Application of the compressible -dependent rheology to chute and shear flow instabilities

Abstract

We consider the instability properties of dense granular flow in inclined plane and plane shear geometries as tests for the compressible inertial-dependent rheology. The model, which is a recent generalisation of the incompressible $\unicode[STIX]{x1D707}(I)$ rheology, constitutes a hydrodynamical description of dense granular flow which allows for variability in the solids volume fraction. We perform a full linear stability analysis of the model and compare its predictions to existing experimental data for glass beads on an inclined plane and discrete element simulations of plane shear in the absence of gravity. In the case of the former, we demonstrate that the compressible model can quantitatively predict the instability properties observed experimentally, and, in particular, we find that it performs better than its incompressible counterpart. For the latter, the qualitative behaviour of the plane shear instability is also well captured by the compressible model.

DEM simulation of dense granular flows in a vane shear cell: Kinematics and rheological laws

“…The new formulation reconciled the observation of particle motion when µ < µ s , but it does not recover another observation of the µ-I relation in annular shear cells, which show that the µ-I relation is not one-to-one in the intermediate regime [25]. In the framework of compressible I-dependent rheology [26,21,27], new rheological relations were built by incorporating two additional parameters: solid fraction and pressure. Although granular flow physics were well predicted in their flow geometries, the determinations of the rheological formulations were more out of stability consideration.…”

Transient Evolution of Rheological Properties of Dense Granular Inertial Flow Under Plane Shear

“…The granular flow has motivated many studies over the past decades, since the rheological properties of dense granular materials play an important role in various natural phenomena and industrial applications such as geographical faults, powder metallurgy, three-body friction, and particle flow lubrication [4][5][6][7][8][9][10]. Generally, three different granular flow regimes are categorized according to the flow state, including quasi-static regime, inertial regime, and collisional regime [11][12][13][14]. In the inertial regime, when a dense granular system is subjected to continuous shear, a local flow near the boundary is first generated after the initial static equilibrium is broken, and gradually a global flow will be achieved and maintained stable finally.…”