Transport in Porous Media

, Volume 94, Issue 1, pp 47–68 | Cite as

Macroscopic Flow Potentials in Swelling Porous Media

Article

Abstract

In swelling porous media, the potential for flow is much more than pressure, and derivations for flow equations have yielded a variety of equations. In this article, we show that the macroscopic flow potentials are the electro-chemical potentials of the components of the fluid and that other forms of flow equations, such as those derived through mixture theory or homogenization, are a result of particular forms of the chemical potentials of the species. It is also shown that depending upon whether one is considering the pressure of a liquid in a reservoir in electro-chemical equilibrium with the swelling porous media, or the pressure of the vicinal liquid within the swelling porous media, a critical pressure gradient threshold exists or does not.

Keywords

Porous media Swelling porous media Threshold pressure gradient Flow Thermodynamics 

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References

  1. Achanta S., Cushman J.H., Okos M.R.: On multicomponent, multiphase thermomechanics with interfaces. Int. J. Eng. Sci. 32(11), 1717–1738 (1994)CrossRefGoogle Scholar
  2. Atkins P., de Paula J.: Physical Chemistry. W.H. Freeman and Company, New York (2002)Google Scholar
  3. Attard P., Mitchell D.J., Ninham B.W.: Beyond Poisson-Boltzmann—images and correlations in the electric double-layer. 1. Counterions only. J. Chem. Phys. 89(7), 4987–4996 (1988a)CrossRefGoogle Scholar
  4. Attard P., Mitchell D.J., Ninham B.W.: Beyond Poisson-Boltzmann—images and correlations in the electric double-layer. 2. Symmetric electrolyte. J. Chem. Phys. 88(8), 4358–4367 (1988b)CrossRefGoogle Scholar
  5. Bennethum L.S., Cushman J.H.: Multiscale, hybrid mixture theory for swelling systems-I: balance laws. Int. J. Eng. Sci. 34(2), 125–145 (1996a)CrossRefGoogle Scholar
  6. Bennethum L.S., Cushman J.H.: Multiscale, hybrid mixture theory for swelling systems-II: constitutive theory. Int. J. Eng. Sci. 34(2), 147–169 (1996b)CrossRefGoogle Scholar
  7. Bennethum L.S., Cushman J.H.: Coupled solvent and heat transport of a mixture of swelling porous particles and fluids: single time-scale problem. Transp. Porous Media 36(2), 211–244 (1999)CrossRefGoogle Scholar
  8. Bennethum L.S., Cushman J.H.: Multicomponent, multiphase thermodynamics of swelling porous media with electroquasistatics: I. Macroscale field equations. Transp. Porous Media 47(3), 309–336 (2002a)CrossRefGoogle Scholar
  9. Bennethum L.S., Cushman J.H.: Multicomponent, multiphase thermodynamics of swelling porous media with electroquasistatics: II. Constitutive theory. Transp. Porous Media 47(3), 337–362 (2002b)CrossRefGoogle Scholar
  10. Bennethum L.S., Weinstein T.: Three pressures in porous media. Transp. Porous Media 54(1), 1–34 (2004)CrossRefGoogle Scholar
  11. Bennethum L.S., Murad M.A., Cushman J.H.: Macroscale thermodynamics and the chemical potential for swelling porous media. Transp. Porous Media 39(2), 187–225 (2000)CrossRefGoogle Scholar
  12. Bergeron V.: Forces and structure in thin liquid soap films. J. Phys. Condens. Matter 11, R215–R238 (1999)CrossRefGoogle Scholar
  13. Callen H.B.: Thermodynamics and an Introduction to Thermostatistics. Wiley, New York (1985)Google Scholar
  14. Castellan G.W.: Physical Chemistry. The Benjamin/Cummings Publishing Co, Menlo Park (1983)Google Scholar
