Jamming of Bidisperse Frictional Spheres

Abstract

By generalizing a geometric argument for frictionless spheres, a model is proposed for the jamming density ${\varphi }_J$ of mechanically stable packings of bidisperse, frictional spheres. The monodisperse, ${\mu }_s$-dependent jamming density ${\varphi }_J^{\mathrm{mono}}({\mu }_s)$ 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 ${\varphi }_J$ 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 ${\varphi }_J$ varies nonmonotonically with the volume fraction of small spheres $f^s$ for all ${\mu }_s$, its maximum value ${\varphi }_{J,\max }$ at an optimal $f_{\max }^s$ are both ${\mu }_s$-dependent. The optimal $f_{\max }^s$ is characterized by a sharp transition in the fraction of small rattler particles.

arXiv commentAccepted version; 5 pages, 4 figures

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• Flow and Arrest in Stressed Granular Materials
• Universal behavior in fragmenting brittle, isotropic solids across material properties
• Molecular Dynamics Simulations of Binary Sphere Mixtures
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