  We consider the problem of electromigration of a sample ion (analyte) within
a uniform background electrolyte when the confining channel undergoes a sudden
contraction. One example of such a situation arises in microfluidics in the
electrokinetic injection of the analyte into a micro-capillary from a reservoir
of much larger size. Here the sample concentration propagates as a wave driven
by the electric field. The dynamics is governed by the Nerst-Planck-Poisson
system of equations for ionic transport.A reduced one dimensional nonlinear
equation describing the evolution of the sample concentration is derived.We
integrate this equation numerically to obtain the evolution of the wave shape
and determine how the the injected mass depends on the sample concentration in
the reservoir.It is shown that due to the nonlinear coupling of the ionic
concentrations and the electric field, the concentration of the injected sample
could be substantially less than the concentration of the sample in the
reservoir.
