Journal of Applied Electrochemistry

, Volume 47, Issue 12, pp 1323–1338 | Cite as

Pore network modeling of phase change in PEM fuel cell fibrous cathode

  • Mahmoudreza Aghighi
  • Jeff Gostick
Research Article
Part of the following topical collections:
  1. Fuel cells


A pore network model has been applied to the cathode side of a fuel cell membrane electrode assembly to investigate the mechanisms leading to liquid water formation in the cell. This model includes mass diffusion, liquid water percolation, thermal and electrical conduction to model phase change which is highly dependent on the local morphology of the cathode side. An iterative algorithm was developed to simulate transport processes within the cathode side of PEMFC applying a pseudo-transient pore network model at constant voltage boundary condition. This algorithm represents a significant improvement over previous pore network models that only considered capillary invasion of water from the catalyst layer and provides useful insights into the mechanism of water transport in the electrodes, especially condensation and evaporation. The electrochemical performance of PEMFCs was simulated under different relative humidity conditions to study the effect of water phase change on the cell performance. This model highlights the ability of pore network models to resolve the discrete water clusters in the electrodes which is essential to the two-phase transport behavior especially the transport of water vapor to and from condensed water clusters.

Graphical Abstract


Pore network model PEM fuel cell Phase change Iterative algorithm Relative humidity 



The authors thank the Natural Science and Engineering Research Council of Canada financial support throughout the course of this project, and the Automotive Fuel Cell Cooperation for support through the Collaborative Research and Development program.


Funding was provided by Natural Sciences and Engineering Research Council of Canada.


