Relaxation phenomenon in electrolytic cells limited by Ohmic electrodes

The electric response of an electrolytic cell submitted to an external electric field is investigated. It is assumed that the cell is limited by Ohmic electrodes, in which the conduction current at the electrodes is proportional to the surface electric field. In this framework, employing a model based on the equations of continuity for the ions and the equation of Poisson for the actual electric field inside the sample, we determine the relaxation time to reach the steady state. Our investigation generalises previous works devoted to the relaxation phenomena in electrolytic cell performed assuming blocking electrodes, in the presence of surface adsorption or in the presence of reversible trapping reaction. According to our analysis, the presence of a non-vanishing surface electric conductivity is responsible for reducing the relaxation time, with respect to that corresponding to blocking electrodes. The evolution of the bulk density of ions and of the electric potential profiles are deduced. Special attention is devoted to the electric current in the equilibrium state and during the transient time to reach the equilibrium state. An equivalent electric circuit of the cell is proposed, formed by a series of a bulk resistance with a parallel of surface capacitance and resistance due to the surface layers of thickness comparable with the Debye length. The influence of the rise time of the external power supply on the relaxation phenomenon is considered, supposing a simple exponential behaviour of the applied difference of potential.