TRANSPORT OF CHARGED MACROMOLECULES IN AN ELECTRIC-FIELD BY A NUMERICAL-METHOD .1. APPLICATION TO A SPHERE

The discretized integral equation (DIE) method by Youngren and Acrivos (J. Fluid Mech. 1975,69,377) is generalized to include the effect of time-independent external forces on the transport of rigid macromolecules undergoing Stokes flow in an incompressible, unbounded fluid. According to Ladyzhenskaya (The Mathematical Theory of Viscous Incompressible Flow; Gordon and Breach: New York, 1963), this is achieved by adding additional terms to the integral equations for the fluid pressure and velocity fields in the vicinity of the macromolecule. The generalized DIE method should be useful in modeling electrophoresis and related electrokinetic phenomenon of charged polyions in solution. To verify the method, it is applied to an insulating charged sphere subjected to a constant external electric field in which relaxation of the ion atmosphere from its equilibrium distribution is ignored. Numerical solutions of the electrophoretic mobility as well as pressure and velocity fields around the polyion are in good agreement with the predictions of Henry (Proc. R. Soc. London, 1931, A133,106).