Note on a sphere theorem for the axisymmetric stokes flow of a viscous fluid

Abstract

An expression for the Stokes's stream-function for a slow steady axisymmetrical motion of viscous fluid due to a hydrodynamical distribution in the presence of a sphere has been given by the author [1] in terms of the stream-function for the motion due to the same distribution in unbounded fluid, this latter motion being assumed irrotational. The author has since been able to obtain a more general expression for the stream-function by not assuming the motion in unbounded fluid to be irrotational, this result being given in his Ph.D. dissertation [2]. Hasimoto [3] has since given these results, the second in a different form from that of the author. Since the general expression derived by the author is considerably simpler than that found by Hasimoto, it is given in this note. A corresponding result for the motion in a region bounded by a plane is also given.