This paper is concerned with the calculation of disturbance velocity fields due to the translation and rotation of bodies in fluids in motion when the Reynolds number is small. The author extends previous work on prolate spheroids to the case of general ellipsoids.
The solutions obtained by the author’s method, known as the singularity method, are simpler in form but equivalent to the older, alternative approach via separation of variables in ellipsoidal coordinates. In particular, this method enables new forms of the Faxen laws, utilized in a long-established method of reflections technique due to Smoluchowski [Bull. Acad. Sci. Cracovie A 1, 28-39 (1911), see also Happel and Brenner, Low Reynolds number hydrodynamics. Sijthoff and Noordhoff. The Hague (1973)], to be obtained for ellipsoids. They are used to calculate hydrodynamic interactions between two or more arbitrarily oriented ellipsoids. Some specific mobility problems are solved directly to \(O(R^{-5})\) where R is the separation of the centroids of the ellipsoids.