Flux Models in NF

For relatively porous nanofiltration membranes, simple pore flow models based on convective flow will be adapted to incorporate the influence of the parameters mentioned above. The Hagen-Poiseuille model and the Jonsson and Boesen model, which are commonly used for aqueous systems permeating through porous media, such as microfiltration and ultrafiltration membranes, take no interaction parameters into account, and the viscosity as the only solvent parameter. It is expected that these equations will be insufficient to describe the performance of solvent resistant nanofiltration membranes. Machado et al. [62] developed a resistance-in-series model based on convective transport of the solvent for the permeation of pure solvents and solvent mixtures  

Polymeric membranes with a less porous structure, pervaporation membranes as well as nanofiltration membranes, can be described by a solution-diffusion mecha- 

This model combines different approaches of existing models by introducing at the same time the solvent viscosity, the molar volume Vm (as a measure for the molecular size), the surface tension of the solid membrane material and a sorption value ( (as a measure for membrane-solvent interactions). Other SD-based transport models were presented by White [14], providing a predictive model for feed solutions with a high concentration of aromatics, by Scarpello et al. [67] and by Gibbins et al. [68]. A slightly modified equation was proposed by Geens et al. [69]  

A new approach is the application of chemometrics (and neural networks) in modeling [73]. This should allow identification of the parameters of influence in solvent-resistant nanofiltration, which may help in further development of equations. Development of a more systematic model for description and prediction of solute transport in nonaqueous nanofiltration, which is applicable on a wide range of membranes, solvents and solutes, is the next step to be taken. The Maxwell-Stefan approach [74] is one of the most direct methods to attain this. 

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