  1. 1.
    Gostick JT et al (2009) On the role of the microporous layer in PEMFC operation. Electrochem Commun 11(3):576–579CrossRefGoogle Scholar
  2. 2.
    Ramasamy RP et al (2008) Investigation of macro-and micro-porous layer interaction in polymer electrolyte fuel cells. Int J Hydrog Energy 33(13):3351–3367CrossRefGoogle Scholar
  3. 3.
    Owejan JP et al (2009) Water management studies in PEM fuel cells, Part I: fuel cell design and in situ water distributions. Int J Hydrog Energy 34(8):3436–3444CrossRefGoogle Scholar
  4. 4.
    Secanell M, Wishart J, Dobson P (2011) Computational design and optimization of fuel cells and fuel cell systems: a review. J Power Sources 196(8):3690–3704CrossRefGoogle Scholar
  5. 5.
    Weber AZ et al (2014) A critical review of modeling transport phenomena in polymer-electrolyte fuel cells. J Electrochem Soc 161(12):F1254–F1299CrossRefGoogle Scholar
  6. 6.
    Gostick JT et al (2010) Impact of liquid water on reactant mass transfer in PEM fuel cell electrodes. J Electrochem Soc 157(4):B563CrossRefGoogle Scholar
  7. 7.
    Lu Z et al (2010) Water management studies in PEM fuel cells, part III: dynamic breakthrough and intermittent drainage characteristics from GDLs with and without MPLs. Int J Hydrog Energy 35(9):4222–4233CrossRefGoogle Scholar
  8. 8.
    Cindrella L et al (2009) Gas diffusion layer for proton exchange membrane fuel cells—a review. J Power Sources 194(1):146–160CrossRefGoogle Scholar
  9. 9.
    Djilali N (2007) Computational modelling of polymer electrolyte membrane (PEM) fuel cells: challenges and opportunities. Energy 32(4):269–280CrossRefGoogle Scholar
  10. 10.
    Bachmat Y, Bear J (1987) On the concept and size of a representative elementary volume (REV). In: Advances in transport phenomena in porous media. Springer, Berlin, pp 3–20CrossRefGoogle Scholar
  11. 11.
    Garcia-Salaberri PA et al (2015) Effective diffusivity in partially-saturated carbon-fiber gas diffusion layers: effect of local saturation and application to macroscopic continuum models. J Power Sources 296:440–453CrossRefGoogle Scholar
  12. 12.
    Rebai M, Prat M (2009) Scale effect and two-phase flow in a thin hydrophobic porous layer. Application to water transport in gas diffusion layers of proton exchange membrane fuel cells. J Power Sources 192(2):534–543CrossRefGoogle Scholar
  13. 13.
    Aghighi M et al (2016) Simulation of a full fuel cell membrane electrode assembly using pore network modeling. J Electrochem Soc 163(5):F384–F392CrossRefGoogle Scholar
  14. 14.
    Blunt MJ (2001) Flow in porous medi—pore-network models and multiphase flow. Curr Opin Coll Interface Sci 6(3):197–207CrossRefGoogle Scholar
  15. 15.
    Blunt MJ et al (2013) Pore-scale imaging and modelling. Adv Water Resour 51:197–216CrossRefGoogle Scholar
  16. 16.
    Sahimi M (2011) Flow and transport in porous media and fractured rock: from classical methods to modern approaches. Wiley, HobokenCrossRefGoogle Scholar
  17. 17.
    Chatzis I, Dullien F (1977) Modelling pore structure by 2-D And 3-D networks with application to sandstones. J Can Pet Technol 16(01):33CrossRefGoogle Scholar
  18. 18.
    Celia MA, Reeves PC, Ferrand LA (1995) Recent advances in pore scale models for multiphase flow in porous media. Rev Geophys 33(S2):1049–1057CrossRefGoogle Scholar
  19. 19.
    Blunt MJ (1998) Physically-based network modeling of multiphase flow in intermediate-wet porous media. J Petrol Sci Eng 20(3):117–125CrossRefGoogle Scholar
  20. 20.
    Gostick JT (2008) Multiphase mass transfer and capillary properties of gas diffusion layers for polymer electrolyte membrane fuel cells. University of Waterloo, WaterlooGoogle Scholar
  21. 21.
    Sinha PK, Wang C-Y (2007) Pore-network modeling of liquid water transport in gas diffusion layer of a polymer electrolyte fuel cell. Electrochim Acta 52(28):7936–7945CrossRefGoogle Scholar
  22. 22.
    Wang Z, Wang C, Chen K (2001) Two-phase flow and transport in the air cathode of proton exchange membrane fuel cells. J power sources 94(1):40–50CrossRefGoogle Scholar
  23. 23.
    Nam JH, Kaviany M (2003) Effective diffusivity and water-saturation distribution in single-and two-layer PEMFC diffusion medium. Int J Heat Mass Transfer 46(24):4595–4611CrossRefGoogle Scholar
