The present work describes a procedure to calculate the effective diffusivity of a porous composite medium from the three-dimensional reconstruction of its microstructure. We perform Monte Carlo simulations based on the mean-square displacement method on numerical models of composite materials microstructures. First, computations of the effective diffusivity in the bulk diffusion regime account for the effect of the tortuosity of the geometry on gas diffusion. The Bruggeman equation, which is often used in the literature to relate the effective diffusivity to the porosity of the structure, appears to be inaccurate for porosities ε<0.40. A more accurate correlation for this range of porosities is provided based on the results of our simulations. Second, the Bosanquet equation, which accounts for the effect of pore confinement on gas diffusion, is validated provided that the definition of the Knudsen number is based on the appropriate characteristic length. The procedure to calculate this characteristic length is demonstrated for analytical geometries. However, in practice, geometries obtained from experimental measurements are discrete. For discrete geometries, we show the effect of the resolution of the geometry on the accuracy of the calculation of the effective diffusivity and other properties of the porous material. In addition, the tesselation of solid surfaces affects the calculation of the chord-length distribution regardless of the resolution. This hinders the accurate estimation of the characteristic length necessary to compute the Knudsen number and the effective diffusivity.
This article presents a numerical framework for the computation of the effective transport properties of solid oxide fuel cells (SOFCs) porous electrodes from three-dimensional (3D) constructions of the microstructure. Realistic models of the 3D microstructure of porous electrodes are first constructed from measured parameters such as porosity and particle size distribution. Then each phase in the model geometries is tessellated with a computational grid. Three different types of grids are considered: Cartesian, octree, and body-fitted/cut-cell with successive levels of surface refinement. Finally, a finite volume method is used to compute the effective transport properties in the three phases (pore, electron, and ion) of the electrode. To validate the numerical approach, results obtained with the finite volume method are compared to those calculated with a random walk simulation for the case of a body-centred cubic lattice of spheres. Then, the influence of the sample size is investigated for random geometries with monosized particle distributions. Finally, effective transport properties are calculated for model geometries with polydisperse particle size distributions similar to those observed in actual SOFC electrodes.
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