Normal stress effects in the gravity driven flow of granular materials

TL;DR

This study investigates the gravity-driven flow of granular materials between inclined planes, introducing a modified stress tensor that accounts for particle compactness and normal stress effects, impacting flow behavior.

Contribution

It proposes a new isotropic stress component related to particle packing, enhancing the modeling of granular flow dynamics under gravity.

Findings

The new stress tensor significantly influences velocity profiles.

Normal stress effects alter the volume fraction distribution.

The model prevents particle over-compaction beyond maximum packing.

Abstract

In this paper, we study the fully developed gravity-driven flow of granular materials between two inclined planes. We assume that the granular materials can be represented by a modified form of the second-grade fluid where the viscosity depends on the shear rate and volume fraction and the normal stress coefficients depend on the volume fraction. We also propose a new isotropic (spherical) part of the stress tensor which can be related to the compactness of the (rigid) particles. This new term ensures that the rigid solid particles cannot be compacted beyond a point, namely when the volume fraction has reached the critical/maximum packing value. The numerical results indicate that the newly proposed stress tensor has an obvious and physically meaningful effects on both the velocity and the volume fraction fields.