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Electromigration dispersion in a capillary in the presence of electro-osmotic flow

The differential migration of ions in an applied electric field is the basis for separation of chemical species by capillary electrophoresis. Axial diffusion of the concentration peak limits the separation efficiency. Electromigration dispersion is observed when the concentration of sample ions is comparable to that of the background ions. Under such conditions, the local electrical conductivity is significantly altered in the sample zone making the electric field, and therefore, the ion migration velocity concentration dependent. The resulting nonlinear wave exhibits shock like features, and, under certain simplifying assumptions, is described by Burgers' equation (S. Ghosal and Z. Chen Bull. Math. Biol. 2010, vol.72, pg. 2047).In this paper, we consider the more general situation where the walls of the separation channel may have a non-zero zeta potential and are therefore able to sustain an electro-osmotic bulk flow. The main result is a one dimensional nonlinear advection diffusion equation for the area averaged concentration. This homogenized equation accounts for the Taylor-Aris dispersion resulting from the variation in the electro-osmotic slip velocity along the wall. It is shown that in a certain range of parameters, the electro-osmotic flow can actually reduce the total dispersion by delaying the formation of a concentration shock. However, if the electro-osmotic flow is sufficiently high, the total dispersion is increased because of the Taylor-Aris contribution.