  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.
