The diffusion of liquid and gas through porous solids is of considerable technological interest and has been investigated for decades in a wide spectrum of disciplines encompassing chemical, civil, mechanical, and petroleum engineering. Porous solids of interest are made of either natural materials (e.g., soil, sand) or man-made materials (e.g., industrial filters, membranes). In both cases, liquids (e.g., water, crude oil) and gases (e.g., air, oxygen, natural gas) are driven through the voids in the porous solid by naturally or artificially induced pressure. Nafion⃝R is an important example of a well-characterized man-made porous medium due to its extensive use in proton- exchange membrane fuel cells. Here, while the fuel cell is in operation, a mixture of air and water diffuses through the pores of a Nafion⃝R membrane. The efficiency of the fuel cell is affected by the variation in water concentration. In addition, high water concentration has been experimen- tally shown to cause substantial volumetric deformation (swelling) of the membrane, which may compromise the integrity of the device.

In this dissertation, a continuum approach for modeling diffusion of fluid through a porous elastic solid is proposed. All balance laws are formulated relative to the frame of a macroscopic solid resulting from the homogenization of the dry solid and the voids. When modeling only liquid diffusion through the macroscopic solid, the displacement of the macroscopic solid and the liquid volume fraction are chosen to characterize the state of the porous medium, and Fick's law is used as the governing equation for liquid flow. When modeling multiphase diffusion through the macroscopic solid, the displacement of the solid, the gas pressure and the liquid saturation are chosen as state variables, and both fluid diffusions are assumed to follow Darcy's law. Both single phase and multiphase diffusion models are implemented in the finite element method, and tested with various loading conditions on different types of materials. Numerical simulation results are presented to show the predictive capability of the two models.