Hydrodynamic interaction of two permeable spheres I: The method of reflections

The Debye-Bueche description of the frictional properties of dilute polymer solutions is extended to semidilute solutions where the hydrodynamic interaction of two nearby molecules is significant. The method of reflections is set up as a formal iterative procedure for the calculation of the fluid velocity field in successive powers of the inverse particle separation. General expressions for the forces and torques on the two particles are obtained and are shown to depend only on the asymptotic form of the velocity field at infinity. A cartesian tensor ansatz is given for the solution of the Debye-Bueche equations for one permeable particle in the presence of a general source velocity field.