  Transport phenomena in porous media are commonplace in our daily lives.
Examples and applications include heat and moisture transport in soils, baking
and drying of food stuffs, curing of cement, and evaporation of fuels in wild
fires. Of particular interest to this study are heat and moisture transport in
unsaturated soils. Historically, mathematical models for these processes are
derived by coupling classical Darcy's, Fourier's, and Fick's laws with volume
averaged conservation of mass and energy and empirically based source and sink
terms. Recent experimental and mathematical research has proposed modifications
and suggested limitations in these classical equations. The primary goal of
this thesis is to derive a thermodynamically consistent system of equations for
heat and moisture transport in terms of the chemical potential that addresses
some of these limitations. The physical processes of interest are primarily
diffusive in nature and, for that reason, we focus on using the macroscale
chemical potential to build and simplify the models. The resulting coupled
system of nonlinear partial differential equations is solved numerically and
validated against the classical equations and against experimental data. It
will be shown that under a mixture theoretic framework, the classical Richards'
equation for saturation is supplemented with gradients in temperature, relative
humidity, and the time rate of change of saturation. Furthermore, it will be
shown that restating the water vapor diffusion equation in terms of chemical
potential eliminates the necessity for an empirically based fitting parameter.
