Analysis of representative elementary volume and through-plane regional characteristics of carbon-fiber papers: diffusivity, permeability and electrical/thermal conductivity

Understanding the transport processes that occur in carbon-fiber papers (CFPs) used in fuel cells, electrolyzers, and metal-air/redox flow batteries is necessary to help predict cell performance and durability, optimize materials and diagnose problems. The most common technique used to model these thin, heterogeneous, anisotropic porous media is the volume-averaged approximation based on the existence of a representative elementary volume (REV). However, the applicability of the continuum hypothesis to these materials has been questioned many times, and the error incurred in the predictions is yet to be quantified. In this work, the existence of a REV in CFPs is assessed in terms of dry effective transport properties: mass diffusivity, permeability and electrical/thermal conductivity. Multiple sub-samples with different widths and thicknesses are examined by combining the lattice Boltzmann method with X-ray tomography images of four uncompressed CFPs. The results show that a meaningful length scale can be defined in the material plane in the order of 1-2 mm, which is comparable to the rib/channel width used in the aforementioned devices. As for the through-plane direction, no distinctive length scale smaller than the thickness can be identified due to the lack of a well-defined separation between pore and volume-averaged scales in these inherently thin heterogeneous materials. The results also show that the highly porous surface region (amounting up to 20% of the thickness) significantly reduces the through-plane electrical/thermal conductivity. Overall, good agreement is found with previous experimental data of virtually uncompressed CFPs when approximately the full thickness is considered.