Scaling laws for velocity profile of granular flow in rotating drums

We theoretically and numerically investigate the steady flow of two-dimensional granular materials in a rotating drum using the discrete element method and a continuum model with the μ(I)-rheology. The velocity fields obtained from both methods are in quantitative agreement. The granular flow exhibits two distinct regions: a surface flow layer and a static flow regime corresponding to rigid rotation near the drum bottom. The thickness of the surface flow layer increases with the drum diameter and shows a weak dependence on the angular velocity of the drum. Using dimensional analysis of the continuum equations, we analytically identify nondimensional parameters for the velocity profile and the surface flow layer thickness, which lead to scaling laws characterizing the flow in rotating drums with low Froude number and large system size. The validity of the scaling laws is confirmed by numerical simulations.