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

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.