Coupled translational and rotational motions of a sphere in a fluid

Abstract

Starting from the exact steady state Navier-Stokes equation and taking the quadratic inertia term into account in an appropriate way one can show the existence of a coupling of the translational and rotational motions of a rigid sphere in an incompressible fluid. No-slip boundary conditions are used. The coupling consists in a transverse force proportional to the cross product of the linear and angular velocities of the sphere. This force is closely related to the Magnus effect. It is of interest for the theory of Brownian motion of particles with internal degrees of freedom. © 1968, Walter de Gruyter. All rights reserved.