Alternative pore hindrance factors: What one should be used for nanofiltration modelization?

In nanofiltration it is important for predictive purposes to obtain retentions and/or reflection coefficients from known sizes of the pores and the molecules of uncharged solutes. This correlation is also needed in order to model the mass transport of salts or other charged species. To complete these model and predictive needs, the hindrance factors have to be correlated with the ratio between the pore and the molecule sizes, λ. There are several correlations proposed in the literature. Moreover, the effect of the applied pressure was not accounted for in these correlations until recent revisions of the transport model. In some cases the action of the pore-wall friction has been also neglected. Here we make a revision of these different assumptions on the hindrance factors, we discuss their effect on the transport and we show some conditions that a correct correlation should accomplish. It is shown that it is important to consider both the pressure and the pore-wall friction because the corresponding terms have important contributions to both retention and reflection. It is, nevertheless, less relevant an accurate choice of a relationship for the pore hindrance factors in terms of λ, as far as, both retention and reflection are mainly controlled by partitioning in the ranges where the different proposed correlations differ, what leads to the same transport predictions. In any case a theoretically correct correlation can be chosen attending to the conditions that the pore reflection must accomplish.

We have shown that, when the pore reflection coefficient is considered, the best pore hindrance correlation is that proposed by Bungay and Brenner. Nevertheless, the influence in the retention coefficient or the reflection coefficient of the membrane system is limited with much higher relevance of the applied pressure gradient for small solutes and of the pore-wall friction for large solutes. Inappropriately, neglecting these contributions may lead to very significant errors in the prediction of performances of nanofiltration membranes, mainly for intermediate retentions. It is important to note that we have focused our attention in the phenomena of hindrance appearing through membranes that can be assumed as consistent in a bunch of parallel equal pores. The existence of relatively wide pore size distributions could change the details but we think that the substance of our conclusions should remain unmodified.