Transient analysis of granular materials flowing over an inclined plane.*

The popular inertial number based rheology of dense granular flows as proposed by Jop et. al. (2006) [Nature. 441, 727–730] is able to describe the flow behavior in various configurations. In comparison to the steady-state flow behavior, relatively little attention has been given to the transient study of the granular flow. In this study, we numerically solve the unsteady state momentum balance equations along with a viscoplastic rheological constitutive model given by the μ - I rheology and predict the transient flow profiles of the velocity, solids fraction, inertial number, shear stress, pressure, and shear rate. We also compute these flow properties by performing two-dimensional discrete element method (DEM) simulations of slightly polydisperse particles flowing down a rough and bumpy inclined surface. At any given inclination, the particles which were initially at a settled state start to flow under the influence of gravity. The predicted profiles obtained by using the unsteady state momentum balance equations from the numerical results at different instants are compared with the DEM simulations. The validity of the numerical method for low as well as moderate inertial numbers will be discussed in this work. The applicability of the inertial number based μ - I rheology at the moderate and high inertial numbers and its detailed study will be the main focus of this work.