Steady granular flow in a rotating drum: A theoretical nonlocal model for characterizing stress, velocity, and packing fraction profiles, encompassing grain shape effects from convex to highly concave
Weiyi Wang, Jonathan Barés, Mathieu Renouf, Émilien Azéma
Abstract
In this work, we investigate the effect of particle shape, ranging from spherical to highly concave, on steady flows in a rotating drum, a system that facilitates a continuous transition from a jamming state at greater depths to an unjamming state at shallower regions. We develop an analytical model to elucidate granular behavior within the rotating drum: (i) First, by decomposing the shear stress, we reconcile the discrepancy between simulation data and theoretical predictions, establishing a relationship with the angle of repose. (ii) Second, we extend the generalized Bagnold scaling, coupled with a nonlocal fluidity relation based on packing fraction, providing a framework for a correlation between shear stress, shear rate, and packing fraction. Additionally, we introduce a characteristic length to quantify the influence of particle shape and drum speed. This analytical model offers explicit functional forms for physical quantity profiles, which are validated experimentally in a thin rotating drum and numerically in a two-dimensional rotating drum. Our results demonstrate that this model accurately describes the change in velocity from the bottom of the drum to the free surface. Moreover, for different shapes of particle and drum speeds, the characteristic length captures the interplay between shear stress, shear rate, and the variation of packing fraction. Published by the American Physical Society 2024