Mass transfer modeling for salt transport in amphoteric nanofiltration membranes

The mass transfer in the tangential turbulent flow inside a nanofiltration tubular membrane is described by a modified eddy diffusivity model, which accounts for the effect of high permeation fluxes on the mass transfer rates through a permeation Reynolds number. The correlation achieved for the polarization modulus in this situation is C = exp(0.162Re(p)(0.93)Re(-0.29)Sc(2/3)). The ionic transport in the membrane active layer is described through the extended Nernst-Planck equations and the Donnan equilibrium at the membrane-solution interfaces. The active layer of the nanofiltration membrane is made of an amphoteric polymer containing quaternary amine and sulfonic acid groups. In the experiments of permeation of sodium chloride solutions, the Reynolds number ranges from 9.6 x 10(3) to 1.1 x 10(5), the pressure from 10 to 25 bar, and the feed concentration from 1.8 to 193 mol/m(3). A good agreement is observed between the experimental and the calculated permeation fluxes and the salt rejections. The membrane effective charge depends on the feed concentration upon the relationship In C-M (mol/m(3)) = 4.14 + 0.527 ln C-Sf (mol/m(3)).