Abstract
The ?oupled solution-diffusion model based on the Maxwell-Stefan theory was developed to describe the solute rejection from dilute nonelectrolyte solutions by polymeric membranes applied in organic solvent nanofiltration. In certain cases, the advanced equation for the solute rejection can be reduced to the familiar expressions of the solution-diffusion and the Spiegler-Kedem models. The model was verified by the experimental results on the dyes nanofiltration through poly(1-trimethylsilyl-1-propyne) and poly(4-methyl-2-pentyne) membranes. Two binary separating systems were considered: first, the dilute ethanol solutions of three dyes with virtually the same molecular weight, and second, the selected dye dissolved in three different solvents. In contrast to the solution-diffusion model, the proposed approach provides an accurate description of both positive and negative solute rejection as a function of the transmembrane pressure. The contribution from the coupled solute flux to the total solute flux was quantitatively estimated. It is shown that the coupled solute flux becomes predominant over the direct diffusion flux when the membrane Peclet number reached the values of 1-2.