  The current study extends previous analytical and numerical solutions of
chronopotentiometric response of one-dimensional systems consisting of three
layers to the more realistic two-dimensional heterogeneous ion-permselective
medium. An analytical solution for the transient concentration-polarization
problem, under the local electro-neutrality approximation and ideal
permselectivity, was obtained using the Laplace transform and separation of
variables. Then the two-dimensional electric potential was obtained numerically
and was compared to the full Poisson-Nernst-Planck solution. It was then shown
that the resultant voltage drop across the system varies between the initial
Ohmic response and that of the steady-state accounting for
concentration-polarization. Also, field-focusing effect in a two-dimensional
system is shown to result in a faster depletion of ions at the permselective
interface.
