## 3 Results and Discussion
### Phenomena Related to Shifts in Chemical Equilibria during Electrodialysis of Multivalent Ions
#### 3.1.1 Chronopotentiometric Features
In this case, the increase in U\({}_{\text{m}}\) takes place more gradually than in the curves of Figure 2a and includes some rough oscillations. The response obtained once the current application ceases also showcases a different relaxation of the membrane potential depending on the previously applied current density. At the lowest current, the membrane potential evolves very fast during the relaxation process, dropping directly towards a value very close to zero after ceasing application of current and decreasing slowly later, until definitely reaching zero. In the cases where the second increase in U\({}_{\text{m}}\) was registered, the membrane potential drops initially to a value higherthan 0.4 V. The relaxation profile of membrane potential is thus connected with the second increase of U\({}_{\text{m}}\) displayed when high currents are applied. After registration of these curves, a Ni(OH)\({}_{2}\) precipitate layer was observed at the anodic side of the cation-exchange membrane. Consequently, the second increase in U\({}_{\text{m}}\) can be attributed to the formation of precipitate layers, which builds up an additional resistance to ion transport. The significantly high remaining potential (>0.4 V) seems therefore to be related to a limitation in the restoration of concentration profiles to the initial equilibrium state. This limitation may be caused by a strong polarization process and a hindrance in the re-equilibration of concentration profiles, as it will be analyzed in more detail below. The obtained responses have been obtained with solutions composed of multivalent metals, like Ni(II), Fe(III) and Cr(III). Except for the case of Figure 2b, the level of polarization at which the peculiar features are observed is significantly above the corresponding i\({}_{\text{lim}}\). However, in general, oscillations in membrane voltage drop typically associated with electroconv  
Figure 2: Examples of chronopotentiograms characteristic of phenomena related to shifts in the equilibrium at the depleting diffusion boundary layer of cation-exchange membranes. (**a**) Curves obtained when different species become depleted at the membrane surface, experiments conducted with 2.5 \(\times\) 10\({}^{-3}\) M Cr\({}_{2}\)(SO\({}_{4}\))\({}_{3}\); (**b**) Curves obtained when equilibrium is shifted towards formation of more mobile ions using 2 \(\times\) 10\({}^{-2}\) M Fe\({}_{2}\)(SO\({}_{4}\))\({}_{3}\) solutions; (**c**) Curves obtained during formation of precipitates at the membrane surface using 10\({}^{-2}\) M NiSO\({}_{4}\) solutions; (**d**) Membrane potential relaxation profile after formation of precipitates at the membrane surface. It seems that other processes related to the transport of salts of multivalent cations are responsible for the atypical chronopotentiometric features. Such processes occur even before electroconvective vortices start to be noticeable in the chronopotentiograms. Due to the complicated interplay between chemical equilibria and concentration polarization, the speciation diagrams at different concentrations serve as a helpful tool to explain the obtained responses. To describe the multi-stage concentration polarization process in the case of Cr\({}_{2}\)(SO\({}_{4}\))\({}_{3}\) solutions, the fraction of different species at the initial concentration are represented in Figure 3 as a function of pOH and pSO\({}_{4}\). The straight lines show the initial equilibrium conditions in the solution. Because of the Donnan exclusion effect for co-ions in the membrane, higher pOH and pSO\({}_{4}\) values prevail in the membrane phase. As the level of current density is increased and the DBL adjacent to the membrane gets depleted of ions, Donnan exclusion of co-ions is enhanced, since the difference between the concentration of fixed charges in the membrane and the concentration of ions at the membrane/solution interface increases.