Secondary flows in slow granular flows

Abstract

Recent findings by Krishnaraj and Nott [1] show that a granular material sheared in a cylindrical Couette cell at low shear rates forms a single secondary vortex. The vortex spans the entire width of the Couette cell and has a sense opposite to the centrifugally driven Taylor-Couette vortex in a Newtonian fluid – it is in fact shown to be driven by shear-induced dilation. Krishnaraj and Nott [1] show that the vortex also explains a Theological anomaly observed earlier [2], wherein all components of the stress on the outer cylinder increase nearly exponentially with depth from the free surface. In this study, we test the robustness of this vortex by varying the parameters of the grain contact model. We show that the presence of a free surface is not essential for the formation of the secondary vortex. The vortex forms even when a rigid plate of finite weight confines the granular column at the top. We find that as the shear rate is increased, an additional centrifugally-driven vortex appears. This new vortex keeps growing until, at Savage number close to one, the dilation-driven vortex disappears. We also present the variation of the wall stresses at the inner cylinder with depth. Finally, we argue that the secondary flow can also help to understand the rheological behaviour observed in geometries such as the split-bottom Couette device [3].