Singularity solutions for ellipsoids in low-Reynolds-number flows: With applications to the calculation of hydrodynamic interactions in suspensions of ellipsoids

Abstract

The disturbance velocity fields due to translational and rotational motions of an ellipsoid in a uniform stream. constant vorticity and constant rate-of-strain. required in fundamental studies of behavior of suspensions. have been obtained by the singularity method. These solutions extend earlier solutions for prolate spheroids. Although equivalent solutions problems were obtained by Oberbeck. Edwardes and Jeffery by separation of variables in ellipsoidal coordinates. the singularity solutions are far more simple in form. Other significant results obtained by the singularity method include the exposition of the unified structure shared by the three boundary value problems and the construction of new forms of the Faxen laws for ellipsoids through application of the reciprocal theorem. The disturbance solutions and Faxen laws. the basis for Smoluchowski's method-of-reflections technique. are used to calculate hydrodynamic interactions between two or more arbitrarily oriented ellipsoids. In particular. mobility problems are solved directly to order R −5 . where R is the centroid-to-centroid separation between the ellipsoids.