Three Pressures in Porous Media
 Lynn S. Bennethum,
 Tessa Weinstein
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In a thermodynamic setting for a single phase (usually fluid), the thermodynamically defined pressure, involving the change in energy with respect to volume, is often assumed to be equal to the physically measurable pressure, related to the trace of the stress tensor. This assumption holds under certain conditions such as a small rate of deformation tensor for a fluid. For a twophase porous medium, an additional thermodynamic pressure has been previously defined for each phase, 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 how these three macroscopic pressures (the two thermodynamically defined pressures and the pressure relating to the trace of the stress tensor) are related and discuss the physical interpretation of each of them. In the process, we show how one can convert directly between different combinations of independent variables without reexploiting the entropy inequality. The physical interpretation of these three pressures is investigated by examining four media: a single solid phase, a porous solid saturated with a fluid which has negligible physicochemical interaction with the solid phase, a swelling porous medium with a noninteracting solid phase, such as welllayered clay, and a swelling porous medium with an interacting solid phase such as swelling polymers.
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 Title
 Three Pressures in Porous Media
 Journal

Transport in Porous Media
Volume 54, Issue 1 , pp 134
 Cover Date
 20040101
 DOI
 10.1023/A:1025701922798
 Print ISSN
 01693913
 Online ISSN
 15731634
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 pressure
 porous media
 mixture theory
 swelling
 constitutive equations
 clay
 polymers
 Industry Sectors
 Authors

 Lynn S. Bennethum ^{(1)}
 Tessa Weinstein ^{(1)}
 Author Affiliations

 1. Center for Computational Mathematics, University of Colorado at Denver, Campus Box 170, 1250 14th St. Suite 600, P.O. Box 173364, Denver, CO, 802173364, USA