Abstract
While the application of membrane devices in the field of artificial organs is covered in the second part of this book, this chapter presents the basic principles of mass transport through membranes and a general description of the different types of membranes available. The aim is to provide a theoretical framework for the analysis of the performance of separation units based on this technology. This chapter is mainly focused on the use of membranes to separate specific compounds from liquid solutions; however, at the end of the chapter, membrane gas separation is also shortly presented.
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Notes
- 1.
Pore size in dense membranes lies within the range of the thermal motion of polymer chains; widely accepted theories assume dense membranes to have no pores at all.
- 2.
Rigorously, the partial molar volume of the solvent in the solution.
- 3.
The water activity is usually expressed in terms of osmotic coefficient, \(\varPhi _{w}\), as \(\ln a_{w}=\varPhi _{w}\ln x_{w}\); as for diluted solutions \(\ln x_{w}=\ln \left( 1-x_{s}\right) \simeq -x_{s}=c_{s}/v_{w}\) so that \(\pi =\varPhi _{w}RTc_{S}\).
- 4.
For weak electrolytes, which are only partially dissociated in water with a degree of dissociation \(\alpha \), the concentration of species in solution is \(c_{s}[1+\alpha (\nu -1)]\); therefore, the osmotic pressure of a dilute solution containing a weak electrolyte is \(\pi =RTc_{s}[1+\alpha (\nu -1)]\).
- 5.
- 6.
Actually, the concentrations to be considered are those in the liquid phase in contact with the membrane surface; such concentrations are generally different from those in the bulk of the fluid phase, due to the resistance to mass transport in the boundary layers near the membrane surfaces (see Sects. 3.5 and 3.5.2).
- 7.
As already underlined in the footnote 6, here, we refer to the concentrations and all the other properties of the liquid phases at the interface with the membrane; these properties may be different from those in the bulk fluid phases.
- 8.
If the effect of pressure on the chemical potential is considered, a term depending on the solute volume and pressure gradient is included in the diffusive term; this effect becomes more important as the effective pressure driving force increases [10].
- 9.
It is worth noting the different dimensions of the permeability coefficients used for gases and liquids.
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Annesini, M.C., Marrelli, L., Piemonte, V., Turchetti, L. (2017). Membrane Operations. In: Artificial Organ Engineering. Springer, London. https://doi.org/10.1007/978-1-4471-6443-2_3
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DOI: https://doi.org/10.1007/978-1-4471-6443-2_3
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