An improved phenomenological model for prediction of solvent permeation through ceramic NF and UF membranes

Permeation of water and organic solvents through ceramic nano-filtration and ultra-filtration membranes is investigated and a predictive model is proposed. The development of the model started from the Hagen–Poiseuille equation, which assumes the viscosity as the main influencing parameter for the permeation, and introduces several correction factors to account for the surface phenomena that arise in a nanotube due to solvent–membrane surface interactions: capillarity, polarity and steric hindrance. The correction terms are functions of the pore size, so that the model can be applied indistinctly to both UF and NF membranes. The model shows good predictive capability for pure solvent permeation in both ranges. The model is extended to both aqueous and organic solvent mixtures. Only the physical parameters of the single solvents are needed to have good predictions, with the exception of the mixture viscosity. Only the mixture acetonitrile/water shows an anomalous behavior. This is explained with the formation of complexes, which are increasing the effective radius of the mixture.