A multi-scale approach to material modeling of fuel cell diffusion media. (English) Zbl 1402.76123

Summary: Effective diffusivity of porous media in fuel cells has been identified as a relevant material property in automotive applications. Pore-scale simulations utilizing imaging data sets of real materials or virtual model representations provide such diffusivity numbers. However, components like the microporous layer (MPL) or the gas diffusion electrode have not been covered adequately so far by efficient and practical modeling approaches due the small pore sizes and resulting Knudsen contribution to diffusion. In this publication we report the development of a numerical method which allows for the determination of binary diffusion coefficients for all Knudsen numbers and demonstrate the application to fuel cell diffusion media in a multi-scale modeling approach. For high Knudsen numbers effective diffusivity is determined by tracking a large number of individual molecules that collide with the pore walls. For low Knudsen numbers, effective diffusivity is determined by solving the Laplace equation on the pore space. Both contributions to the overall diffusivity are merged by applying Bosanquet’s formula. The resulting diffusivity can be used as an effective number for a microporous layer coating of a spatially resolved fibrous diffusion medium. As this multi-scale method is also based on a 3D voxel grid, we could study any distribution of the MPL on and inside the gas diffusion layer (GDL) with this model, e.g. cracks, different penetration depths, etc.


76S05 Flows in porous media; filtration; seepage
76R50 Diffusion


Full Text: DOI


[1] Helmolt, R. V.; Eberle, U.: Fuel cell vehicles: status 2007, J. power sources 165, 833-843 (2007)
[2] Cindrella, L.; Kannan, A. M.; Lin, J. F.; Saminathan, K.; Ho, Y.; Lin, C. W.; Wertz, J.: Gas diffusion layer for proton exchange membrane fuel cells – a review, J. power sources 194, 146-160 (2009)
[3] Gostick, J.; Ioannidis, M.; Fowler, M.; Pritzker, M.: Pore network modeling of fibrous gas diffusion layers for polymer electrolyte membrane fuel cells, J. power sources 173, 277-290 (2007)
[4] Epstein, N.: On tortuosity and the tortuosity factor in flow and diffusion through porous media, Chem. eng. Sci. 44, 777-779 (1989)
[5] Quick, Ch.; Ritzinger, D.; Lehnert, W.; Hartnig, Ch.: Characterization of water transport in gas diffusion media, J. power sources 190, 110-120 (2009)
[6] T. Berning, Ch. Wieser, P.-Y. Chuang, Th. Trabold, Method for Optimizing Diffusion Media with Spatially Varying Mass Transport Resistance, United States Patent Application Publication US 2009/0024373 A1.
[7] Gostick, J.; Fowler, M.; Ioannidis, M.; Pritzker, M.; Volfkovich, Y.; Sakars, A.: Capillary pressure and hydrophilic porosity in gas diffusion layers for polymer electrolyte fuel cells, J. power sources 156, 375-387 (2006)
[8] Mathias, M.; Roth, J.; Fleming, J.; Lehnert, W.: Diffusion media materials and characterisation, Technology and applications, fuel cell technology and applications 3 (2003)
[9] Becker, J.; Flückiger, R.; Reum, M.; Büchi, F. N.; Marone, F.; Stampanoni, M.: Determination of material properties of gas diffusion layers – experiments and simulations using phase contrast tomographic microscopy, J. electrochem. Soc. 156, No. 10, B1175-B1181 (2009)
[10] Schulz, V.; Becker, J.; Wiegmann, A.; Mukherjee, P.; Wang, C. -Y.: Modeling of two-phase behavior in the gas diffusion medium of pefcs via full morphology approach, J. electrochem. Soc. 154, B419-B426 (2007)
[11] Kang, K.; Ju, H.: Numerical modeling and analysis of micro-porous layer effects in polymer electrolyte fuel cells, J. power sources 194, 763-773 (2009)
[12] Becker, J.; Wiegmann, A.; Schulz, V.: Numerical determination of two-phase material parameters of a gas diffusion layer using tomography images, J. fuel cell sci. Technol. 5, 021006-021009 (2008)
[13] Medalia, A.; Heckman, F.: Morphology of aggregates – II. Size and shape factors of carbon black aggregates from electron microscopy, Carbon 7, 567-582 (1969)
[14] Volfkovich, Y.; Bagotzky, V.; Sosenkin, V.; Blinov, I.: The standard contact porosimetry, Colloids surfaces A physicochem. Eng. aspects 187-188, 349-365 (2001)
[15] Schladitz, K.; Peters, S.; Reinel-Bitzer, D.; Wiegmann, A.; Ohser, J.: Design of acoustic trim based on geometric modeling and flow simulation for non-woven, Comp. mat. Sci. 38, 56-66 (2006)
[16] Soille, P.: Morphological image analysis, (1999) · Zbl 0976.68168
[17] Tomadakis, M.; Sotirchos, S.: Effective Knudsen diffusivities in structures of randomly overlapping fibers, Aiche J. 37, 74-86 (1991)
[18] Tomadakis, M.; Sotirchos, S.: Ordinary and transition regime diffusion in random fiber structures, Aiche J. 39, 397-412 (1993)
[19] Knudsen, M.: Die gesetze der molecularströmung und der inneren reibungsströmung der gase durch röhren, Ann. d. Phys. 28, 75-130 (1909) · JFM 40.0825.02
[20] Pollard, W. G.; Present, R. D.: On gaseous self-diffusion in long capillary tubes, Phys. rev. 73, 762 (1948)
[21] Keil, F.: Diffusion und chemische reaktionen in der gas/feststoff-katalyse, (1999)
[22] Kerkhof, P. J. A.M.: A modified Maxwell – Stefan model for transport through inert membranes: the binary friction model, Chem. eng. J. 64, 319-343 (1996)
[23] Zalc, J. M.; Reyes, S. C.; Iglesia, E.: The effects of diffusion mechanism and void structure on transport rates and tortuosity factors in complex porous structures, Chem. eng. Sci. 759, 2947-2960 (2004)
[24] Fraunhofer ITWM, GeoDict. Available from: <http://www.geodict.com>, ©  2001 – 2010.
[25] A. Wiegmann, A. Zemitis, EJ-HEAT: a fast explicit jump harmonic averaging solver for the effective heat conductivity of composite materials, Bericht des Fraunhofer ITWM 94 (2006).
[26] Hornung, U.: Homogenization and porous media, (1997) · Zbl 0872.35002
[27] Babovsky, H.: On Knudsen flows within thin tubes, J. stat. Phys. 44, 865-878 (1986) · Zbl 0629.76079
[28] CRC Handbook of Chemistry and Physics, 81st ed., CRC Press, 2000 – 2001. · Zbl 0609.34009
[29] Baker, D.; Caulk, D.; Neyerlin, K.; Murphy, M.: Measurement of oxygen transport resistance in PEM fuel cells by limiting current methods, J. electrochem. Soc. 156, B991-B1003 (2009)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.