Influence of pore size distribution and applied cross-flow on ion rejection and separation

To improve the understanding of the separation mechanism of ions through membrane filtration, ion transport through a membrane with non-uniform pore sizes is investigated theoretically by solving the coupled Poisson-Nernst-Planck and Navier-Stokes equations under various conditions. The model focuses on a membrane with pore sizes following a log-normal distribution and considers the flow interaction between pores. The rejection performance for different pore arrangements is addressed for a rational assessment of the best ion rejection and selectivity in membrane filtration processes. In addition to the dead-end setting, a cross-flow is applied on the feed side to alleviate the concentration polarization effect. In the presence of positively charged nanopore surfaces, both the cases of a single salt (NaCl) and mixed salts (NaCl, MgCl2) present in the liquid are considered. We show that the uniform pore system outperforms non-uniform ones in terms of the overall rejection and selectivity between salts. When pore size polydispersity is present, the arrangement among the larger and smaller pores impacts the local rejection and volumetric flux of pores. Moreover, the competitive transport between cationic co-ions makes Mg2+ demonstrate generally higher rejection in all the pore arrangements considered. As uniform pores show lower flow rates, the separation efficiency of ions may be improved by pore size polydispersity at the same concentration and pressure difference.