ELECTRODIFFUSIONAL FREE-BOUNDARY PROBLEM IN CONCENTRATION POLARIZATION IN ELECTRODIALYSIS

A singular perturbation problem, modeling one-dimensional time-depende nt electrodiffusion in an electrolyte layer flanked by charge-selectiv e walls (electrodes, ion-exchange membranes), is analyzed for galvanos tatic (fixed electric current) conditions. It is shown that, as the pe rturbation parameter tends to zero, the solution of the perturbed prob lem tends to the solution of a certain limiting problem which is, depe nding on the input data, either a conventional diffusion problem or a diffusional free boundary problem equivalent to the one-phase Stefan p roblem with superheating. Spatial boundary layers in the perturbed pro blem are analyzed in both cases, together with the extended space char ge zone which develops for electric currents above a certain critical (''limiting'') value. In this framework. the relaxational, vanishing a t steady state, components of the ionic fluxes are being introduced an d evaluated along with the respective parts of the electrochemical pot entials of the ions. The analysis is constructive and yields, in parti cular, the explicit ionic concentration and electric potential profile s in the typical regions in the system.