Reduced-order modelling of concentration polarization with varying permeation: Analysis of electro-osmosis in membranes

Concentration polarization is a major challenge to water desalination process. It affects membrane performances by reducing permeate flux and increasing the risk of fouling. One promising approach to reduce concentration polarization is to use external forces such as electro-osmosis. Previously developed reduced-order model either assumed dissolving wall condition, which does not represent the real process mechanism or does not incorporate the effect of electro-osmotic flow (EOF) slip velocity. In this work, we bridge the research gap by proposing a reduced-order model with permeation for membrane systems by considering the effect of EOF slip velocity. The proposed model is shown to provide accurate prediction when compared with computational fluid dynamics (CFD) results. Additionally, the model can complete simulations in seconds, which is 2 orders of magnitude faster as compared to CFD. Using the validated model, we study the mechanism of mixing caused by the slip velocity. Results show that improved mixing and enhanced mass transfer is concentrated in the region between electrodes. We also propose analytical expressions to determine shear stress and pressure drop, which are linked to mass transfer enhancement and energy requirement respectively. This leads us to obtain an optimal electrode spacing to improve mass transfer. •A reduced-order model with varying permeation and electro-osmosis is developed.•The model can complete simulations two orders of magnitude faster than CFD.•Improved mixing and enhanced mass transfer between electrodes•Analytical expressions are proposed to determine shear stress and pressure drop.•The state-space model is used to optimize electrode spacing.