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 motion of a circular disk through an unbounded fluid satisfying Stokes equation. Four elementary motions are considered within the same mathematical framework: broadside translation, edgewise translation, in-plane rotation and out-of-plane rotation of a disk. Stokes equations are reduced to a set of dual integral expressions relating the velocity and traction in the plane of the disk. The dual integral equations are solved exactly for each motion and lead, in turn, to closed-form analytical expressions for the velocity and pressure fields. Although many of these results have been previously reported, the approach described here unifies the analysis of the four different motions and presents a straightforward solution technique.