Velocity depth profile of granular matter in a horizontal rotating drum

Using MRI velocimetry, we verify that the velocity depth profile of the flowing layer near the axial center of a half-filled 3D drum has the form Vm[1 − (r/r0)2]-Ω r, where r is the depth measured from the cylinder center, except very close to the free surface where it lies below the quadratic form. We confirm that this deviation is due in part to particles reaching the surface with large components of their velocity in the azimuthal direction. We used a 3D cylinder with a radial “paddle” placed at approximately the dynamic angle of repose, covering the top third of the flow, so as to null any azimuthal velocity. It was found that the deviation from the quadratic form was reduced by the presence of the paddle when the comparison is made at the same solid body rotation rate, at the same free surface velocity, and with the paddle placed at different positions, so long as it makes good contact with the surface. Thus, we conclude that a quadratic velocity depth profile may be a fundamental property of granular shear flows in this geometry, when the sole effect of the cylinder rotation is to transport the particles from the end of the flow to the beginning without imparting velocity perpendicular to the flow.