Salt and Water Transport in Reverse Osmosis Membranes: Beyond the Solution-Diffusion Model

Understanding the salt-water separation mechanisms of reverse osmosis (RO) membranes is critical for the further development and optimization of RO technology. The solution-diffusion (SD) model is widely used to describe water and salt transport in RO, but it does not describe the intricate transport mechanisms of water molecules and ions through the membrane. In this study, we develop an ion transport model for RO, referred to as the solution-friction model, by rigorously considering the mechanisms of partitioning and the interactions among water, salt ions, and the membrane. Ion transport through the membrane is described by the extended Nernst-Planck equation, with the consideration of frictions between the species (i.e., ion, water, and membrane matrix). Water flow through the membrane is governed by the hydraulic pressure gradient and the friction between the water and membrane matrix as well as the friction between water and ions. The model is validated using experimental measurements of salt rejection and permeate water flux in a lab-scale, cross-flow RO setup. We then investigate the effects of feed salt concentration and hydraulic pressure on salt permeability, demonstrating strong dependence of salt permeability on feed salt concentration and applied pressure, starkly disparate from the SD model. Lastly, we develop a framework to analyze the pressure drop distribution across the membrane, demonstrating that cross-membrane transport dominates the overall pressure drop in RO, in marked contrast to the SD model that assumes no pressure drop across the membrane.