Creeping granular motion under variable gravity levels

Abstract

In a rotating tumbler that is more than one-half filled with a granular material, a core of material forms that should ideally rotate with the tumbler. However, the core rotates slightly faster than the tumbler (precession) and decreases in size (erosion). The precession and erosion of the core provide a measure of the creeping granular motion that occurs beneath a continuously flowing flat surface layer. Since the effect of gravity on the subsurface flow has not been explored, experiments were performed in a 63% to 83% full granular tumbler mounted in a large centrifuge that can provide very high g-levels. Two colors of 0.5 mm glass beads were filled side by side to mark a vertical line in the 45 mm radius quasi-two-dimensional tumbler. The rotation of the core with respect to the tumbler (precession) and the decrease in the size of the core (erosion) were monitored over 250 tumbler revolutions at accelerations between 1g and 12g. The flowing layer thickness is essentially independent of the g-level for identical Froude numbers, and the shear rate in the flowing layer increases with increasing g-level. The degree of core precession increases with the g-level, while the core erosion is essentially independent of the g-level. Based on a theory for core precession and erosion, the increased precession is likely a consequence of the higher shear rate. Core erosion, on the other hand, is related to the creep region decay constant, which is connected with slow diffusion in the bed and unaffected by gravity.