A predictive model for the performance of a nanofiltration membrane in
separating the components of a dye/salt solution was developed It is
based on the extended Nernst-Planck equation with incorporation of con
centration polarization for mixtures of charged ions. Excellent agreem
ent between predicted and experimental rejections of anions and cation
s was obtained for batch nanofiltration at different ratios of dye/sal
t assuming that the membrane charge density (X-d) depends on the total
concentration of negative charges in the solutions. Prediction for di
afiltration experiments was also excellent by allowing for variation i
n X-d as the salt concentration in the solution changed as a function
of time. The model was used to investigate optimization of the process
ing conditions. The overall diafiltration process operated best in a t
wo-phase mode, in which the dye solution was preconcentrated to the fi
nal required dye concentration before diafiltration.