EFFECTS OF DIRECT AND HYDRODYNAMIC-FORCES ON MACROMOLECULAR DIFFUSION

A rigorous treatment of the N-particle Smoluchowski-Einstein equation by Ackerson is extended to incorporate more exact hydrodynamics, including the zero-velocity-of-approach-at-contact constraint due to stick boundary conditions, and is reformulated to give a more transparent result. In the absence of hydrodynamic interactions, the N-particle treatment differs from the result of conventional irreversible thermodynamics by the correction factor (1-c2 V2), due to neglect of solvent-solute interactions. For dilute hard-spheres in the long-wavelength limit, the effect of the contact constraint is to eliminate all contributions of direct and hydrodynamic forces to the diffusion coefficient, apart from backflow and solvent-solute correction terms. It is shown how the alternate approximate treatments of Phillies and Lee and Schurr can be obtained rigorously in the long-wave length limit. However, a critical assumption in those theories is seen to fail at large wavevector. For dilute solutions of macromolecules interacting by long-range repulsive forces, it may still be concluded that hydrodynamic interactions always oppose the direct forces, but never reverse the sign of the correction term. © 1979.