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Thermodynamic approach to effective stress in partially saturated porous media. (English) Zbl 1034.74019

The authors derive an expression for equilibrium effective stress acting on the solid phase of a porous medium containing two immiscible fluid phases. The derivation makes use of the thermodynamics of the system at a macroscale (a scale of the order of tens of pore diameters, but much smaller than the entire system). This scale in also referred to as the core scale or Darcy scale. At this scale, geometric quantities such as porosity, saturation, and interfacial area per volume can be meaningfully defined and included in the analysis. A macroscale point thus includes a mix of phase interfaces, and the common line where the interfaces are of interest. The analysis leads to an expression for capillary pressure as a function of phase pressures and the disjoining pressure.

MSC:

74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74A15 Thermodynamics in solid mechanics
74Q15 Effective constitutive equations in solid mechanics
76S05 Flows in porous media; filtration; seepage
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