  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.
