Equivalent packing diameter of bidisperse spheres

The equivalent packing diameter (De) is the key parameter to evaluate the relative packing size of non-spherical particles to spheres. In this work, we extend the concept of De to bidisperse spheres. We generate mixtures of monodisperse and bidisperse spheres via the Lubachevsky-Stillinger algorithm, and determine the De for bidisperse spheres by minimizing the packing density of mixtures. We verify the linear superposition state of the specific volume (the reciprocal of packing density) of the mixtures under De, and propose an empirical formula to estimate the De of bidisperse spheres. We further verify that mixtures of two species of bidisperse spheres with equal De manifest the linear superposition state, as well as bidisperse spheres and non-spherical particles having the same De,which indicates that non-spherical particles can be mutually equivalent to bidisperse spheres in the sense of packing density.