Evaluation of weighted Voronoi decompositions of physicochemical ensembles

Voronoi diagrams are widely used to model disperse systems such as foams, powders, polycrystals and atoms in the classical limit. Voronoi tessellations partition the continuous phase into compartments, or cells, that encompass all space closer to the assigning dispersed object than any other in the system. To account for heterogeneity in object size, weights are applied to avoid unphysical partitioning across non-contacting objects. Power and additive weighting are the most common weighting schemes, wherein power is more computationally tractable but additive weighting correlates more directly with size. In general, the two schemes produce distinct spatial decompositions for any non-monodisperse system. To calibrate the divergent volumetric metrics from the two schemes, and to gain physical insight into their divergence, we compared power and additively weighted Voronoi diagrams of polydisperse ensembles representing physically relevant ranges of polydispersity, density, and overlap. When tested against experimental distributions of gas foams, the results related their divergent power and additively weighted decompositions to the polydispersity of their particle size distributions. Geometric analysis of the Voronoi cells implicated the subpopulation of small objects as the primary contributors to the divergence through their preferential assignment of larger, aspherical power cells relative to their additively weighted counterparts.