A mechanistic model for salt and water transport in leaky membranes: Implications for low-salt-rejection reverse osmosis membranes

The transport of salt and water through "leaky" membranes is of fundamental importance in many disciplines of science and engineering. One important application is in low-salt-rejection reverse osmosis (LSRRO), an emerging membrane-based brine concentration technology with the potential to reduce the energy consumption and cost of brine management. For further development and optimization of the LSRRO technology, models that accurately describe salt transport through LSRRO membranes are critically needed. In this work, we use the solution-friction model to describe salt transport in LSRRO and demonstrate that the model can be simplified to the classic Spiegler-Kedem-Katchalsky model, where the phenomenological parameters of salt permeability and reflection coefficient are expressed in terms of friction and partitioning coefficients. We obtained membranes with different salt permeabilities by treating commercial polyamide RO membranes with an alkaline chlorine solution. Our results reveal the dependence of the phenomenological membrane parameters on the feed salt concentration, with salt permeability increasing and reflection coefficient decreasing as salt concentration increases. We further quantify the frictions among salt, water, and membrane for the chlorine-treated membranes with different salt permeabilities. We find that the friction between water and membrane is inversely proportional to water permeability, while friction between the salt ions and water is relatively insensitive to the feed concentration and chlorine treatment. Further, the salt-membrane friction coefficient is shown to be controlled by the friction between co-ions and membrane. Overall, our study presents a framework to quantify the frictions between water and salt ions as they move through LSRRO membranes, providing mechanistic insights and accurate model for salt transport in LSRRO.