An improved mrt lattice boltzmann model for calculating anisotropic permeability of compressed and uncompressed carbon cloth gas diffusion layers based on x-ray computed micro-tomography

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Colleges, School and Institutes

External organisations

  • University of Liverpool
  • Loughborough University
  • School of Mechanical and Manufacturing Engineering


The gas diffusion layers (GDLs) in polymer proton exchange membrane fuel cells are under compression in operation. Understanding and then being able to quantify the reduced ability of GDLs to conduct gases due to the compression is hence important in fuel cell design. In this paper, we investigated the change of anisotropic permeability of GDLs under different compressions using the improved multiple-relaxation time (MRT) lattice Boltzmann model and X-ray computed micro-tomography. The binary 3D X-ray images of GDLs under different compressions were obtained using the technologies we developed previously, and the permeability of the GDLs in both through-plane and inplane directions was calculated by simulating gas flow at micron scale through the 3D images. The results indicated that, in comparison with the single-relaxation time (SRT) lattice Boltzmann model commonly used in the literature, the MRT model is robust and flexible in choosing model parameters. The SRT model can give accurate results only when using a specific relaxation parameter whose value varies with porosity. The simulated results using the MRT model reveal that compression could lead to a significant decrease in permeability in both through-plane and in-plane directions, and that the relationship between the decreased permeability and porosity can be well described by both Kozeny-Carman relation and the equation derived by Tomadakis and Sotirchos (1993, "Ordinary and Transition Rdgime Diffusion in Random Fiber Structure," AIChE J., 39, pp. 397-412) for porosity in the range from 50% to 85%. Since GDLs compression takes place mainly in the through-plane direction, the results presented in this work could provide an easy way to estimate permeability reduction in both through-plane and in-plane directions when the compressive pressure is known.


Original languageEnglish
Article number041010
JournalJournal of Fuel Cell Science and Technology
Issue number4
Publication statusPublished - 1 Dec 2012


  • Anisotropic permeability, Carbon cloth gas diffusion layer, Compressed and uncompressed gdls, Lattice boltzmann method, Multiple-relaxation time (mrt)