Three Pressures in Swelling Porous Media

For a two-phase swelling porous medium, two pressures have been previously defined thermodynamically in terms of intensive variables for each phase: one relating the change in energy with respect to specific volume, and the other relating the change in energy with respect to volume fraction. Within the framework of Hybrid Mixture Theory and hence the Coleman and Noll technique of exploiting the entropy inequality, we show that a different choice of independent variables allows the comparison of these pressures with the extensive (and hence more classically defined) pressure. In the process we show how one can convert directly between different combinations of independent variables without re-exploiting the entropy inequality and discover the relationship between three thermodynamically defined pressures. The physical interpretation of these three pressures is investigated by examining two media: a swelling porous medium with a non-interacting solid phase, such as well-layered clay, and a swelling porous medium with an interacting solid phase such as swelling polymers.