Concentration effects on membrane sieving: development of a stagnant filmmodel incorporating the effects of solute-solute interactions

Recent theoretical analyses have demonstrated that the actual membrane sieving coefficient increases with increasing solute concentration due to the effects of solute-solute interactions at high concentration. In contrast, experimental studies in stirred and crossflow filtration devices have generally failed to detect any significant concentration dependence for the sieving coefficient, even though solute concentrations at the membrane surface are often quite large due to the high degree of concentration polarization. We propose that this apparent discrepancy arises from the effect of solute-solute interactions on bulk solute transport. We have developed a stagnant film model that explicitly accounts for this effect by incorporating a concentration-dependent activity coefficient and a concentration-dependent frictional hindrance factor into the convective-diffusion equation. The results indicate that solute-solute interactions increase the rate of solute diffusion away from the membrane, an effect which balances the corresponding increase in the actual sieving coefficient. Theoretical calculations demonstrate that the apparent discrepancy between previous experimental results and the theoretical analyses can be resolved by incorporation of the effect of solute-solute interactions into the stagnant film model for bulk mass transport.