Estimating random close packing in polydisperse and bidisperse hard spheres via an equilibrium model of crowding.

We show that an analogy between crowding in fluid and jammed phases of hard spheres captures the density dependence of the kissing number for a family of numerically generated jammed states. We extend this analogy to jams of mixtures of hard spheres in d = 3 dimensions and, thus, obtain an estimate of the random close packing volume fraction, ϕRCP, as a function of size polydispersity. We first consider mixtures of particle sizes with discrete distributions. For binary systems, we show agreement between our predictions and simulations using both our own results and results reported in previous studies, as well as agreement with recent experiments from the literature. We then apply our approach to systems with continuous polydispersity using three different particle size distributions, namely, the log-normal, Gamma, and truncated power-law distributions. In all cases, we observe agreement between our theoretical findings and numerical results up to rather large polydispersities for all particle size distributions when using as reference our own simulations and results from the literature. In particular, we find ϕRCP to increase monotonically with the relative standard deviation, sσ, of the distribution and to saturate at a value that always remains below 1. A perturbative expansion yields a closed-form expression for ϕRCP that quantitatively captures a distribution-independent regime for sσ < 0.5. Beyond that regime, we show that the gradual loss in agreement is tied to the growth of the skewness of size distributions.

Shear flow of non-Brownian rod-sphere mixtures near jamming.

We use the discrete element method, taking particle contact and hydrodynamic lubrication into account, to unveil the shear rheology of suspensions of frictionless non-Brownian rods in the dense packing fraction regime. We find that, analogously to the random close packing volume fraction, the shear-driven jamming point of this system varies in a nonmonotonic fashion as a function of the rod aspect ratio. The latter strongly influences how the addition of rodlike particles affects the rheological response of a suspension of frictionless non-Brownian spheres to an external shear flow. At fixed values of the total (rods plus spheres) packing fraction, the viscosity of the suspension is reduced by the addition of "short"(≤2) rods but is instead increased by the addition of "long"(≥2) rods. A mechanistic interpretation is provided in terms of packing and excluded-volume arguments.