Jamming of Bidisperse Frictional Spheres

TL;DR

This paper develops a model for the jamming density of bidisperse frictional spheres based on geometric arguments, validated by large-scale simulations, revealing nonmonotonic behavior and a sharp transition in rattler particles.

Contribution

It introduces a generalized model for the jamming density of bidisperse frictional spheres using monodisperse data, validated by extensive simulations across various parameters.

Findings

Jamming density varies nonmonotonically with small sphere fraction.

Maximum jamming density depends on friction coefficient.

Sharp transition in rattler particle fraction at optimal composition.

Abstract

By generalizing a geometric argument for frictionless spheres, a model is proposed for the jamming density $\phi_J$ of mechanically stable packings of bidisperse, frictional spheres. The monodisperse, $\mu_s$-dependent jamming density $\phi_J^{\mathrm{mono}}(\mu_s)$ is the only input required in the model, where $\mu_s$ is the coefficient of friction. The predictions of the model are validated by robust estimates of $\phi_J$ obtained from computer simulations of up to $10^7$ particles for a wide range of $\mu_s$, and size ratios up to 40:1. Although $\phi_J$ varies nonmonotonically with the volume fraction of small spheres $f^s$ for all $\mu_s$, its maximum value $\phi_{J,\mathrm{max}}$ at an optimal $f^{s}_{\mathrm{max}}$ are both $\mu_s$-dependent. The optimal $f^{s}_{\mathrm{max}}$ is characterized by a sharp transition in the fraction of small rattler particles.