Determination of the parameters of the Spiegler–Kedem–Katchalsky model for nanofiltration of single electrolyte solutions

The parameters of the model comprising the polarization layer and the Spiegler–Kedem–Katchalsky model ofmembrane 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 NaClas 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 dependenceof the real retention coefficient, R, on the electrolyte permeability coefficient, Ps, was described by the empirical relation R=(1+q0Psqi)−1. No regular relationship between Robs and the reflection coefficient, σ, was found. For some membranes the inequality σ<1 was obtained. A strong relation between the thickness of polarization layer, lpol, and R was found, expressed by the power function lpol = d0Rdi (r2 = 0.986). Thus, in the modeling of membrane transport, one should include the polarization layer into the model instead of applying the ready correlations which do not take into account the membrane properties.