Electric response of an electrolytic cell to a periodic excitation in the dc limit

We evaluate the electrical impedance of an electrolytic cell submitted to a low frequency external voltage. We show that in the limit where the circular frequency of the applied voltage, ω, is small with respect to Debye relaxation circular frequency, ωD, the response of the cell can be evaluated by means of a perturbational calculation, where the expansion parameter is x=ω/ωD. Simple expressions for the reactance and resistance in the dc limit of the electrolytic cell are obtained in the case where the electrodes are blocking and the diffusion coefficients of the negative and positive ions are equal. The case where the diffusion coefficients are different is also considered. In this framework, our analysis indicates that in the considered frequency range the effective diffusion coefficient coincides with the ambipolar diffusion coefficient. A possible extension of our approach to the case where the electrodes are not blocking is discussed too.