The translational and rotational motions of an n -dimensional hypersphere through a viscous fluid at small Reynolds numbers

Abstract

Expressions are derived for the n-dimensional Stokes velocity and pressure fields (and stream function) corresponding, respectively, to the translation and rotation of a hypersphere in a viscous fluid at rest at infinity. These are utilized to calculate the force and first antisymmetric stress moment (‘torque’) on the n-dimensional hypersphere. They are also utilized to derive the generalizations of Faxén's laws for the force and stress moment corresponding to arbitrarily prescribed velocity fields on the hypersphere surface and at infinity.