Friction relations for the Oseen hydrodynamic interactions of spheres at large separations

Abstract

We consider the hydrodynamic forces, exerted by the incompressible fluid, having a uniform velocity U at infinity, on a finite number of fixed rigid spheres. The convective inertia effects of the fluid are described by the Oseen equations. The hydrodynamic interactions between the spheres are treated as multiple scattering events of the perturbations of the uniform velocity U. The hydrodynamic forces are considered under the assumption that the characteristic Reynolds number is small.