Percolation of binary disk systems: Modeling and theory

Abstract

The dispersion and connectivity of particles with a high degree of polydispersity is relevant to problems involving composite material properties and reaction decomposition prediction and has been the subject of much study in the literature. This work utilizes Monte Carlo models to predict percolation thresholds for a two-dimensional systems containing disks of two different radii. Monte Carlo simulations and spanning probability are used to extend prior models into regions of higher polydispersity than those previously considered. A correlation to predict the percolation threshold for binary disk systems is proposed based on the extended dataset presented in this work and compared to previously published correlations. A set of boundary conditions necessary for a good fit is presented, and a condition for maximizing percolation threshold for binary disk systems is suggested.

Multi-scale modeling of the chloride diffusivity and the elasticity of Portland cement paste

“…Statistical physical studies confirm that the connectivity of the phases, characterized by their percolation thresholds, strongly depends on the shape of the particles [30][31][32][33] but also indicate that it depends on the particles size distribution (PSD) [34,35], which is not accounted for by the self-consistent scheme. Indeed, while statistical physical studies provide accurate values of the percolation thresholds on explicit morphological models, the self-consistent scheme in which the morphology is implicitly accounted for provides only "poor man's percolation" [33].…”

Evaluation of Effective Heat Transport and Temperature Gradients in Thermally Anisotropic Particulate Arrangements

“…In binary mixtures, cluster formation is always present. Therefore, percolation theory directly links the microstructure and macroscopic properties of the material . A significant concept in this context is the percolation threshold.…”