Advertisement

Heat and Mass Transfer

, Volume 53, Issue 1, pp 205–212 | Cite as

A comparison of Fick and Maxwell–Stefan diffusion formulations in PEMFC gas diffusion layers

  • Michael Lindstrom
  • Brian WettonEmail author
Original

Abstract

This paper explores the mathematical formulations of Fick and Maxwell–Stefan diffusion in the context of polymer electrolyte membrane fuel cell cathode gas diffusion layers. The simple Fick law with a diagonal diffusion matrix is an approximation of Maxwell–Stefan. Formulations of diffusion combined with mass-averaged Darcy flow are considered for three component gases. For this application, the formulations can be compared computationally in a simple, one dimensional setting. Despite the models’ seemingly different structure, it is observed that the predictions of the formulations are very similar on the cathode when air is used as oxidant. The two formulations give quite different results when the Nitrogen in the air oxidant is replaced by helium (this is often done as a diagnostic for fuel cells designs). The two formulations also give quite different results for the anode with a dilute Hydrogen stream. These results give direction to when Maxwell–Stefan diffusion, which is more complicated to implement computationally in many codes, should be used in fuel cell simulations.

Keywords

Polymer Electrolyte Membrane Fuel Cell Binary Diffusivity Diagonal Approximation Serpentine Flow Field Cathode Operation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

The first author thanks NSERC for a graduate scholarship and the Automotive Fuel Cell Corporation (AFCC) and the MITACS Accelerate Internship programme for funding for this work. The second author acknowledges research funding support from an NSERC Canada grant. We would both like to thank the referee that suggested extending the air cathode results to the helox cathode and dilute hydrogen anode.

References

  1. 1.
    Wagner W, Kretzschmar HJ (2008) International steam tables: properties of water and steam based on the industrial formulation IAPWS-IF97, 2nd edn. Springer-Verlag, Berlin, HeidelbergGoogle Scholar
  2. 2.
    Lide DR (ed) (2009) CRC handbook of chemistry and physics, 90th edn. CRC press (Taylor and Francis Group), Boca Raton, FLGoogle Scholar
  3. 3.
    Bear J, Bachmat Y (1990) Introduction to modelling of transport phenomena in porous media. Kluwer, DordrechtCrossRefzbMATHGoogle Scholar
  4. 4.
    Borup R, Meyers J, Pivovar B, Kim YS, Mukundan R, Garland N, Myers D, Wilson M, Garzon Fernando, Wood D, Zelenay P, More K, Stroh K, Zawodzinski T, Boncella James, McGrath James E, Inaba M, Miyatake K, Hori M, Ota K, Ogumi Z, Miyata S, Nishikata A, Siroma Z, Uchimoto Y, Yasuda K, Kimijima K, Iwashita N (2007) Scientific aspects of polymer electrolyte fuel cell durability and degradation. Chem Rev 107(10):3904–3951CrossRefGoogle Scholar
  5. 5.
    Burheim OS, Ellila G, Fairweather JD, Labouriau A, Kjelstrup S, Pharoah JG (2013) Ageing and thermal conductivity of porous transport layers used for PEM fuel cells. J Power Sources 221:356–365CrossRefGoogle Scholar
  6. 6.
    Cayan Fatma N, Pakalapati Suryanarayana R, Elizalde-Blancas F, Celik I (2009) On modeling multi-component diffusion inside the porous anode of solid oxide fuel cells using fick’s model. J Power Sources 192(2):467–474CrossRefGoogle Scholar
  7. 7.
    Chang P, Kim GS, Promislow K, Wetton B (2007) Reduced dimensional computational models of polymer electrolyte membrane fuel cell stacks. J Comput Phys 223(2):797–821MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Jeon DH, Greenway S, Shimpalee S, Van Zee JW (2008) The effect of serpentine flow-field designs on PEM fuel cell performance. Int J Hydrog Energy 33(3):1052–1066CrossRefGoogle Scholar
  9. 9.
    Martinez Michael J, Shimpalee S, Van Zee JW (2008) Comparing predictions of PEM fuel cell behavior using Maxwell–Stefan and CFD approximation equations. Comput Chem Eng 32(12):2958–2965CrossRefGoogle Scholar
  10. 10.
    Promislow K, Chang P, Haas H, Wetton B (2008) Two-phase unit cell model for slow transients in polymer electrolyte membrane fuel cells. J Electrochem Soc 155(7):A494–A504CrossRefGoogle Scholar
  11. 11.
    Promislow K, St-Pierre J, Wetton B (2011) A simple, analytic model of polymer electrolyte membrane fuel cell anode recirculation at operating power including nitrogen crossover. J Power Sources 196(23):10050–10056CrossRefGoogle Scholar
  12. 12.
    Promislow K, Stockie J, Wetton B (2006) A sharp interface reduction for multiphase transport in a porous fuel cell electrode. Proc R Soc A Math Phys Eng Sci 462(2067):789–816MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Reshetenko T, St Pierre J (2014) Separation method for oxygen mass transport coefficient in gas and Ionomer phases in PEMFC GDE, J Electrochem Soc 161:F1089–F1100CrossRefGoogle Scholar
  14. 14.
    St-Pierre J (2011) Hydrogen mass transport in fuel cell gas diffusion electrodes. Fuel Cells 11(2):263–273CrossRefGoogle Scholar
  15. 15.
    Stockie J, Promislow K, Wetton B (2003) A finite volume method for multicomponent gas transport in a porous fuel cell electrode. Int J Numer Methods Fluids 462:186–789zbMATHGoogle Scholar
  16. 16.
    Suwanwarangkul R, Croiset E, Fowler MW, Douglas PL, Entchev E, Douglas MA (2003) Performance comparison of ficks, dusty-gas and Stefan–Maxwell models to predict the concentration overpotential of a SOFC anode. J Power Sources 122(1):9–18CrossRefGoogle Scholar
  17. 17.
    Taylor M, Krishna R (1993) Multicomponent mass transfer. Wiley, HobokenGoogle Scholar
  18. 18.
    Larminie J, Dicks A (2003) Fuel cell systems explained, 2nd edn. Hoboken, WileyCrossRefGoogle Scholar
  19. 19.
    Wilkinson DP, Zhang J, Hui R, Fergus J, Li X (2009) Proton exchange membrane fuel cells: materials properties and performance. CRC Press, Boca RatonGoogle Scholar
  20. 20.
    Yang WJ, Wang HY, Kim YB (2013) Effects of the humidity and the land ratio of channel and rib in the serpentine three-dimensional pemfc model. Int J Energy Res 37(11):1339–1348CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Mathematics DepartmentUniversity of British ColumbiaVancouverCanada
  2. 2.Mathematics DepartmentUniversity of California Los Angeles Los AngelesUSA

Personalised recommendations