Packing and percolation of poly-disperse discs and spheres

TL;DR

This paper investigates how poly-dispersity affects packing density and percolation thresholds in disc and sphere systems, revealing non-monotonic packing fractions and monotonic percolation behavior with increasing size diversity.

Contribution

It demonstrates that poly-dispersity causes a minimum in packing fraction and a monotonic change in percolation thresholds, providing new insights into disordered packing and connectivity.

Findings

Packing fraction has a minimum at certain poly-dispersity levels.

Percolation thresholds vary monotonically with poly-dispersity.

Long-bond neighbors increase near the minimum packing fraction.

Abstract

For the binary discs packed in two dimensions, the packing fraction of disc assembly becomes lower than that of the monodisperse system when the size ratio is close to unity. We show that the suppressed packing fraction is caused by an increase of the adjacent neighbours with long bonds where the adjacent neighbours is defined on the basis of the Laguerre (radical) tessellation. For the poly-disperse systems in two and three dimensions, the packing fraction is shown to have a minimuma as a function of the poly-dispersity. Percolation process in the densely packed discs and spheres is also studied. The critical area (volume) fraction in two (three) dimensions is shown to be a monotonically increasing (decreasing) function of the poly-dispersity.