Journal of Applied Mathematics
Volume 2011 (2011), Article ID 318907, 15 pages
Research Article

Resistance Functions for Two Spheres in Axisymmetric Flow—Part I: Stream Function Theory

Institute for Theoretical Physics C, RWTH Aachen University, 52056 Aachen, Germany

Received 19 August 2011; Accepted 20 October 2011

Academic Editor: Md. Sazzad Chowdhury

Copyright © 2011 Thanaa El Naqeeb and Rudi Schmitz. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We consider low-Reynolds-number axisymmetric flow about two spheres using a novel, biharmonic stream function. This enables us to calculate analytically not only the forces, but also the dipole moments (stresslets and pressure moments) and the associated resistance functions. In this paper the basics properties of axisymmetric flow and the stream function are discussed. Explicit series expansions, obtained by separation in bispherical coordinates, will be presented in a follow-up paper.