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Membranes 2020, 10, 221 7 of 72 Figure 4. Schematic ion concentration profiles in the diffusion boundary layers (DBL) close to a cation-exchange membrane under an electric field, under the limiting current density, and the different mass transfer mechanisms involved in cation migration (Adapted from Bazinet and Castaigne [11]). 3.2. Concentration Gradient and Concentration Polarization 3.2.1. Concentration Gradient When a current is applied to an electrodialysis cell, a variation in the concentration profile close to the membranes appears, in the DBLs relative to the concentrate and diluate, between the turbulent zones of the solution and the membrane. After a short transitional period, concentration gradients are established (Figure 5a). Two phenomena are combined to establish this non-uniform concentration profile of the solution at the membrane interface [19]: 1. The presence of a laminar flow diffusion boundary layer at the vicinity of the membranes; 2. The difference of ion transport numbers in the solution and in the membrane, which results in a difference between the ionic flux in the solution and in the membrane. For example, for NaCl in aqueous solution, it was reported that the flux of Na+ ion through the cationic membrane NbtMemb ≈ 1 is higher than the transport of this same ionic species in the Na+ solution NbtSol ≈ 0.39, while NbtMemb is close to zero and NbtSol ≈ 0.61 [20,21]. NbtMemb is close to 1 + Na+ Cl− Cl− Na+ since Na is the only cationic species present, in this case, able to transport the current through the cation-exchange membrane and vice versa for Cl− with the anion-exchange membrane (NbtMemb ≈ 1). Cl− Furthermore, at steady state, at any point of the solution and even of the ED module, the ion flux is proportional to the transport number.PDF Image | Electrodialytic Processes
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