Behavior of an electrolytic cell containing two groups of ions submitted to a step-like external voltage

The transient and equilibrium behaviors of an electrolytic cell containing two groups of ions submitted to an external voltage is considered. The analysis is performed analytically and numerically, considering the electrolytic solution as a dispersion of ions in an insulating liquid. According to our results, the dynamic of the system corresponds to a multirelaxation problem and the relaxation time related to a new type of free diffusion is able to capture the essential characteristics of the evolution of the variables of the system. We also show that, contrary to what expected, the relaxation time related to the ambipolar diffusion is not a solution of the eigenvalues equation.