical simulation with experiments performed in our laboratory. Then this technique is extended to the surface segregation. For the two kinds of segregation, we study the transverse diffusion and obtain a good agreement with experimental results. That our numerical simulation based on a rigorous geometric analysis of the medium is in agreement with inter-particle percolation and surface segregation experiments shows the importance of the study of the geometry of granular materials.