Pore model for nanofiltration: History, theoretical framework, key predictions, limitations, and prospects

This review introduces the development history of the widely used NF model, i.e., the Donnan-Steric Pore Model with Dielectric Exclusion (DSPM-DE), from the emergence of its predecessors to its current form. We present the details of DSPM-DE with assumptions and equations that account for each mechanism. Model inputs and outputs, as well as the key parameters and the experimental procedures for determining these parameters are also explained. Furthermore, the DSPM-DE is applied to investigate NF performance under various conditions. Specifically, the DSPM-DE is employed to provide a mechanistic interpretation of the well-known selectivity-permeability tradeoff that is more typically applied to describe the behavior of non-porous membrane. Based on the simulations using the DSPM-DE, we also discuss strategies on enhancing NF performance via tuning membrane properties. NF membranes with thin active layer and small nanopores that are strongly hydrophilic and charged are beneficial to achieving a high perm-selectivity. Analysis is also performed on the separation of divalent and monovalent cations using DSPM-DE. Finally, we discuss the uncertainties of model parameters and their impacts on the model prediction. We also discuss the validity of fundamental model assumptions and the prospects on potential improvements of NF modeling to enhance the utility in predicting NF performance. Machine learning-based models, once trained with a large set of data, are likely more powerful than DSPE-DE or any physical NF model in future application of performance prediction.