Transport in Porous Media

, Volume 114, Issue 3, pp 815–821 | Cite as

Note on Coussy’s Thermodynamical Definition of Fluid Pressure for Deformable Porous Media

Article

Abstract

In a lifetime of work, Dr. Olivier Coussy developed a complete theoretic framework for porous media that researchers in a broad range of fields including (but not limited to) concrete, hydrology, swelling clay, and \(\hbox {CO}_2\)-induced swelling of coal have continued to use as a foundation. However, in some of these works where a framework is developed for a deformable porous media, a dissipative inequality is assumed that implicitly results in a thermodynamical form of liquid pressure that is inconsistent with the classical thermodynamical form of pressure found in thermodynamic textbooks for a single phase. In this note, we compare this definition of pressure with those developed in other mixture-theoretic frameworks and demonstrate this inconsistency by mathematically showing that the thermodynamic quantity is most closely related to the solid pressure and explain how this inconsistency came about.

Keywords

Coussy Porous media Thermodynamics Pressure Deformation 

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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsWashington State UniversityPullmanUSA

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