Nernst-Planck transport theory for (reverse) electrodialysis: II. Effect   of water transport through ion-exchange membranes
  Transport of water through ion-exchange membranes is of importance both for electrodialysis (ED) and reverse electrodialysis (RED). In this work, we extend our previous theory [J. Membrane Sci., 510, (2016) 370-381] and include water transport in a two-dimensional model for (R)ED. Following a Maxwell-Stefan (MS) approach, ions in the membrane have friction with the water, pore walls, and one another. We show that when ion-ion friction is neglected, the MS-approach is equivalent to the hydrodynamic theory of hindered transport, for instance applied to nanofiltration. After validation against experimental data from literature for ED and RED, the model is used to analyze single-pass seawater ED, and RED with highly concentrated solutions. In the model, fluxes and velocities of water and ions in the membranes are self-consistently calculated as function of the driving forces. We investigate the influence of water and coion leakage under different operational conditions. 
M. Tedesco, H.V.M. Hamelers, and P.M. Biesheuvel
physics.chem-ph cond-mat.soft