In swelling porous media, the potential for flow is much more than pressure, and derivations for flow equations have yielded a variety of equations. In this paper we show that the macroscopic flow potentials are the electro-chemical potentials of the components of the fluid and that other forms of flow equations, such as those derived through mixture theory or homogenization, are a result of particular forms of the chemical potentials of the species. It is also shown that depending upon whether one is considering the pressure of a liquid in a reservoir in electro-chemical equilibrium with the swelling porous media, or the pressure of the vicinal liquid within the swelling porous media, a critical pressure gradient threshold exists or does not.
Here we theoretically derive the Terzaghi stress principle for saturated and partially saturated isotropic, porous media with compressible phases. We use previously derived thermodynamic deinitions of the drained and unjacketed compressibilities and total differentials to theoretically determine how the total pressure relates to isotropic strain and changes in luid pressures. We show that under simplifying assumptions we recover the varying forms of the Biot coeficient for saturated porous media and the Bishop parameter for partially saturated porous media. We compare this approach with four modern constructions: the mixture theoretic approaches of Coussy and Borja, Wang's differential approach, and the thermodynamically constrained averaging theory approach of Gray and Schreler. In doing so we theoretically clarify the often confused deinitions of the solid compressibility coeficient, the unjacketed and drained compressibilities, and the generalized Terzaghi stress principle in differential form.
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