Non-steric mechanisms of nanofiltration: superposition of Donnan and dielectric exclusion

Abstract

Abstract At present, the only established non-sieving rejection mechanism of nanofiltration is the Donnan exclusion of coions, due to their interactions with fixed electric charges. The Donnan exclusion is marked by a characteristic dependence of rejection on the electrolyte valence type — an increase with the increasing coion charge and a decrease with the increasing counterion charge. Though sometimes observed, such a correlation is far from being universal. Meanwhile, a difference in the dielectric constants of constituent phases is a universal property of any heterogeneous medium. The dielectric exclusion occurs due to the interactions of ions with polarised interfaces between media of different dielectric constants. The polarisation charge is proportional to that of ion charge. Therefore, the exclusion energy is proportional to the square of ion charge and both cations and anions are excluded from pores. Recently, the present state of the theory of dielectric exclusion has been reviewed in A.E. Yaroshchuk, Adv. Colloid Interface Sci. 85 (2000) 193. This paper goes on with the analysis of DE as a mechanism of nanofiltration, extending it to non-symmetrical binary electrolytes and their mixtures in neutral and charged pores. The theory of pressure-driven transmembrane transport of electrolyte solutions is outlined. It is shown in what way the membrane transport properties are controlled by ion distribution coefficients. Approximations in the transport theory that enable one to avoid the numerical solution of transport problem are considered. The equilibrium theory of DE is developed within the scope of the Debye–Huckel approach. The reflection coefficients of binary non-symmetrical salts are considered. It is found that the combinations of dielectric and Donnan exclusions, with different extents of contribution of each of them, may explain the qualitative differences in the dependencies of salt rejections on the salt valence type observed with different NF membranes. In non-symmetrical electrolyte mixtures, the DE gives rise to strong non-additives in ion rejections. The trends in the dependency of ion rejections on the feed composition in neutral membranes with dielectric exclusion are found to be the opposite of those in the charged membranes (in mixtures with several coions). There is a smooth transition between two kinds of behaviour with increasing fixed charge density. In mixtures with several counterions, the introduction of small to moderate fixed charge may impair the membrane performance in water softening.