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 $\varphi$, 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 $\varphi$ is increased to the jamming ${\varphi }_J$. From an analysis of Herschel-Bulkley rheology above jamming, we estimate ${\varphi }_J$ as a function of $\alpha$ and show that the variation of ${\varphi }_J$ 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.

arXiv comment25 pages, 28 figures, updated to published version; some figures added, some material rearranged

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• Shear-Driven Flow of Athermal, Frictionless, Spherocylinder Suspensions in Two Dimensions: Particle Rotations and Orientational Ordering
• Athermal shearing of frictionless cross-shaped particles of varying aspect ratio
• Extended $\mu (J)$-rheology for dense suspensions at oscillatory shear flows
• Exploring noisy Jeffery orbits: A combined Fokker-Planck and Langevin analysis in 2D and 3D
• Shear-Driven Flow of Athermal, Frictionless, Spherocylinder Suspensions in Two Dimensions: Spatial Structure and Correlations
• Depletion Forces in Athermally Sheared Mixtures of Frictionless Disks and Rods in Two Dimensions
• Distinct impacts of polar and nematic self-propulsion on active unjamming
• Packings of frictionless spherocylinders
• Orientational arrest in dense suspensions of elliptical particles under oscillatory shear flows
• Translational and rotational velocities in shear-driven jamming of ellipsoidal particles
• Start-up shear of spherocylinder packings: effect of friction