Scaling laws for velocity profile of granular flow in rotating drums

Abstract

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 $\mu (I)$-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 characterising the flow in rotating drums with low Froude number and large system size. The validity of the scaling laws is confirmed by numerical simulations.

References in corpus (13)

• On dense granular flows
• A constitutive law for dense granular flows
• Rheophysics of dense granular materials : Discrete simulation of plane shear flows
• Granular flow down an inclined plane: Bagnold scaling and rheology
• Frictionless bead packs have macroscopic friction, but no dilatancy
• Boundary Effects on the Angle of Repose in Rotating Cylinders
• Power-law scaling in granular rheology across flow geometries
• Experimental study of granular surface flows via a fast camera: a continuous description
• Rheology of surface granular flows
• Granular Flows in a Rotating Drum: the Scaling Law between Velocity and Thickness of the Flow
• Compressibility regularizes the "$\mu (I)$" rheology for granular flows
• Numerical simulation of 2D steady granular flows in rotating drum: On surface flows rheology
• Relevance of visco-plastic theory in a multi-directional inhomogeneous granular flow