Linearized transport model for nanofiltration: Development and assessment

Abstract

Finite difference linearization of pore concentration gradient in nanofiltration membranes greatly simplifies the solution of a three‐parameter model (pore radius, membrane charge, and pore dielectric constant) for electrolyte rejection by removing the requirement for numerical integration of the extended Nernst–Planck equation. The validity of the linearized model is first experimentally tested by comparing with a rigorous characterization of the Desal‐DK nanofiltration membrane, the linearized model closely agreeing with the numerical solution of the full model. Investigation of pore concentration profiles showed the assumption of linearity to be valid over a wide range of nanofiltration conditions. The linearized model was also successfully extended to ternary electrolyte mixtures, highlighting its main advantage over analytic solutions. Overall, the model is a powerful tool for characterization of nanofiltration membranes and subsequent prediction of separation performance. Computational demands are modest in terms of time and complexity.