  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 for special cases such as the motion of spherical particles. In this paper
the method of images is used to derive simple ordinary differential equations
describing the sedimentation of arbitrarily oriented prolate and oblate
spheroids at zero Reynolds number near a vertical or inclined plane wall. The
differential equations may be solved analytically in many situations, and full
trajectories are predicted which compare favorably with complete numerical
simulations. The simulations are 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 glancing, reversing,
and wobbling.
