Transport of MgSO4, MgCl2, and Na2SO4 across an amphoteric nanofiltration membrane

The transport of multivalent ions across an amphoteric nanofiltration membrane is described through an integrated model involving the extended Nernst–Planck equations and the Donnan equilibrium at the membrane-solution interfaces. The membrane-forming aqueous phase consists of an amine and an ampholytic polymer containing quaternary amine groups and sulphonic acid groups. In the permeation experiments of single solutions of MgSO4, MgCl2, and Na2SO4, the pressure ranges from 10 to 25 bar, the feed circulation velocity from 0.44 to 5.1 m/s and the feed concentration from 1.8 to 193 mol/m3. The membrane active layer acquires a negative surface charge distribution, by adsorption of anions from the solution, and this charge distribution mainly determines the membrane performance. The experimental evidence of the effects of both ions valences and the feed concentration on the salt rejections is in agreement with the Donnan exclusion principle. The relative errors between the experimental and the calculated permeation fluxes and the salt rejections are lower than 22 and 12%, respectively. The sole model parameter, the membrane effective charge, is found to depend on the salt nature and concentration upon the correlation, CM (mol/m3)=a CSfb (mol/m3), where the parameters a and b areParameterMgSO4MgCl2Na2SO4a (mol/m3)91.922.350.7b0.9041.060.704 The parameter b is related to the salt stoichiometry and the cation valence by the equation: b=(ϑCzC)ZC/2/2.