Electrolyte transport through nanofiltration membranes by the space-charge model and the comparison with Teorell-Meyer-Sievers model

Abstract

The space-charge (SC) model was applied to predict salt rejection with charged capillaries in reverse osmosis as a model system of nanofiltration membranes. Straightforward numerical calculation was carried out using parameters of feed concentration, pore radius and surface charge density. The rejection dependency on Peclet number by the SC model has been compared with that obtained by the Teorell-Meyer-Sievers (TMS) model which does not take into account the radial distributions of electric potential and ion concentration. The two models show good agreement for capillaries having smaller radius and lower surface charge density. Membrane parameters, reflection coefficient σ and solute permeability coefficient ω have been numerically calculated using the SC model as a function of two dimensionless parameters: the ratio of pore radius to Debye length r p λ d and the dimensionless potential gradient in the pore surfaces q 0, and the comparison of σ and ω calculated by the SC model with those by the Smit method and by the TMS model has been carried out. It is shown that the TMS model shows good agreement with the SC model in the calculation of the membrane parameters when q 0 is less than 1.0, while σ and ω by the Smit method show excellent agreement with those by the SC model when rejection is larger than 0.5.