The electrophoresis of a deformable polyelectrolyte (PE) is studied theoretically by considering a Poisson-Nernst-Planck model coupled with modified Navier-Stokes equations, taking account of the effects of double-layer polarization, counterion condensation, and electroosmotic flow. The influences of the local electric field and the effective PE charge on the PE mobility are discussed, thereby providing a complete picture for the phenomenon under consideration. Our model explains successfully the presence of a local minimum in the mobility of a highly charged PE as the bulk salt concentration varies, as observed experimentally. Numerical simulation also reveals several interesting and important results. For example, the more a PE is stretched in the direction of electrophoresis, the larger is its mobility. As the double layer becomes thin, the local electric field becomes independent of the PE shape, and its behavior mainly depends upon its effective charge. We show that the force that stretches a PE is maximal when it is spherical and decreases with an increasing aspect ratio, which has not been reported previously.

The sedimentation of an isolated, charged polyelectrolyte (PE) subjected to an applied field is modeled theoretically, taking into account the variation of its shape. In particular, the effects of double-layer relaxation, effective charge density, and strength of the induced relaxation electric field are examined. We show that the interaction of these effects yields complex and interesting sedimentation behaviors. For example, the behavior of the electric force acting on a loosely structured PE can be different from that on a compactly structured one; the former is dominated mainly by the convective fluid flow. For thick double layers, electric force has a local maximum as the Reynolds number varies, but tends to increase monotonically with increasing Reynolds number if the layer is thin. The drag factor is found to behave differently from literature results. The shape of a PE significantly influences its sedimentation behavior by affecting the amount of counterions attracted to its interior and the associated local electric field. Interestingly, a more stretched PE has a higher effective charge density but experiences a weaker electric force.