Rheology of dense granular flows in two dimensions: Comparison of fully two-dimensional flows to unidirectional shear flow

Abstract

This work utilizes soft-particle discrete element simulations to examine the rheology of steady two-dimensional granular flows with reference to a unidirectional shear flow, which has been extensively employed for validating the local visco-plastic model of Jop et al. [Nature 441, 727--730 (2006)]. The $\mu$-$I$ scaling proposed by Jop et al. is found to be valid in both two-dimensional and unidirectional flows, as observed in previous studies, however, each flow type results in a different curve. Here $\mu$, ratio of the shear stress magnitude to the pressure, is the friction coefficient and $I$ is the dimensionless inertial number, which is proportional to the ratio of the magnitude of the rate of strain tensor, $\dot{\gamma }$, to the square root of the pressure. The friction coefficient is found not to scale in a simple way with the flow classification parameter $\psi$, which characterizes the local flow type. All the data collapse to a single curve using the scaling proposed by Zhang and Kamrin [Phys. Rev. Lett. 118, 058001 (2017)], in which the scaled granular fluidity ($f=1/(\mu T)$, where $T\propto u/\dot{\gamma }$ and $u$ is the fluctuation velocity) is found to depend only on the solid fraction $\varphi$. The data for variation of $\varphi$ with inertial number $I$ collapse to a single curve for all the flows.

6 pages, 6 figures

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Cited by in corpus (5)

• Viscometric flow of dense granular materials under controlled pressure and shear stress
• Analysis of granular rheology in a quasi-two-dimensional slow flow by means of discrete element method based simulations
• Mesoscopic model for soft flowing systems with tunable viscosity ratio
• Velocity scaling in the region of orifice influence in silo draining under gravity
• Interplay between hysteresis and nonlocality during onset and arrest of flow in granular materials