Sedimentation of two arbitrarily oriented spheroids in a viscous fluid

The translational and rotational motions of two prolate spheroids sedimenting in a viscous fluid have been determined by the method of reflections. No restrictions are imposed on the spheroid orientations or relative sizes. As is the case in many mobility problems, the method converged rapidly for all but almost touching configurations. The results extend earlier work on special cases such as Wakiya's work on horizontal orientations and agree with Gluckman, et. al., and Liao and Krueger's boundary collocation solution of axisymmetric problems. Analysis of sedimentation with inclined axes and mirror symmetric geometry reveal both periodic and single-encounter particle trajectories. The calculation of the separatrix between the two behaviors required the use of the higher reflections introduced in this work.