On the hydrodynamic interactions between two spheres in stokes flow

This paper examines the interactions between two spheres in an unbounded fluid. Using bispherical coordinates, no-slip and far-field boundary conditions, an exact solution of Stokes equations for the translational motion of two spheres of arbitrary size and arbitrary orientation with respect to their directions of motion are obtained. This solution is in form of truncated infinite series. The various hydrodynamic forces exerted on the spheres are calculated. The results from the force calculations show that when the two spheres are in close proximity, greater number of terms has to be retained in the series before convergence is achieved.