Transport model for solvent permeation through nanofiltration membranes

This paper describes a new, semi-empirical model for solvent transport through nanofiltration membranes. The model is based on different existing models: Hagen–Poiseuille, Jonsson and Boesen, Machado et al. and Bhanushali et al. The newly developed model introduces a correction to the Bhanushali model. Solvent flux appears to be dependent on viscosity, molecular size and the difference in surface tension between the membrane and the solvent. The model was tested on the results of a series of permeability experiments of binary mixtures of water, methanol and/or ethanol, carried out with seven (hydrophilic and hydrophobic) membranes: Desal-5-DK, Desal-5-DL, N30F, NF-PES-010, MPF-44, MPF-50 and SolSep-030505. The model fits indicated a high correlation with experimental results. The new model showed similar fitting results as existing models for hydrophilic membranes. The solvents used have a relatively high degree of affinity for hydrophilic surfaces, resulting in small repulsion forces and consequently a reduced influence of the membrane–solvent interactions. Thus, existing models are sufficient for hydrophilic membranes and the correction for membrane–solvent interactions proposed here has only a small influence. However, a significant improvement was found for the description of the solvent permeability through hydrophobic membranes. For hydrophobic membranes, the relative importance of membrane–solvent interactions/repulsions is increasing for polar solvents. Existing models could not describe the steep increase in permeability for mixtures with high alcohol fractions, whereas the new model fits significantly better.