Katchalsky model for nanofiltration of single electrolyte solutions

The parameters of the model comprising the polarization layer and the Spiegler–Kedem–Katchalsky model of membrane transport were determined for a series of nanofiltration membranes. Membranes with different NaCl retentions were chosen. The experiments were performed at the same hydrodynamic conditions using 0.1 M NaCl as feed. Different approaches to the calculation of parameters are presented, including the concentration dependence of Ps and σ. It was found that only Ps = f (cs) substantially improved the fitting of the model. A strong dependence of the real retention coefficient, R, on the electrolyte permeability coefficient, Ps, was described by the empirical

The parameters — thickness of polarization layer, lpol; electrolyte permeability coefficient, Ps; and reflection coefficient, σ — were determined for a series of NF membranes with NaCl retention varying from 20% to 95%. It was found that there is a strong dependence of the real retention coefficient, R, on the electrolyte permeability coefficient, Ps; it can be approximately described by the empirical relation −1 R = 1 + q0 Psq1 with the determination coeffi2 cient r = 0.984. There was no regular relationship between the retention coefficient and σ. For some membranes the inequality σ >1 was obtained. The values of σ closest to 1 were obtained using the Monte Carlo method and criterion (19). There is a strong relation between lpol and R, which for the range R 0(0.3, 0.95) is practically linear (r2 = 0.989). Adding the condition lpol (R = 0) = 0, it is possible to describe this dependd ence using the power function l pol = d 0 R i (r2= 0.986). Thus, in the modeling of membrane transport, the polarization layer should be considered as an integral part of the model. The application of correlations such as Eq. (3) for that purpose, which do not take into account the membrane properties, is rather doubtful. Compared to the model discussed, the simple osmotic model, ( ) based on the assumption σ = 1, yields higher values of lpol for the membranes of higher retention (Robs >0.5). Regarding the concentration dependence of Ps and σ described by the power function, only that of Ps substantially improved the fitting of the model.