The Hydrodynamic Interaction of Two Spheres in a Viscous Fluid at Small Non-Zero Reynolds Number —Axisymmetric Case—

Abstract

The hydrodynamic interaction between two (equal and unequal) spherical particles moving in a fluid is investigated by the method of matched asymptotic expansions in the small Reynolds number (Re). The particles are considered so close that each lies in the inner region of expansion of the other. The flow is assumed axisymmetric. The drag forces on one of the spheres in the leading and in the trailing positions of a uniform flow are determined upto the term of O(Re) for an arbitrary separation between the spheres’ centers. Results for large separation are favourably compared with those reported previously by the method of reflection and the case of small separation is discussed. For equal spheres, the minimum value of interactive (attractive) force is obtained approximately at the spheres’ separation of 3.5.