Studies of the crossed ionic fluxes through a cation-exchange membrane in the case of Donnan dialysis

This paper first presents a set of experimental data on the measurements of the ionic fluxes through a cationexchange membrane separating two electrolyte solutions with the same concentration, the same co-ion but different counter-ions (bi-ionic system). Then these results are compared with the theoretical predictions given by the resolution of the corrected Nernst–Planck’s equation in the cases of the homogeneous and heterogeneous models of ion-exchange membranes. Good agreement between the experimental results and the computed values is observed only in the case of the heterogeneous model. This confrontation confirms (1) the existence of three concentration domains: low, medium and high concentrations, corresponding, respectively, to a complete diffusion boundary layers (DBLs) control, a mixed control and a complete membrane control of the inter-diffusion process; (2) the homogeneous model, even if it is convenient for a good interpretation of the bi-ionic potential (BIP) results, cannot explain quantitatively the transmembrane ionic fluxes, which are of extensive quantities; and (3) the bi-phasic model gives the best predictions for both fluxes and BIPs.

From the present experimental study of the counter-ions transport through the CM2 cationexchange membrane and for a large concen- tration domain, we can emphasize the following points. For very low concentrations, the DBLs have a dominating effect on the counter-ions transport. Moreover, the membrane remains excluded from this process. For medium concentrations, both the DBLs and the ion-exchange membrane control the inter-diffusion process through the membrane. For very high concentrations, only the membrane has an important function on the inter-diffusion fluxes. A satisfactory agreement is obtained between the theoretical predictions of the ionic fluxes and the experimental results in the case of a heterogeneous model composed of two phases. This simple model can be considered as a first-order representation of an ion-exchange membrane to estimate both extensive and intensive quantities. However, a homogeneous model can be used only to describe intensive quantities.