Fractal model for predicting the effective binary oxygen diffusivity of the gas diffusion layer in proton exchange membrane fuel cells

We propose an analytical model to predict the effective binary oxygen diffusivity of the porous gas diffusion layer (GDL) in proton exchange membrane fuel cells (PEMFCs). In this study, we consider the fractal characteristics of the porous GDL as well as its general microstructure, and we adopt the Bosanquet equation to derive effective diffusivity. The fractal characterization of GDL enables us to model effective diffusivity in a continuous manner while taking into account the effect of pore size distribution. Comparison to two other theoretical models that are generally accepted in the simulation of PEMFCs shows similar trends in all three models, indicating that our proposed model is well founded. Furthermore, the predicted effective binary oxygen diffusivities of two samples show that after treatment with polytetrafluoroethylene (PTFE), the effective binary diffusivity of the GDL decreases. Based on the parametric effect analysis, we conclude that effective binary diffusivity is negatively correlated with tortuosity fractal dimension but positively correlated with the fractal dimension of pore area, porosity, or mean pore diameter. The proposed model facilitates fast prediction of effective diffusivity as well as multi-scale modeling of PEMFCs and thus facilitates the design of the GDLs and of PEMFCs.

[1]  M. Pan,et al.  A fractal permeability model for the gas diffusion layer of PEM fuel cells , 2006 .

[2]  G. Armatas,et al.  Determination of the effects of the pore size distribution and pore connectivity distribution on the pore tortuosity and diffusive transport in model porous networks , 2006 .

[3]  S. V. Sotirchos,et al.  Effective Kundsen diffusivities in structures of randomly overlapping fibers , 1991 .

[4]  Ranga Pitchumani,et al.  A fractal geometry model for evaluating permeabilities of porous preforms used in liquid composite molding , 1999 .

[5]  Jon G. Pharoah,et al.  On effective transport coefficients in PEM fuel cell electrodes: Anisotropy of the porous transport layers , 2006 .

[6]  J. Sato,et al.  FRACTAL GENERATION OF CHAR PORES THROUGH RANDOM WALK , 2007 .

[7]  Robert E. Wilson,et al.  Fundamentals of momentum, heat, and mass transfer , 1969 .

[8]  Jie Shen,et al.  Computing the effective diffusivity using a spectral method , 2001 .

[9]  Hans-Jörg Vogel,et al.  Quantification of pore structure and gas diffusion as a function of scale , 2002 .

[10]  G. Armatas,et al.  Estimation of diffusion parameters in functionalized silicas with modulated porosity. Part I: chromatographic studies. , 2005, Journal of chromatography. A.

[11]  B. Elberling.  Gas phase diffusion coefficient in cemented porous media , 1996 .

[12]  Peter M. A. Sloot,et al.  Tortuosity of an Unsaturated Sandy Soil Estimated using Gas diffusion and Bulk Soil Electrical Conductivity: Comparing analogy-based Models and Lattice-Boltzmann Simulatons , 2001 .

[13]  A. Hasmy,et al.  Numerical Study of Pore Sizes Distribution in Gels , 2003 .

[14]  Y. F. Houst,et al.  Influence of porosity and water content on the diffusivity of CO2 and O2 through hydrated cement paste , 1994 .

[15]  J. Sato,et al.  NUMERICAL SIMULATIONS OF GAS DIFFUSION AND REACTION IN FRACTAL PORES DURING CHAR COMBUSTION , 2007 .

[16]  S. Bartelt-Hunt,et al.  Measurement of effective air diffusion coefficients for trichloroethene in undisturbed soil cores. , 2002, Journal of contaminant hydrology.

[17]  M. Hunt,et al.  Discrete element simulations for granular material flows: effective thermal conductivity and self-diffusivity , 1997 .

[18]  M. Pan,et al.  Fractal model for prediction of effective thermal conductivity of gas diffusion layer in proton exchange membrane fuel cell , 2008 .

[19]  Michel Aubertin,et al.  Measurement and Prediction of the Oxygen Diffusion Coefficient in Unsaturated Media, with Applications to Soil Covers , 2004 .

[20]  Chaoyang Wang,et al.  Three-dimensional analysis of transport and electrochemical reactions in polymer electrolyte fuel cells , 2004 .

[21]  Chaitanya J. Bapat,et al.  Effect of anisotropic thermal conductivity of the GDL and current collector rib width on two-phase transport in a PEM fuel cell , 2008 .

[22]  P. Mu,et al.  Fractal analysis of gas diffusion layer in PEM Fuel Cells , 2006 .

[23]  Yi Cheng,et al.  The measurement of gas diffusivity in porous materials by temporal analysis of products (TAP) , 2007 .

[24]  Enrique Iglesia,et al.  The effects of diffusion mechanism and void structure on transport rates and tortuosity factors in complex porous structures , 2004 .

[25]  A. McBratney,et al.  On Diffusion in Fractal Soil Structures , 2000 .

[26]  E. S. and,et al.  Diffusion Coefficients Calculated for Microporous Solids from Structural Parameters Evaluated by Fractal Geometry , 1997 .

[27]  Balakrishnan,et al.  Analytic calculation of the diffusion coefficient for random walks on strips of finite width: Dependence on size and nature of boundaries. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.