Finite ion size effects on electrolyte transport in nanofiltration membranes

The pressure-driven electrolyte transport through nanofiltration membrane pores with specified wall potential is investigated theoretically. The finite ion size effect is taken into account by introducing an additional term to electrochemical potential. The two-dimensional Navier–Stokes, Poisson, and modified Nernst–Planck equations are solved numerically in a high aspect ratio nanopore connecting two reservoirs with a larger diameter. The calculations are performed for potassium chloride aqueous solution. In the case of point-like ions, the non-physical rise of counter-ion concentration is observed near the pore wall at large applied voltages. When finite ion size is taken in account, the concentration of counter-ions decreases significantly and saturates to the maximum value. It leads to lower osmotic pressure jump and larger magnitude of potential in the pore. The stronger co-ion depletion observed for finite size ions results in the increase of salt rejection, membrane potential, and required pressure drop.