A GENERAL-APPROACH FOR ANALYZING THE ARBITRARY MOTION OF A CIRCULAR DISK IN A STOKES-FLOW

A concise analytic method is developed to investigate the arbitrary mo tion of a circular disk through an unbounded fluid satisfying Stokes e quation. Four elementary motions are considered within the same mathem atical framework: broadside translation, edgewise translation, in-plan e rotation and out-of-plane rotation of a disk. Stokes equations are r educed to a set of dual integral expressions relating the velocity and traction in the plane of the disk. The dual integral equations are so lved exactly for each motion and lead, in turn, to closed-form analyti cal expressions for the velocity and pressure fields. Although many of these results have been previously reported, the approach described h ere unifies the analysis of the four different motions and presents a straightforward solution technique.