Voronoi tesselation analysis of sets of randomly placed finite-size spheres

TL;DR

This paper investigates how finite particle size influences the spatial distribution characteristics of randomly placed spheres, using Monte Carlo simulations and Voronoi tessellations to provide insights for analyzing particulate systems.

Contribution

It quantifies the effects of finite particle size on Voronoi volume distributions and offers guidelines for using RPP data as a reference in particulate system analysis.

Findings

Standard deviation of Voronoi volumes decreases with solid volume fraction.

Exponential approximation of deviation from point set data.

Finite domain size affects particle distribution analysis.

Abstract

The purpose of this note is to clarify the effect of the finite size of spherical particles upon the characteristics of their spatial distribution through a random Poisson process (RPP). This information is of special interest when using RPP data as a reference for the analysis of the spatial structure of a given (non-RPP) particulate system, in which case ignoring finite-size effects upon the former may yield misleading conclusions. We perform Monte Carlo simulations in triply-periodic spatial domains, and then analyze the particle-centered Voronoi tesselations for solid volume fractions ranging from 10^(-5) to 0.3. We show that the standard-deviation of these volumes decreases with the solid volume fraction, the deviation from the value of point sets being reasonably approximated by an exponential function. As can be expected, the domain size for which the random assemblies of finite-size particles are generated has a constraining effect if the number of particles per realization is chosen too small. This effect is quantified, and recommendations are given. We have also revisited the case of random point sets (i.e. the limit of vanishing particle diameter), for which we have confirmed the accuracy of the earlier data by Tanemura [Forma, 18(4):221-247, 2003].