In this thesis, two numerical modeling methods are used to investigate the thermal conductivity of the polymer electrolyte membrane (PEM) fuel cell gas diffusion layer (GDL). First, an analytical model is used to study the through-plane thermal conductivity from representative physical GDL models informed by microscale computed tomography imaging of four commercially available GDL materials. The effect of the heterogeneity of the through-plane porosity of the GDL and polytetrafluoroethylene (PTFE) treatment is studied and it is noted that the high porosity surface transition regions have a dominating effect over the addition of PTFE in impacting the overall thermal conductivity. Next, the lattice Boltzmann method (LBM) is employed to study both the in-plane and through-plane thermal conductivity of stochastic numerically generated GDL modeling domains. The effect of GDL compression, binder content, PTFE treatment, addition of a microporous layer (MPL), heterogeneous porosity distributions, and water saturation on the thermal conductivity are investigated.

In this thesis, two numerical modeling methods are used to investigate the thermal conductivity of the polymer electrolyte membrane (PEM) fuel cell gas diffusion layer (GDL). First, an analytical model is used to study the through-plane thermal conductivity from representative physical GDL models informed by microscale computed tomography imaging of four commercially available GDL materials. The effect of the heterogeneity of the through-plane porosity of the GDL and polytetrafluoroethylene (PTFE) treatment is studied and it is noted that the high porosity surface transition regions have a dominating effect over the addition of PTFE in impacting the overall thermal conductivity. Next, the lattice Boltzmann method (LBM) is employed to study both the in-plane and through-plane thermal conductivity of stochastic numerically generated GDL modeling domains. The effect of GDL compression, binder content, PTFE treatment, addition of a microporous layer (MPL), heterogeneous porosity distributions, and water saturation on the thermal conductivity are investigated.

The Pleistocene carbonate rock Biscayne Aquifer of south Florida contains laterally-extensive bioturbated ooltic zones characterized by interconnected touching-vug megapores that channelize most flow and make the aquifer extremely permeable. Standard petrophysical laboratory techniques may not be capable of accurately measuring such high permeabilities. Instead, innovative procedures that can measure high permeabilities were applied. These fragile rocks cannot easily be cored or cut to shapes convenient for conducting permeability measurements. For the laboratory measurement, a 3D epoxy-resin printed rock core was produced from computed tomography data obtained from an outcrop sample. Permeability measurements were conducted using a viscous fluid to permit easily observable head gradients (~2 cm over 1 m) simultaneously with low Reynolds number flow. For a second permeability measurement, Lattice Boltzmann Method flow simulations were computed on the 3D core renderings. Agreement between the two estimates indicates an accurate permeability was obtained that can be applied to future studies.

Melting and melt segregation are key processes in the geochemical evolution of the Earth. However, mechanism and time scale of melt transport from the source to the surface are still not well understood and are dependent on the grain-scale distribution of melt. A related question is the retention of melt in partially molten regions of the Earths upper mantle. Seismic observations from mid-ocean ridges (MOR) and subduction zones are interpreted to show in-situ melt contents up to 3%, while geochemical observations from MOR basalts are inferred to indicate very efficient extraction of melt (porosities of order 0.1%). Earlier theoretical models of the melt distribution were based on the balance of surface tension between melt and uniform crystalline grains, predicting a simple net- work of melt along three-grain edges. Analyses of experimentally produced samples of olivine and basaltic melt show that the melt geometry is much more complex, and includes wetted two-grain boundaries. I reconstructed the melt geometry of two experimentally produced samples by serial sectioning and 3-D rendering of the pore geometry which demonstrates for the first time that melt exists in thin layers on two-grain boundaries. This confirms the inferences from previous 2-D observations and has significant implications for physical properties of partially molten regions, for example seismic velocities and attenuation. The wetted two-grain boundaries are inferred to be a consequence of continuous grain growth. Due to the complexity of the 3-D melt geometry the perme- ability of partially molten rocks can not be predicted from simple models. I therefore investigated the permeability as a function of porosity for both synthetic and ex- perimentally determined pore geometries using a lattice-Boltzmann method. The calculated permeability is not a simple function of porosity, but increases rapidly at a critical fraction of wetted two-grain boundaries. In order to extrapolate the experimentally based findings to grain sizes expected in natural rocks I examined the geometry of secondary phases inferred to represent relict melt in mantle peridotites from the Krivaja massif in Bosnia. These findings corroborate the experimental observations of wetted two-grain boundaries.