I. Rubinstein et B. Zaltzman, ELECTRODIFFUSIONAL FREE-BOUNDARY PROBLEM IN CONCENTRATION POLARIZATION IN ELECTRODIALYSIS, Mathematical models and methods in applied sciences, 6(5), 1996, pp. 623-648
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.