Over-limiting currents and deionization "shocks" in current-induced polarization: local-equilibrium analysis

The problem is considered theoretically of dynamics of current-induced concentration polarization of interfaces between ideally perm-selective and non-ideally perm-selective ("leaky") ion-exchange media in binary electrolyte solutions under galvanostatic conditions and at negligible volume flow. In contrast to the previous studies, the analysis is systematically carried out in terms of local thermodynamic equilibrium in the approximation of local electric neutrality in virtual solution. For macroscopically homogeneous media, this enables one to obtain model-independent results in quadratures for the stationary state as well as an approximate scaling-form solution for the transient response to the step-wise increase in electric-current density. These results are formulated in terms of such phenomenological properties of the "leaky" medium as ion transport numbers, diffusion permeability to salt and specific chemical capacity. An easy-to-solve numerically 1D PDE is also formulated in the same terms. A systematic parametric study is carried out within the scope of fine-pore model of "leaky" medium in terms of such properties as volumetric concentration of fixed electric charges and diffusivities of ions of symmetrical electrolyte. While previous studies paid principal attention to the shape and propagation rate of the so-called deionization "shocks", we also consider in detail the time evolution of voltage drop and interface salt concentration. Our analysis confirms the previously predicted pattern of propagating deionization "shocks" within the "leaky" medium but also reveals several novel features. In particular, we demonstrate that the deionization-shock pattern is really pronounced only at intermediate ratios of fixed-charge concentration to the initial salt concentration and at quite high steady-state voltages where the model used in this and previous studies is applicable only at relatively early stages of concentration-polarization process.