WIAS Preprint No. 1375, (2008)

Mathematical modeling of channel-porous layer interfaces in PEM fuel cells


  • Ehrhardt, Matthias
  • Fuhrmann, Jürgen
    ORCID: 0000-0003-4432-2434
  • Linke, Alexander
    ORCID: 0000-0002-0165-2698
  • Holzbecher, Ekkehard

2010 Mathematics Subject Classification

  • 76S05 35Q35 76D05

2008 Physics and Astronomy Classification Scheme

  • 47.56.+r


  • fluid-porous interface, porous media, PEM fuel cell, incompressible flow, Stokes equation, Darcy equation, Brinkman extension, Beavers-Joseph-Saffman interface conditions




In proton exchange membrane (PEM) fuel cells, the transport of the fuel to the active zones, and the removal of the reaction products are realized using a combination of channels and porous diffusion layers. In order to improve existing mathematical and numerical models of PEM fuel cells, a deeper understanding of the coupling of the flow processes in the channels and diffusion layers is necessary.
After discussing different mathematical models for PEM fuel cells, the work will focus on the description of the coupling of the free flow in the channel region with the filtration velocity in the porous diffusion layer as well as interface conditions between them.
The difficulty in finding effective coupling conditions at the interface between the channel flow and the membrane lies in the fact that often the orders of the corresponding differential operators are different, e.g., when using stationary (Navier-)Stokes and Darcy's equation. Alternatively, using the Brinkman model for the porous media this difficulty does not occur.
We will review different interface conditions, including the well-known Beavers-Joseph-Saffman boundary condition and its recent improvement by Le Bars and Worster.

Appeared in

  • M. Ehrhardt, J. Fuhrmann, A. Linke, E. Holzbecher, Proceedings of FDFC2008 --- Fundamentals and Developments of Fuel Cell Conference 2008, Nancy, France, December 10--12 (CD), 2008, pp. 8 pages

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