On the motion and Brownian motion of n spheres in a viscous fluid

An extension of Faxén's theorem is given for the case that n spheres move with arbitrary velocities through a fluid in non-uniform steady flow. Explicit expressions for the friction- and mutual friction tensors, valid to order R-3, where R is a typical distance between spheres, are obtained together with this extension. These expressions contain 2-, 3- and 4-sphere contributions. Brownian motion of n spheres as a consequence of fluid fluctuations is discussed on the basis of the relationships derived.