Erratum to “Determination of concentration-dependent transport coefficients in nanofiltration: Defining and optimal set of coefficients” [J. Membr. Sci. 310 (2008) 586–593

Abstract

• The paragraph following Eq. (29) should have appeared as follows: Heren=1 fornon-electrolyte andn=2 for 1:1 salts. Unlikeboth thepermeability coefficient and the reflection coefficient,A contains only the solute/water friction and the volume fraction of water in the membrane. It does not depend on the friction with the membrane matrix and on solute exclusion mechanism, but reflects only the friction between solute and water in the membrane, both for non-electrolytes and electrolytes. • In Section 3, paragraph two and three should have appeared as follows: The present analysis of salt transport in NF membranes, by diffusion and convection, delineates the role of solute of salt uptake and of the kinetic factor. It was shown above, however, that the factor A defined by Eq. (29) does not depend on salt distribution. A large body of information on material properties, experimental results on homogeneous membranes and model consideration for NF membranes, all indicate that the main reason for the concentration dependence of the transport coefficients is the variation in the salt distribution. For two major mechanisms of salt rejection, dielectric exclusion and Donnan equilibrium, the distribution coefficient hence, P as well as 1− , increases with increasing salt concentration and it is well-known that the salt passage of NF and RO membranes follow the same trend [23]. On the other hand, the friction coefficient fsw and hence the parameter A is implicitly expected by a variety of models such as Hindered Transport [4,5], Teorell–Meyer–Sievers (TMS) [8], extended Nernst–Planck equations (ENP) [24–27], Donnan-steric (DS) [9], and more complex combinations of exclusion mechanism [10–14] to be independent of concentration. Only significant changes in the state of membrane (swelling or shrinkage) may lead to large changes in water fraction and effective pore size that will influence fsw. Such changes have been reported for some extreme conditions, e.g., pH extremes, highly saline feeds [28,29] or highly dilute ones [30], but inmany cases they are fairly minor and may be ignored. The assumption of constant A instead of constant P and will lead to better computation of transport coefficients. The differential equation for the solute flow (Eq. (1)) can be rewritten in a more convenient form containing only one concentration dependent coefficient P and another one, A = (1− )/P, that may be expected to be constant, or at least much less dependent on concentration (c= cs).