Theoretical study of the bi-ionic potential and confrontation with experimental results

Abstract

A theoretical study of the bi-ionic potential (BIP) has been carried out using the extended Nernst–Planck equation in the case of a mixed control of the interdiffusion process by the ion-exchange membrane (IEM) and the diffusion boundary layers (DBLs), a non-zero co-ion flux, a non-zero water flux, a variable selectivity coefficient and an affinity coefficient different from unity. The numerical integration of the two coupled differential transport equations allowed, for a given common concentration C 0, the computation of the BIP from the values of 12 parameters required. Three of these 12 parameters are taken from the literature, the others are determined from independent experiments except the DBL thickness and the co-ion diffusion coefficient in the membrane. We have developed a procedure to deduce these two parameters from the experimental curves of the BIP vs. C 0. For the NaCl/CM2/LiCl bi-ionic system, the DBL thickness changes from 59 μm at high stirring rate to 196 μm in the absence of stirring. The chloride diffusion coefficient in the CM2 membrane has been estimated to be equal to 2.1×10 −7 cm 2 s −1. Using these values, we have studied theoretically the influence of each of the three parameters: affinity coefficient, selectivity coefficient and water flow. We have shown that the affinity coefficient has the most important contribution but the selectivity coefficient and the water flow influence only the BIP at high common concentrations.