  24. 24.
    Gostick JT et al (2007) Pore network modeling of fibrous gas diffusion layers for polymer electrolyte membrane fuel cells. J Power Sources 173(1):277–290CrossRefGoogle Scholar
  25. 25.
    Gostick JT (2013) Random pore network modeling of fibrous PEMFC gas diffusion media using Voronoi and Delaunay tessellations. J Electrochem Soc 160(8):F731–F743CrossRefGoogle Scholar
  26. 26.
    Hinebaugh J, Fishman Z, Bazylak A (2010) Unstructured pore network modeling with heterogeneous PEMFC GDL porosity distributions. J Electrochem Soc 157(11):B1651CrossRefGoogle Scholar
  27. 27.
    El Hannach M, Pauchet J, Prat M (2011) Pore network modeling: application to multiphase transport inside the cathode catalyst layer of proton exchange membrane fuel cell. Electrochim Acta 56(28):10796–10808CrossRefGoogle Scholar
  28. 28.
    Wu R et al. (2012) Pore network modeling of cathode catalyst layer of proton exchange membrane fuel cell. Int J Hydrog Energy 37(15):11255–11267CrossRefGoogle Scholar
  29. 29.
    Zenyuk IV et al Coupling continuum and pore-network models for polymer-electrolyte fuel cells. Int J Hydrog Energy 40(46), 16831–16845Google Scholar
  30. 30.
    Hartnig C et al (2009) High-resolution in-plane investigation of the water evolution and transport in PEM fuel cells. J Power Sources 188(2):468–474CrossRefGoogle Scholar
  31. 31.
    Hartnig C et al (2008) Cross-sectional insight in the water evolution and transport in polymer electrolyte fuel cells. Appl Phys Lett 92(13):134106CrossRefGoogle Scholar
  32. 32.
    Caulk DA, Baker DR (2010) Heat and water transport in hydrophobic diffusion media of PEM fuel cells. J Electrochem Soc 157(8):B1237–B1244CrossRefGoogle Scholar
  33. 33.
    Hickner M (2008) In situ high-resolution neutron radiography of cross-sectional liquid water profiles in proton exchange membrane fuel cells. J Electrochem Soc 155(4):B427–B434CrossRefGoogle Scholar
  34. 34.
    Yortsos YC, Stubos AK (2001) Phase change in porous media. Curr Opin coll Interface Sci 6(3):208–216CrossRefGoogle Scholar
  35. 35.
    Prat M (1993) Percolation model of drying under isothermal conditions in porous media. Int J Multiphase Flow 19(4):691–704CrossRefGoogle Scholar
  36. 36.
    Prat M (2007) On the influence of pore shape, contact angle and film flows on drying of capillary porous media. Int J Heat Mass Transfer 50(7–8):1455–1468CrossRefGoogle Scholar
  37. 37.
    Prat M (2011) Pore network models of drying, contact angle, and film flows. Chem Eng Technol 34(7):1029–1038CrossRefGoogle Scholar
  38. 38.
    Yiotis AG et al (2005) Pore-network modeling of isothermal drying in porous media. Transp Porous Media 58(1–2):63–86CrossRefGoogle Scholar
  39. 39.
    Owejan JP et al (2010) Water transport mechanisms in PEMFC gas diffusion layers. J Electrochem Soc 157(10):B1456–B1464CrossRefGoogle Scholar
  40. 40.
    Louriou C, Prat M (2012) Pore network study of bubble growth by vaporisation in a porous medium heated laterally. Int J Therm Sci 52(0):8–21CrossRefGoogle Scholar
  41. 41.
    Medici EF, Allen JS (2011) Incorporation of evaporation and vapor transport in pore level models of fuel cell porous media. ECS Trans 41(1):141–152CrossRefGoogle Scholar
  42. 42.
    Fritz DL (2012) An implementation of a phenomenological evaporation model into a porous network simulation for water management in low temperature fuel cells. Michigan Technological University, HoughtonGoogle Scholar
  43. 43.
    Hinebaugh J, Bazylak A (2010) Condensation in PEM fuel cell gas diffusion layers: a pore network modeling approach. J Electrochem Soc 157(10):B1382CrossRefGoogle Scholar
  44. 44.
    Boillat P et al (2012) Impact of water on PEFC performance evaluated by neutron imaging combined with pulsed helox operation. J Electrochem Soc 159(7):F210–F218CrossRefGoogle Scholar
  45. 45.
    Oberholzer P, Boillat P (2014) Local characterization of PEFCs by differential cells: systematic variations of current and asymmetric relative humidity. J Electrochem Soc 161(1):F139–F152CrossRefGoogle Scholar
  46. 46.
    Straubhaar B, Pauchet J, Prat M (2015) Water transport in gas diffusion layer of a polymer electrolyte fuel cell in the presence of a temperature gradient. Phase change effect. Int J Hydrog Energy 40(35):11668–11675CrossRefGoogle Scholar
