### Abstract:

Non-dilute salt strength solutions occur in many near surface geologic environments.
In order to better understand the occurrence and movement of the water and salt,
mathematical models for this non-ideal fluid need to be developed. Initial boundary
value problems may then be solved to predict behavior for comparison with
observations. Using the principles of equilibrium reversible and irreversible
thermodynamics, relationships describing the thermo-physics of non-dilute saline
solutions in variably saturated porous media are investigated. Each of four central
chapters investigates a particular aspect of the flow of saline solutions through porous
media. The first chapter derives the general relationships describing the effects of salt
on the vapor content in the gas phase and also on the liquid pressure. The second
chapter summarizes an example using the new theory for sodium chloride (NaCl) from
zero to saturated strength. Additional terms beyond the dilute approximation are
shown to be more important in very dry, fine textured soils with significant salt
content. The third chapter derives the salt corrections for Darcy-type flow laws for
variably saturated porous media, and an example for NaCl is given. Agreement
between theory and experimental data is good, though there appear to be some
unaccounted for effects. These effects may be the result of ionic interaction of the salt
with the loamy sand used, and/or the effect of hysteresis of the water content-pressure
relationship. The final chapter investigates two fundamental assumptions commonly
used in process thermodynamics when considering mixtures described by porous
media, saline water, and moist air. The first assumption is that temperature is the
generalized intensive variable associated with entropy. The second assumption is that
the form of the differential of total energy is known a-priori. It is shown that the first
assumption is suspect under some circumstances, and a generalized notion of how to
select extensive variables for a given system is introduced for comparison with the
second assumption. Examples comparing the "usual" and new theories are
accomplished for ideal gases and for isotropic Newtonian liquids, with results being
favorable except possibly for the Gibbs-Duhem Relation of the Newtonian liquid for
the "usual" theory.