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Transport phenomena in porous media are commonplace in our daily lives.Examples and applications include heat and moisture transport in soils, bakingand drying of food stuffs, curing of cement, and evaporation of fuels in wildfires. Of particular interest to this study are heat and moisture transport inunsaturated soils. Historically, mathematical models for these processes arederived by coupling classical Darcy's, Fourier's, and Fick's laws with volumeaveraged conservation of mass and energy and empirically based source and sinkterms. Recent experimental and mathematical research has proposed modificationsand suggested limitations in these classical equations. The primary goal ofthis thesis is to derive a thermodynamically consistent system of equations forheat and moisture transport in terms of the chemical potential that addressessome of these limitations. The physical processes of interest are primarilydiffusive in nature and, for that reason, we focus on using the macroscalechemical potential to build and simplify the models. The resulting coupledsystem of nonlinear partial differential equations is solved numerically andvalidated against the classical equations and against experimental data. Itwill be shown that under a mixture theoretic framework, the classical Richards'equation for saturation is supplemented with gradients in temperature, relativehumidity, and the time rate of change of saturation. Furthermore, it will beshown that restating the water vapor diffusion equation in terms of chemicalpotential eliminates the necessity for an empirically based fitting parameter.

Heat and Moisture Transport in Unsaturated Porous Media -- A Coupled Model in Terms of Chemical Potential