Drag and lift on rotating vanes in granular beds

We have performed systematic experiments on vane intruders of different sizes and aspect ratios that are immersed and slowly rotated in beds of monodisperse glass beads of different diameters. We find that the torque and lift force on the vane increase with bead size. The measured torque on the rotating vanes follows a scaling behavior that depends on the effective immersion depth and the effective vane diameter. The torque increases with the square of the effective immersion depth and the square of the effective vane diameter, and closely resembles the scaling behavior previously reported for the torque on rotating cylinders. We also find that the vertical lift forces have a supralinear dependence on the effective immersion depth, and qualitatively resemble the plunging forces produced when an intruder is slowly immersed into beds of glass beads.