Shear-Driven Flow of Athermal, Frictionless, Spherocylinder Suspensions in Two Dimensions: Stress, Jamming, and Contacts

Abstract

We use numerical simulations to study the flow of a bidisperse mixture of athermal, frictionless, soft-core two dimensional spherocylinders driven in uniform steady state shear. Energy dissipation is via a viscous drag with respect to a uniformly sheared host fluid, giving a model for a non-Brownian suspension with a Newtonian rheology. We study pressure $p$ and deviatoric shear stress $\sigma$ as a function of packing fraction $\phi$, strain rate $\dot\gamma$, and a parameter $\alpha$ that measures the asphericity of the particles. We consider the anisotropy of the stress tensor, the macroscopic friction $\mu=\sigma/p$, and the divergence of the transport coefficient $\eta_p=p/\dot\gamma$ as $\phi$ is increased to the jamming $\phi_J$. From an analysis of Herschel-Bulkley rheology above jamming, we estimate $\phi_J$ as a function of $\alpha$ and show that the variation of $\phi_J$ with $\alpha$ is the main cause for differences in rheology as $\alpha$ is varied. However a detailed scaling analysis of the divergence of $\eta_p$ for our most elongated particles suggests that the jamming transition of spherocylinders may be in a different universality class than that of circular disks. We compute the number of contacts per particle $Z$ in the system and show that at jamming $Z_J$ is a non-monotonic function of $\alpha$ that is always smaller than the isostatic value. We measure the probability distribution of contacts per unit surface length $\mathcal{P}(\vartheta)$ at polar angle $\vartheta$ with respect to the spherocylinder spine, and find that as $\alpha\to 0$ this distribution seems to diverge at $\vartheta=\pi/2$, giving a finite limiting probability for contacts on the vanishingly small flat sides of the spherocylinder. Finally we consider the variation of the average contact force as a function of location on the particle surface.