Jamming of bidisperse frictional spheres

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(mono)(J) (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,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.