Alternative pore hindrance factors: What one should be used
for nanofiltration modelization?
V. Silva, P. Prádanos, L. Palacio, A. Hernández*
Grupo de Superficies y Materiales Porosos (SMAP), Departamento de Física Aplicada, Universidad de
Valladolid, Real de Burgos s/n, Valladolid 47071, Spain
Email: tonhg@termo.uva.es
Received 01 July 2008; revised 28 January 2009; accepted 09 February 2009
Abstract
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 neg-
lected.
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 contribu-
tions 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.
Keywords: Nanofiltration; Hindrance factors; Pressure effect; Pore-wall friction; Reflection coefficient
*Corresponding author.
Presented at the conference Engineering with Membranes 2008; Membrane Processes: Development, Monitoring and
Modelling – From the Nano to the Macro Scale – (EWM 2008), May 25–28, 2008, Vale do Lobo, Algarve, Portugal.
0011-9164/09/$– See front matter © 2009 Elsevier B.V. All rights reserved.
doi: 10.1016/j.desal.0000.00.000
Desalination 246 (2009) 233–240