Mean-field granocentric approach in 2D & 3D polydisperse, frictionless packings

Abstract

We have studied the contact network properties of two and three dimensional polydisperse, frictionless sphere packings at the random closed packing density through simulations. We observe universal correlations between particle size and contact number that are independent of the polydispersity of the packing. This allows us to formulate a mean field version of the granocentric model to predict the contact number distribution P (z). We find the predictions to be in good agreement with a wide range of discrete and continuous size distributions. The values of the two parameters that appear in the model are also independent of the polydispersity of the packing. Finally we look at the nearest neighbour spatial correlations to investigate the validity of the granocentric approach. We find that both particle size and contact number are anti-correlated which contrasts with the assumptions of the granocentric model. Despite this shortcoming, the correlations are sufficiently weak which explains the good approximation of P (z) obtained from the model.

Structure of marginally jammed polydisperse packings of frictionless spheres

“…This value is distinctively higher than the value for monodisperse packings observed in packing simulations, known to be of the order of ∼2% [30]. Using the probability of contact given by Eq.…”

“…For the probability to find a neighboring particle of a certain size p 2 (a), we explicitly consider the influence of size correlations between particles and their shell, previously neglected [26]. Packing simulations suggest [30] …”

“…(5), however, we find excellent agreement with packing simulations, both for monodisperse and polydisperse packings, as shown later in the text. For the numerical evaluation of the eGCM, a limited set of input parameters is taken from packing simulations [30]. The latter suggest isostatic values N J = 14.3 and φ J c = 0.62 for the jamming volume fraction of spheres in contact, independent of polydispersity [30,32].…”

“…For the numerical evaluation of the eGCM, a limited set of input parameters is taken from packing simulations [30]. The latter suggest isostatic values N J = 14.3 and φ J c = 0.62 for the jamming volume fraction of spheres in contact, independent of polydispersity [30,32]. Shells are filled up to a maximum solid angle max , treated as an adjustable parameter in the numerical evaluation of the model.…”

“…We generate 50 000 neighboring shells following the generic approach of Refs. [26] and [30]. Central particles with a contact number Z < 4 are considered as rattlers and all their neighbors are redistributed uniformly.Z J is obtained by taking the average over all central particles with Z 4.…”