Models for Facilitated Transport Membranes: A Review
Abstract
:1. Introduction
Mathematical Background
- C = concentration
- J = flux
- r = dissipative term
- r’ = generative term
- v = velocity
- x, y, z = cartesian directions
- t = time
2. Mobile Carrier Systems
2.1. Models for Mobile Carrier Facilitated Transport Membranes
2.1.1. Friedlander and Keller, 1965. Mass Transfer in Reacting System Near Equilibrium: Use of the Affinity Function
2.1.2. Blumenthal and Katchalsky, 1969. The Effect of Carrier Association–Dissociation Rate on Membrane Permeation
2.1.3. Goddard et al., 1969. On Membrane Diffusion with Near Chemical Equilibrium Reaction
2.1.4. Kreuzer and Hoofd, 1970. Facilitated Diffusion of Oxygen in the Presence of Hemoglobin
2.1.5. Kreuzer and Hoofd, 1972, Factors Influencing Facilitated Diffusion of Oxygen in the Presence of Hemoglobin and Myoglobin
2.1.6. Yung and Probstein, 1973. Similarity Considerations in Facilitated Transport
2.1.7. Smith et al., 1973. An Analysis of Carrier Facilitated Transport
2.1.8. Smith, Quinn, 1979. The Prediction of Facilitation Factors for Reaction-Augmented Membrane Transport
2.1.9. Noble et al., 1986. Effect of Mass Transfer Resistance on Facilitated Transport
2.1.10. Basaran et al., 1989. Facilitated Transport with Unequal Carrier and Complex Diffusivities
2.1.11. Jemaa and Noble, 1992. Improved Analytical Prediction of Facilitation Factors in Facilitated Transport
2.1.12. Teramoto, 1994. Approximate Solution of Facilitation Factor in Facilitated Transport
2.1.13. Morales-Cabrera et al., 2002. Approximate Method for the Solution of Facilitated Transport Problems in Liquid Membranes
3. Fixed Carrier Systems
3.1. Models for Fixed Sites Facilitated Transport Membranes
3.1.1. Dual Mode Theory
- = solute concentration in polymer phase
- = solute concentration trapped in ‘holes’
- = solute concentration dissolved
- = solute partial pressure
- = Henry’s constant
- = holes saturation level concentration
- = affinity constant
3.1.2. Cussler et al., 1989. On the Limits of Facilitated Diffusion
3.1.3. Noble, 1990. Analysis of Facilitated Transport with Fixed Site Carrier Membranes
- -
- the mathematical derivation of the mass balance analog of the mobile carrier case, which allows to use, in analytical approximation methods already known, Equation (2.89) while an excess of carrier is considered.
- -
- the functional dependence of the actual complex diffusivity in such systems on morphological and chemical parameters, Equation (182).
3.1.4. Noble, 1991, Facilitated Transport Mechanism in Fixed Site Carrier Membranes
3.1.5. Noble, 1992, Generalized Microscopic Mechanism of Facilitated Transport in Fixed Site Carrier Membranes
3.1.6. Kang et al., 1995. Analysis of Facilitated Transport in Solid Membranes with Fixed Site Carriers
3.1.7. Zarca et al., 2017. A Practical Approach to Fixed-Site Carrier Facilitated Transport Modeling for the Separation of Propylene/Propane Mixtures Through Silver-Containing Polymeric Membranes
3.1.8. Zarca et al., 2017. Generalized Predictive Modeling for Facilitated Transport Membranes Accounting For Fixed and Mobile Carriers
4. Conclusions
Supplementary Materials
Author Contributions
Funding
Conflicts of Interest
References
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RC circuit | Facilitated Systems | |
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Flux | ||
Driving Force | ||
Proportionality | ||
Capacitor Effect |
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Rea, R.; De Angelis, M.G.; Baschetti, M.G. Models for Facilitated Transport Membranes: A Review. Membranes 2019, 9, 26. https://doi.org/10.3390/membranes9020026
Rea R, De Angelis MG, Baschetti MG. Models for Facilitated Transport Membranes: A Review. Membranes. 2019; 9(2):26. https://doi.org/10.3390/membranes9020026
Chicago/Turabian StyleRea, Riccardo, Maria Grazia De Angelis, and Marco Giacinti Baschetti. 2019. "Models for Facilitated Transport Membranes: A Review" Membranes 9, no. 2: 26. https://doi.org/10.3390/membranes9020026