Ion transport through nanofiltration membranes: the steric, electric and dielectric exclusion model

Abstract

The most widely adopted NF models arebased on the extended Nernst–Planck equationto describe the mass transfer and an equilibriumpartitioning relation to describe the distributionof ions at the pore inlet and outlet. The conven-tional NF theory considers the ion exclusionmechanism at the membrane/solution interfacesas the result of a combination of Donnan exclu-sion (resulting from the electrostatic interactionbetween ions and the fixed charges of themembrane) and steric hindrance. However,the Donnan exclusion theory cannot predict thehigh rejection rates of binary electrolytes withdivalent counterions even if ion size effects aretaken into account. This suggests that additionalphenomena have to be accounted for so as toimprove realism of NF tr ansport modeling. That isthe reason why the so-called dielectric exclusionhas been accorded attention in recent years [1–4]. We present here an improved transportmodel for nanofiltration that includes the dielec-tric exclusion mechanism into the classicaltheory (i.e. steric/electric exclusion). Thismodel, called the SEDE model (steric, electricand dielectric exclusion model), considers thatthe dielectric exclusion mechanism is a combi-nation of the so-called image forces (i.e. theinteraction between ions and the polarizationcharges induced by ions themselves at thedielectric boundary between the pore solutionand the pore walls) and Born effect (i.e. theincrease in ion solvation energy due to changein the solution dielectric constant between bulkand confined solution).