Random fluctuations and oscillatory variations of drag forces on vanes rotating in granular beds

摘要

The torque τ and lift F on a slowly rotating vane partially immersed in a monodisperse bed of glass beads can be separated into the product of three distinct components. The fundamental component is the time average and has a power law dependence on immersion depth (SOLLER R. and KOEHLER S. A. Phys. Rev. E, 74 (2006) 021305). The second component is random temporal fluctuations of the drag about their average values, τ/<τ> and F/. These ratios have log-normal distributions whose width scales with system granularity, G = d/D, which is the ratio of bead-to-vane diameter. For smooth container bottoms, the vane's rotation causes layering that extends upwards from the container bottom. This results in oscillations of the torque and lift, which diminish in strength with increasing vane height, and can persist up to 20 bead diameters.