Relevance of hindrance factors and hydrodynamic pressure gradient in the modelization of the transport of neutral solutes across nanofiltration membranes

Here we show how the usual model for the transport of neutral solutes through porous membranes, lead to equations that can be compared with the thermodynamic equations of transport. This is done in detail and paying special attention to the assumptions made that frequently have been not taken into account.This model can be used to get information on the pore size from functional data on retention and permeability. Two parameters are needed to fit experimental results of retention versus volume flow. We show the total equivalence of using the Staverman reflection coefficient and the solute permeability coefficient as parameters or the pore radius and the ratio of porosity and pore length. It is also equivalent to measure, adequate and separately, the reflection and the permeability coefficients and to evaluate from them the pore radius and the ratio of porosity versus pore length or vice versa. Moreover, the effect of the amplification of viscosity in small pores and the information contained in the pure water permeability are included in the model to reduce the number of required parameters to one, as for example the pore radius.We show that when the pore reflection coefficient is considered some bounds for the values of the pore hindrance factors must be accomplished for big and small molecules as compared to the pore size. Criteria to allow an election among the many expressions proposed for such hindrance factors in literature are proposed based on these requirements. An adequate consideration of pore wall friction and applied pressure gradient is shown to be very important as far as when these factors are inappropriately neglected, very significant errors appear in the prediction of performances of nanofiltration membranes, mainly for intermediate retentions.