An Application of Path-Percolation Theory and Lattice-Boltzmann Model on Mass Transfer in Inhomogeneous Porous Media

In this dissertation, random inhomogeneous porous channels were generated statistically, and single- and multi-phase flow models were developed to investigate diffusion behavior of gases in porous media. Three different methods were used to simulate inhomogeneous porous flow channels. First, the path-percolation theory was adapted in diffusion studies to generate random high-tortuosity (above 1.07) porous channels with a desired porosity within a specified confidence level. Cluster labeling process was applied to simulate paths for the gas molecules, and the resulting effective porosity was investigated statistically. Second, the double-path-percolation theory was introduced to simulate low-tortuosity (between 1.0005 and 1.0700) flow channels. Using a combined void- and solid-cluster labeling process, this new model also simulates paths in both solid and void regions in the channel, hence transport analysis can be performed in both regions. Third, two dimensional slices of the micro-computed tomographies of Mitsubishi Rayon Corp. MRC-105 and Sigracet SGL-25BA gas diffusion layer samples, which are used in polymer electrolyte fuel cells, were digitized, and the effective porosities were determined statistically by cluster labeling process. A single-phase Lattice-Boltzmann model (LBM) was developed to simulate gas flow in the channels generated. Velocity distributions were obtained to evaluate the effective tortuosity in gas diffusion layer samples and different channels generated by single- and double-path-percolation theories. Furthermore, multi-phase LBMs were developed to investigate the impact of liquid formation on mass transfer in porous channels. Statistical results of porosity, effective porosity, and tortuosity of the system with different liquid volumes were investigated. Velocity distributions in porous channels with different solid-liquid-vapor combinations were analyzed. Moreover, a portion of the solid surface inside the channel was set hydrophobic, and multi-phase effects on mass transport were examined. A software was developed for a combined path-percolation – Lattice-Boltzmann model, and the performance was improved by different high-performance computing system implementations. The techniques introduced in this dissertation can be utilized in inhomogeneous porous media application involved with single- and multi-phase mass transport with surface-fluid interactions. This work is unique through its statistical approach and cluster labeling process.