The motion of a prolate ellipsoid in a rotating Stokes flow

Abstract

Results are presented from experimental investigations into the motion of a heavy ellipsoid in a horizontal rotating cylinder, which has been completely filled with highly viscous fluid. The motion can be conveniently classified using the ratio between the maximum radius of curvature of the ellipsoid κmaxand the radius of the drumRd. If κmax<Rdthe ellipsoid adopts a fixed position adjacent to the rising wall for a given cylinder rotation rate. The dependence of this position on wall speed is, surprisingly, independent of the ellipsoid's length, and a Stokes flow model has been developed which predicts both this independence and the speed for the limiting case of an ellipsoid adjacent to a vertical wall. If κmax<Rdthe ellipsoid must tilt in order to maintain the maximum surface area in close proximity to the wall. Once tilted, a component of the viscous drag acts to laterally translate the ellipsoid from end to end of the drum. The ellipsoid with κmax=Rdadopts a series of fixed positions for most drum rotational rates but, between two regions of fixed-point behaviour, it undergoes a transition to oscillatory motion.