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

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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.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Washington State University, Pullman, WA, USA

    Lynn Schreyer

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  1. Lynn Schreyer
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Correspondence to Lynn Schreyer.

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Schreyer, L. Note on Coussy’s Thermodynamical Definition of Fluid Pressure for Deformable Porous Media. Transp Porous Med 114, 815–821 (2016). https://doi.org/10.1007/s11242-016-0745-4

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  • DOI: https://doi.org/10.1007/s11242-016-0745-4

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