Sedimentation of ellipsoidal particles near walls in viscous fluids: glancing, reversing, tumbling, and sliding

William H. Mitchell, Saverio E. Spagnolie

Published 2014-09-29Version 1

The sedimentation of a rigid particle near a wall in a viscous fluid has been studied numerically by many authors, but analytical solutions have been derived only in special cases, such as for spherical particles. In this paper the method of images is used to derive ordinary differential equations describing the sedimentation of arbitrarily oriented prolate and oblate ellipsoids at zero Reynolds number near a vertical or inclined plane wall. The reduced order system may be solved analytically for many special cases, and full trajectories are predicted which compare favorably with complete numerical simulations, performed using a novel double layer boundary integral formulation, a method of Stresslet images. The conditions under which the glancing and reversing trajectories, first observed by Russel et al. (1977), occur are studied for bodies of arbitrary aspect ratio. Several additional trajectories are also described: a periodic tumbling trajectory for nearly spherical bodies, a linearly stable sliding trajectory which appears when the wall is slightly inclined, and three-dimensional generalizations of these dynamics.