The present work reviews the results, obtained by numerical examination of the space and time behavior of ion
charges in electrolytic cell when external electric field is applied. The basic governing equations for free ions have been
generalized for ion-pairs, the simple boundary conditions for blocking electrodes are generalized taking into account the
charge transfer currents at the electrodes, the equilibrium Einstein-Nernst relation between ion mobility and diffusivity is
modified to take into account the transient, non-equilibrium processes. All these problems are tackled with the help of a
common numerical algorithm applied in both linear and nonlinear approximation. Special attention is attributed to nonlinear
processes, to thin cells with nano-scaled inter-electrode gap, to non-equilibrium states and their relaxation to equilibrium,
to the enhancement of the interface electrode polarization and capacity by charge pump through a complementary
electrode etc. Recent patents concerning electrochemical cells and super-capacitors have also been shortly reviewed.
Keywords: Electrolytic cells, electrical double layer, interface capacity, interface polarization, ion-pairs, supercapacitors.
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