I want to study the transport of each component individually in a membrane system and also see the dependency/affinity of one component for another component.
It is simple approach P=SxD: where P is the permeation, S is sorption, and D is diffusion. Permeation depends on the system you have if it is steady flow of permeant or not! Please check the link below Article The Influence of Cu3(BTC)2 metal organic framework on the pe...
Thank you so much sir.
Can I apply the same for multi-component liquid system?
The driving force is the different concentration or pressure between the two side of the membrane. Usually each component has its momentum, and by knowing each liquid concentration you can eventually calculate the transfer for the whole system.
It's as simple as above if the species are neutral. If they are charged (ions) there is strong coupling through electric field. Even if no external field is applied typically there are spontaneously arising fields in pressure- and concentration-driven processes. Modelling this isn't easy. A standard approach is the use of (extended) Nernst-Planck equations, which typically have to be solved numerically. Within the scope of Solution-Diffusion-Electromigration model (no convective ion transfer) for 3 ions the equations have been solved analytically (J.Membr.Sci., 2013, 447, 463–476; J.Membr.Sci., 523 (2017) 361-372). There is also an interesting limiting case (one dominant salt + trace ions) where a simple analytical solution is available (J.Membr.Sci., 2011, 368, 192–201; Chem.Eng.Sci., 2013, 104, 1107–1115).
Thank you Yaroshchuk sir.
The system that I am working with is neutral system without any charged ions and I am looking for some information regarding transport modelling of components in a nanofiltration membrane system.
With neutral species the principal coupling is via volume flow. If your solutions are sufficiently concentrated there may be considerable osmotic flows in the system, and they are controlled by all the components. If your solutions are rather dilute the flows of different species are probably not coupled.
Thank you Yaroshchuk sir.
I believe that the coupling concept will play a major part in my system, still I am unable to find any relevant scientific researches for the same.
It's true that there is not much published on that. You can try yourself and use Spiegler-Kedem model for each of the solutes. This will contain trans-membrane volume flow as a parameter. You solve the equation for each solute and take into account that the volume flow is proportional to the difference of hydrostatic minus difference of osmotic pressure across the membrane. The latter (in the approximation of ideal solutions) is proportional to the difference between the total concentrations of all solutes in the feed and permeate. With this you can find the hydrostatic-pressure difference corresponding to the volume flow. This will show you how (at a given transmembrane hydrostatic-pressure difference) addition of a solute influences the rejection of another solute (what is called coupling).
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