Donnan equilibrium and dielectric exclusion for characterization of nanofiltration membranes

Experimental and modelling analysis is presented for characterization of polymeric nanofiltration membranes; the application considered is the separation of aqueous mixtures containing strong electrolytes and/or uncharged solutes. Mass transfer through the membrane is based on the extended Nernst-Planck equation; ion partitioning is described at the interfaces between the membrane and the external solution taking into account of steric hindrance, Dorman equilibrium and dielectric exclusion. The membrane is characterized through the pore radius, the charge density and the membrane thickness. Weak simplifications are introduced into the general model to obtain analytical relationships for the salt rejection, as well as for the ion concentration profile, as a function of membrane parameters and operative conditions. Model predictions are successfully compared with experimental data for all the mixtures investigated. Dielectric exclusion phenomenon is relevant with respect to Donnan equilibrium in determining the rejection of bivalent ions.