  47. 47.
    Straubhaar B, Pauchet J, Prat M (2016) Pore network modelling of condensation in gas diffusion layers of proton exchange membrane fuel cells. Int J Heat Mass Transfer 102:891–901CrossRefGoogle Scholar
  48. 48.
    Belgacem N, Prat M, Pauchet J (2017) Coupled continuum and condensation–evaporation pore network model of the cathode in polymer-electrolyte fuel cell. Int J Hydrog Energy, 42(12), 8150–8165CrossRefGoogle Scholar
  49. 49.
    Schalenbach M et al (2015) Gas permeation through nafion. Part 2: resistor network model. J Phys Chem C, 119(45), 25156–25169CrossRefGoogle Scholar
  50. 50.
    Gostick J et al (2016) OpenPNM: a pore network modeling package. Comput Sci Eng 18(4):60–74CrossRefGoogle Scholar
  51. 51.
    Putz A et al (2013) Introducing open PNM: an open source pore network modeling software package. ECS Trans 58(1):79–86CrossRefGoogle Scholar
  52. 52.
    Bruggeman D (1935) Dielectric constant and conductivity of mixtures of isotropic materials. Ann Phys (Leipzig) 24:636–679CrossRefGoogle Scholar
  53. 53.
    O’Hayre RP et al (2006) Fuel cell fundamentals. Wiley, New YorkGoogle Scholar
  54. 54.
    Washburn EW (1921) Note on a method of determining the distribution of pore sizes in a porous material. Proc Natl Acad Sci USA 7:115–116CrossRefGoogle Scholar
  55. 55.
    Barabási A-L (1996) Invasion percolation and global optimization. Phys Rev Lett 76(20):3750–3753CrossRefGoogle Scholar
  56. 56.
    Glantz R, Hilpert M (2008) Invasion percolation through minimum-weight spanning trees. Phys Rev E. 77(3):031128CrossRefGoogle Scholar
  57. 57.
    Wilkinson D, Willemsen JF (1983) Invasion percolation: a new form of percolation theory. J Phys A: Math Gen 16(14):3365CrossRefGoogle Scholar
  58. 58.
    Quesnel C et al (2015) Dynamic Percolation and Droplet Growth Behavior in Porous Electrodes of Polymer Electrolyte Fuel Cells. J Phys Chem C 119(40):22934–22944CrossRefGoogle Scholar
  59. 59.
    Gostick JT et al (2009) Characterization of the capillary properties of gas diffusion media. In: Modeling and diagnostics of polymer electrolyte fuel cells. Springer, Berlin, pp 225–254CrossRefGoogle Scholar
  60. 60.
    Pharoah JG, Karan K, Sun W (2006) On effective transport coefficients in PEM fuel cell electrodes: anisotropy of the porous transport layers. J Power Sources 161(1):214–224CrossRefGoogle Scholar
  61. 61.
    Shi Y et al (2008) Fractal model for prediction of effective thermal conductivity of gas diffusion layer in proton exchange membrane fuel cell. J Power Sources 185(1):241–247CrossRefGoogle Scholar
  62. 62.
    Vielstich W, Gasteiger HA, Yokokawa H (2009) Handbook of Fuel Cells. 6 vol Set. Wiley-Blackwell, HobokenGoogle Scholar
  63. 63.
    Reiser CA et al (2005) A reverse-current decay mechanism for fuel cells. Electrochem Solid-State Lett 8(6):A273–A276CrossRefGoogle Scholar
  64. 64.
    Parthasarathy A et al (1992) The platinum microelectrode/Nafion interface: an electrochemical impedance spectroscopic analysis of oxygen reduction kinetics and Nafion characteristics. J Electrochem Soc 139(6):1634–1641CrossRefGoogle Scholar
  65. 65.
    Mathias M et al (2003) Diffusion media materials and characterisation. Handbook of fuel cells. Wiley, New YorkGoogle Scholar
  66. 66.
    Meng H, Wang C-Y (2004) Electron transport in PEFCs. J Electrochem Soc 151(3):A358–A367CrossRefGoogle Scholar
  67. 67.
    Zhang J (2008) PEM fuel cell electrocatalysts and catalyst layers: fundamentals and applications. Springer, BerlinCrossRefGoogle Scholar
  68. 68.
    Iranzo A, Boillat P, Rosa F (2014) Validation of a three dimensional PEM fuel cell CFD model using local liquid water distributions measured with neutron imaging. Int J Hydrog Energy 39(13):7089–7099CrossRefGoogle Scholar
  69. 69.
    Tranter T et al (2017) A method for measuring relative in-plane diffusivity of thin and partially saturated porous media: an application to fuel cell gas diffusion layers. Int J Heat Mass Transfer 110:132–141CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.Department of Chemical EngineeringMcGill UniversityMontrealCanada

Personalised recommendations