Research Progress of Computational Fluid Dynamics in Mixed Ionic–Electronic Conducting Oxygen-Permeable Membranes
Abstract
1. Introduction
2. Fundamentals of MIEC Oxygen-Permeable Membranes
- (1)
- Feed-side convection and diffusion: Oxygen molecules undergo physical adsorption onto membrane surfaces at the feed side through interactions with active surface sites, where adsorption efficiency is determined by binding energy and surface chemical characteristics.
- (2)
- Feed-side surface exchange: Adsorbed oxygen molecules dissociate into atomic oxygen species via surface catalytic reactions. This energy-intensive process requires overcoming activation barriers, typically achieved through thermal activation or catalytic mediation.
- (3)
- Bulk-phase diffusion: Dissociated oxygen atoms are incorporated into the crystal lattice as ionic species through coordination with metal cations, concurrently generating oxygen vacancies that serve as migration pathways. This step involves electron liberation and initiates oxygen ion migration through vacancy-mediated hopping mechanisms.
- (4)
- Permeate-side surface exchange: Migrated oxygen ions recombine into molecular oxygen at the permeate side under partial pressure gradients. The desorption process necessitates overcoming specific energy thresholds to complete the net oxygen transfer across the membrane.
- (5)
- Permeate-side convection and diffusion: Liberated oxygen molecules desorb from the membrane surface and diffuse into the low-oxygen partial pressure gas phase, completing the transmembrane transport cycle.
3. CFD Modeling of MIEC Oxygen-Permeable Membranes
3.1. Mathematical Models
3.1.1. Oxygen Permeation Models
3.1.2. Mass Conservation
3.1.3. Momentum Conservation
3.1.4. Energy Balance
3.1.5. Component Transport
3.2. Geometric Models
4. Application of CFD in MIEC Oxygen-Permeable Membranes
4.1. CFD Studies of Heat and Mass Transfer Phenomena
4.2. CFD Studies of Membrane Reactor Design
4.3. CFD Studies of Membrane Module Design
5. Challenges and Prospects of CFD in MIEC Oxygen-Permeable Membranes
5.1. Challenges
5.2. Prospects
5.2.1. ML in CFD-Based Membrane Design
5.2.2. DTs in CFD-Based Membrane Design
5.2.3. MD in CFD-Based Membrane Design
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Mathematical Model | Model Equation | Application Scenarios |
---|---|---|
Wagner theory model [43] (2014) | This model is suitable for thick membranes, single-phase MIEC membranes, and steady-state high-temperature operations. | |
Xu–Thomson model [44] (1999) | This model is suitable for studies where variations in the oxygen vacancy concentration depend on the oxygen partial pressure. | |
Kim model [46] (1999) | This model is suitable for disc membranes, assuming that the oxygen vacancy density at the membrane interface does not significantly vary with the oxygen partial pressure. | |
Kim model [46] (1999) | This model is suitable for tubular membranes, assuming that the oxygen vacancy density at the membrane interface does not significantly vary with the oxygen partial pressure. | |
Tan and Li model [47] (2002) | This model is suitable for hollow fiber membranes. | |
Zhu model [48] (2012) | This model is suitable for single- and dual-phase disc membranes, where both surface exchange reactions and bulk diffusion limit the process. | |
Liu model [50] (2005) | (n < 1) (n > 0) | This model is suitable for making quick predictions of oxygen permeation performance, particularly for preliminary studies in large-scale industrial applications. |
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Liu, J.; Zhao, J.; Liu, Y.; Zhu, Y.; Zhou, W.; Gu, Z.; Zhang, G.; Liu, Z. Research Progress of Computational Fluid Dynamics in Mixed Ionic–Electronic Conducting Oxygen-Permeable Membranes. Membranes 2025, 15, 193. https://doi.org/10.3390/membranes15070193
Liu J, Zhao J, Liu Y, Zhu Y, Zhou W, Gu Z, Zhang G, Liu Z. Research Progress of Computational Fluid Dynamics in Mixed Ionic–Electronic Conducting Oxygen-Permeable Membranes. Membranes. 2025; 15(7):193. https://doi.org/10.3390/membranes15070193
Chicago/Turabian StyleLiu, Jun, Jing Zhao, Yulu Liu, Yongfan Zhu, Wanglin Zhou, Zhenbin Gu, Guangru Zhang, and Zhengkun Liu. 2025. "Research Progress of Computational Fluid Dynamics in Mixed Ionic–Electronic Conducting Oxygen-Permeable Membranes" Membranes 15, no. 7: 193. https://doi.org/10.3390/membranes15070193
APA StyleLiu, J., Zhao, J., Liu, Y., Zhu, Y., Zhou, W., Gu, Z., Zhang, G., & Liu, Z. (2025). Research Progress of Computational Fluid Dynamics in Mixed Ionic–Electronic Conducting Oxygen-Permeable Membranes. Membranes, 15(7), 193. https://doi.org/10.3390/membranes15070193