Sedimentation and electrophoresis of porous spheres

Abstract An approximate method is developed to calculate the velocity of a polymer molecule in a centrifugal and in an electric field. The model used is a porous sphere. The hydrodynamic interaction between the polymer segments is described by means of Oseen's equations. It is assumed that the force acting on the liquid has spherical symmetry and that the flow derived from this force may be replaced by its average over a spherical surface. The results of the calculation show that this approximation is legitimate. For the sedimentation velocity an equation is obtained which is similar to Debye's though somewhat simpler. In the theory of electrophoresis all relaxation effects are ignored, while for the charge density due to the small ions an expression is used that has been derived on the basis of the Debye‐Hückel approximation for electrolytes. The expression derived for the electrophoretic mobility is quite simple and leads to results almost identical with those obtained in previous work by a straightforward extension of the theories of Brinkman and Debye and Bueche.