Rheology of dense granular materials

Abstract

Granular materials are frequently encountered in our daily lives and are widely used in several industrial processes. Characterising the flow of these materials has always proved challenging due to the lack of simple measurement techniques. Recent work in our group has shown that when granular materials are slowly sheared in a cylindrical Couette device, a standard rheometer accessory, they exhibit an anomalous rheological behaviour. It was shown that all components of stresses measured increased exponentially with depth. In comparison, the stress for a static column of grains saturates with depth. It was further shown that this behaviour could be explained by the presence of a toroidal vortex that spans the entire system. It was proposed that such a vortex was driven by shear-induced dilation or dilatancy, a property of granular materials that has no analogue in fluids. Dilatancy is the decrease in density is regions of shear and is a consequence of rigid granular particles requiring free volume to move. In this work, we ask if dilation is indeed the origin of this vortex and the anomalous stress profile. We test the validity of these claims, first by replicating and validating these results and then checking for the robustness of the vortex flow. We then ask how general the effect of dilation is by testing a more complicated flow namely, the flow in a split-bottom Couette device, a variation of the cylindrical Couette device. In this device, shear originates from the boundary between a moving and stationary base plate. We then show that we get a variety of dilation-driven vortices that have similar features as the vortex observed in the cylindrical Couette device. Despite this effect that dilatancy has on generating these vortices, all constitutive models treat steady granular flows as incompressible and, thus, ignore dilation. We therefore propose an extension to a well-known constitutive model for slow granular flows, the critical state plasticity model. We propose that the deformation at a point is depend...