Jamming of bidisperse frictional spheres

Ishan Srivastava,Jeremy B Lechman,Leonardo E Silbert,Joel T Clemmer,Gary S Grest,Scott A Roberts

doi:10.1103/physrevresearch.3.l032042

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.

Highlights

By generalizing a geometric argument for frictionless spheres, a model is proposed for the jamming density φJ of mechanically stable packings of bidisperse, frictional spheres
The equilibrium [24,35,36] and nonequilibrium [37] rheology of dense, bidisperse particulate materials. Beyond their fundamental jamming characteristics, a robust estimation of φJ for bidisperse particulate materials with realistic interparticle interactions is important towards advancing our knowledge of their mechanics and rheology
We propose a generalized Furnas model [38]—originally proposed for notionally placing small particles in the available volume left by large particles without reference to mechanical constraints or particle properties other than infinite size ratio—that accurately predicts μs-dependent φJ for large α, small deviations from the model are observed for frictional packings at f s < fms ax and very large α

Summary

Introduction

By generalizing a geometric argument for frictionless spheres, a model is proposed for the jamming density φJ of mechanically stable packings of bidisperse, frictional spheres. We use pressure-controlled simulations to simulate mechanically stable jammed packings of frictional, bidisperse spheres for a wide range of particle size ratios 2 α 40 and volume fraction of small particles 0 f s < 1.

Results

Conclusion