Transport in Porous Media

, Volume 89, Issue 3, pp 475–486 | Cite as

Poroelasticity-II: On the Equilibrium State of the Fluid-Filled Penetrable Poroelastic Body

  • S. L. LopatnikovEmail author
  • J. W. GillespieJr.


Part-II of the paper titled “Poroelasticity-II” is devoted to defining the joint equilibrium state of a fluid and elastic penetrable material, encapsulated in a rigid volume, Ω. One can ask different questions in respect to such an equilibrium state, such as: (1) In what physical state will the fluid be, if the porous volume of the poroelastic material is filled with a given mass of fluid? (2) What is the capacity of a volume filled with a penetrable sponge in respect to the fluid being in specific state? etc. The point is that, in the frame of the most popular theory of poroelastic materials, Biot’s theory, such a question cannot be addressed because this theory is formulated as a linear theory in the neighborhood of some equilibrium state. In this article, we continue to describe our theory that can be applied to solve such problems. We consider a simplified case of a linear-elastic matrix and a fluid having a Van der Waals equation of state and address the problem of the equilibrium state.


Poroelastic materials Fluid Van der Waals Equilibrium 

List of Symbols


Biot’s “fluid content” parameter


Vector of matrix displacement in Biot’s nomenclature


Vector of fluid displacement in Biot’s nomenclature


Vector of matrix displacement


Vector of the fluid displacement


Fluid particle velocity


Porosity as the argument of the equation of state


Equilibrium porosity of the poroelastic material body filled with a fluid


Porosity of the “empty” poroelastic material body (non-filled with a fluid)


Volume of the container


Mass of fluid


Density of the fluid as the argument of equation of state


Density of the fluid in the equilibrium state


Density of matrix material in the “empy” state (not filled with a fluid)

a and b

Van der Waals constants


Pressure of the fluid




Tensor of the internal strain (See Part I)


Bulk part of the tensor of the internal strain


Bulk part of the tensor of the internal strain in an equilibrium state of fluid-filled poroelastic material material

\({I_2 = \bar{{\varepsilon}}_{ij}\bar{{\varepsilon }}_{ij}}\)

Second invariant of the strain tensor


Internal energy of the matrix, which we consider (in neglection of heat effects) a function of \({\bar{{\varepsilon}}_{ij}}\) and \({\varphi }\)


Kronecker delta


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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Center for Composite MaterialsUniversity of DelawareNewarkUSA
  2. 2.Department of Civil and Environmental EngineeringUniversity of DelawareNewarkUSA
  3. 3.Department of Materials ScienceUniversity of DelawareNewarkUSA

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