A Maxwell–Stefan Approach to Ion and Water Transport in a Reverse Electrodialysis Stack

Reverse electrodialysis (RED) is one of the methods able to generate energy from the salinity gradient between sea- and river water. The technique is based on the diffusion of ions through membranes that specifically allow either cations or anions to pass through. This ion current is converted into an external electric current at electrodes via suitable redox reactions. Seawater contains mainly eight different ions and the description of transport phenomena in membranes in classical terms of isolated species is not sufficient because the different particles have different velocities—in the same direction or opposite—in the same membrane. More realistic is the Maxwell–Stefan (MS) theory that takes all interactions between the different particles in account; however, such a model is complex and validation is difficult. Therefore, a simplified system is used with solely NaCl in solution, using only 9 diffusivities in the calculation. These values are estimated from the literature and are applied to an MS model of the RED process. Using experimental data of NaCl and water transport as well as power density, these diffusivities are adapted in the MS model. Reliable values for the diffusivities were obtained for the following three interactions: H2O–Na+, H2O–Cl− and Na+–Cl−.