Liquid and gas permeabilities of nanostructured layers: Three-dimensional lattice Boltzmann simulation

Liquid water and gas permeabilities in nanostructured catalyst layers (CLs) (pore size ∼10–150 nm) and microporous layers (MPLs) (pore size ∼50 nm-5 μm) are crucial to reduce the mass transport loss in proton exchange membrane fuel cells (PEMFCs). Experimental measurement of their permeabilities poses great challenges due to their brittle and thin characteristics. Presently, considerable discrepancy exists in the reported permeability values for CLs and MPLs in the literature with variation spanning several orders of magnitude. This study digitally reconstructed various nanostructures of similar pore size as CLs and MPLs to calculate their permeabilities using the Lattice Boltzmann Method (LBM) based on no-slip (e.g. for liquid water flow in MPL and CL's secondary pores) or slip condition (e.g. for gas flow in MPL). Analysis was performed to evaluate the range of pore size in nanostructures for the two boundary conditions. A comprehensive investigation was conducted under various parameters such as the Reynolds number (Re), sphere diameter, porosity, and pore structure. The results revealed that permeability exhibits an increasing trend with the diameter and porosity. The predicted permeability of randomly arranged spheres agrees well with established correlations. The random sphere structure demonstrates higher permeability than their body-centered cubic (BCC) and face-centered cubic (FCC) counterparts. Under slip boundary condition, the permeability was enhanced, compared to the no-slip condition. This study's novelty lies in using distinct boundary conditions to assess the permeabilities of liquid and air, based on flow pattern analysis in the CL and MPL pore structures. A new empirical correlation describing the influence of the Knudsen number (Kn) on the slip permeability was developed, exhibiting consistency with simulation across the entire porosity spectrum.