(394f) Ellipsoidal Microhydrodynamics: New Velocity Representations for Stokes Flow in Ellipsoidal Geometries

The ellipsoid and its degenerate version (the spheroid) is a most convenient starting point for the study of nonspherical effects in many physical systems including fluid mechanics. The classical work for the steady translational motion of an ellipsoid in Stokes flow dates to Oberbeck's (1876) solution, but more recently, a new velocity representation for the ellipsoidal geometry has been discovered thanks to an eigenfunction analysis of the Stokes double layer operator, with special linkages to Brenner's (1960s) papers on Stokes flow past an ellipsoid. The power of the new approach will be illustrated with examples from biofluid dynamics and colloidal hydrodynamics.