Statistics for simulated assemblies of particles from mathematical models

Abstract

This study examines particle statistics using simulated particle assemblies derived from mathematical models. This approach serves as a complement to investigations that analyze samples of real particles to assess the accuracy of measurement and statistical methods. Three mathematical particle models, all based on tessellations of three-dimensional space, including the well-known Voronoi tessellation, are employed to generate random convex polyhedra. A key advantage of this approach is that the true statistical properties of the particles and particle assemblies are well understood, allowing for a realistic evaluation of statistical methods. Furthermore, the analyses performed can be easily replicated or verified by other researchers in parallel studies. The approach is applied to the evaluation of two commonly used statistical methods: estimating the volume-weighted particle size distribution function from image analysis data, and estimating the specific surface area when particle volumes are measured. The simulation results indicate that image analysis methods yield accurate results for particle size distributions. Additionally, estimating the specific surface area using particle size distributions produces acceptable results when incorporating the mean sphericity of the aggregates, without accounting for particle roughness, which is not a significant factor for the particles under consideration.