Time-dependent ion transport in heterogeneous permselective systems

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 (2D) heterogeneous ion-permselective medium. An analytical solution for the transient concentration-polarization problem, under the local electroneutrality approximation and assumption of ideal permselectivity, was obtained using the Laplace transform and separation of variables technique. Then the 2D 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, the field-focusing effect in a 2D system is shown to result in a faster depletion of ions at the permselective interface.