Membrane permeability and salt rejection of a γ-alumina nanofiltration membrane were studied and modeled for different salt solutions. Salt rejection was predicted by using the Donnan-steric pore model, in which the extended Nernst-Planck equation was applied to predict ion transport through the pores. The solvent flux was modeled by using the Hagen-Poiseuille equation by introducing electroviscosity instead of bulk viscosity. γ-Alumina particles were used for ζ-potential measurements. The ζ-potential measurements show that monovalent ions did not adsorb on the γ-alumina surface, whereas divalent ions were highly adsorbed. Thus, for divalent ions, the model was modified, owing to pore shrinkage caused by ion adsorption. The ζ-potential lowered the membrane permeability, especially for membranes with a pore radius lower than 3 nm, a ζ-potential higher than 20 mV, and an ionic strength lower than 0.01 m. The rejection model showed that, for a pore radius lower than 3 nm and for solutions with ionic strengths lower than 0.01 m, there is an optimum ζ-potential for rejection, because of the concurrent effects of electromigration and convection. Hence, the model can be used as a prediction tool to optimize membrane perm-selectivity by designing a specific pore size and surface charge for application at specific ionic strengths and pH levels.
Keywords: electroviscous effects; ion adsorption; membranes; modeling; nanofiltration.
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