New constitutive equations for the rapid flow of granular materials—II

This paper compliments a previous paper, (J. Non-Newtonian Fluid Mech.,9(1981) 147), which discussed new constitutive equations for rapid collisionally maintained flow of granular materials as a non-Newtonian microfluid in which the gradient of microrotation played an important role as a kinematic variable. In this article we discuss another variation of such constitutive equations; one for which we do not consider the effects of gradients of the mean microrotation of grains. Derived are expressions for the dispersive normal and shear stresses for a plane shear rapid flow of a granular material in the presence of intergranular slip and friction. These expressions reduce to classical results if friction is set equal to zero. A graph of the variation of stresses versus the friction factor is also presented which reveals a kind of choking phenomenon at larger values of μ_k.