Tutorial review of reverse osmosis and electrodialysis

Reverse osmosis (RO) and electrodialysis (ED) are the two most important membrane technologies for water desalination and treatment. Their desalination and transport mechanisms are very different, but on a closer look also have many similarities. In this tutorial review, we describe state-of-the-art theory for both processes, focusing on simple examples that are helpful for the non-specialist and for classroom teaching. We describe relevant theory for ion and water transport and the coupling with theory for chemical and mechanical equilibrium on membrane/solution interfaces. For RO of neutral solutes, we explain the solution-friction (SF) model which is closely related to the classical sieving or pore flow model. The SF model includes advection, diffusion, and solute partitioning, and leads to simple relationships for the coupled fluxes of water and solutes (and thus for solute retention as well), also when a diffusion boundary (or concentration polarization) layer is included in the model. Subsequently this theory is extended to describe RO for symmetric salt solutions with charged membranes. For the desalination of salt solutions, both for RO and ED we present two-dimensional module-scale calculations which lead to a characteristic curve that determines optimum operational conditions based on a simple cost calculation that offsets energy and material costs. We discuss the two-fluid model (TFM) that comprehensively describes ion and water flow both in RO and ED, and we explain how this theory also accurately describes osmosis experiments where water and ions are transported in opposite directions through a membrane. Finally, we present results of optimization studies of the combination of multiple modules for RO and ED, and we evaluate the relevance of concentration polarization by using a 3D model for cross-current flow in an ED module.