Jamming of bidisperse frictional spheres

Abstract

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