  15. Coleman B.D., Noll W.: The thermodynamics of elastic materials with heat conduction and viscosity. Arch. Rational Mech. Anal. 13, 167–178 (1963)CrossRefGoogle Scholar
  16. Coussy O.: Mechanics of Porous Continua. Wiley, New York (1995)Google Scholar
  17. Derjaguin B.V., Churaev N.: On the question of determining the concept of disjoining pressure and its role in the equilibrium and flow of thin films. J. Colloid Interface Sci. 66(3), 389–398 (1978)CrossRefGoogle Scholar
  18. Derjaguin B.V., Churaev N., Muller V.M.: Surface Forces. Consultants Bureau, New York (1987)Google Scholar
  19. Eriksson J.C., Toshev B.V.: Disjoining pressure in soap film thermodynamics. Colloids Surf. 5, 241–264 (1982)CrossRefGoogle Scholar
  20. Frijns A., Huyghe J., Janssen J.D.: A validation of the quadriphasic mixture theory for intervertebral disc tissue. Int. J. Eng. Sci. 35(15), 1419–1429 (1997)CrossRefGoogle Scholar
  21. Grim R.E.: Clay Mineralogy. McGraw-Hill, New York (1968)Google Scholar
  22. Hassanizadeh S.M., Gray W.G.: Mechanics and thermodynamics of multiphase flow in porous media including interphase boundaries. Adv. Water Resour. 13, 169–186 (1990)CrossRefGoogle Scholar
  23. Huyghe J.M., Janssen J.D.: Quadriphasic mechanics of swelling incompressible porous media. Int. J. Eng. Sci. 35(8), 793–802 (1997)CrossRefGoogle Scholar
  24. Huyghe J.M., Janssen J.D.: Thermo-chemo-electro-mechanical formulation of saturated charged porous solids. Transp. Porous Media 34, 129–141 (1999)CrossRefGoogle Scholar
  25. Israelachvili J.: Intermolecular and Surface Forces. Academic Press, New York (1995)Google Scholar
  26. Kralchevsky P.A., Ivanov I.B.: Micromechanical description of curved interfaces, thin films, and membranes - II: Film surface tensions, disjoining pressure and interfacial stress balances. J. Colloid Interface Sci. 137(1), 234–252 (1990)CrossRefGoogle Scholar
  27. Low P.F.: Structural component of the swelling pressure of clays. Langmuir 3, 18–25 (1987)CrossRefGoogle Scholar
  28. Low P.F.: The clay/water interface and its role in the environment. Prog. Colloid Polym. Sci. 40, 500–505 (1994)Google Scholar
  29. McBride M.: A critique of diffuse double layer models applied to colloid and surface chemistry. Clays Clay Miner. 45(4), 598–608 (1997)CrossRefGoogle Scholar
  30. Miller R.J., Low P.F.: Threshold gradient for water flow in clay systems. Soil Sci. Soc. Am. Proc. 27(6), 605–609 (1963)CrossRefGoogle Scholar
  31. Moyne C., Murad M.A.: A two-scale model for coupled electro-chemo-mechanical phenomena and Onsager’s reciprocity relations in expansive clays: i homogenization analysis. Transp. Porous Media 62(3), 333–380 (2006)CrossRefGoogle Scholar
  32. Nitao J.J., Bear J.: Potentials and their role. Transp. Porous Media 32(2), 225–250 (1996)Google Scholar
  33. Newman J., Thomas-Alyea K.: Electrochemical Systems. Wiley, Hoboken (2004)Google Scholar
  34. S’anchez M., Villar M.V., Lloret A., Gens A.: Analysis of the expansive clay hydration under low hydraulic gradient. In: Schanz, T. (eds) Experimental Unsaturated Soil Mechanics, Springer, Paris (2007)Google Scholar
  35. Swartzendruber D.: Modification of Darcy’s Law for the flow of water in soils. Soil Sci. 93(1), 22–29 (1962)CrossRefGoogle Scholar
  36. van Olphen H.: An Introduction to Clay Colloid Chemistry. Krieger Publishing Company, Malabar, Florida (1991)Google Scholar
  37. Verwey E., Overbeek J.: Theory of the Stability of Lyophobic Colloids, the Interaction of Sol Particles Having and Electric Double Layer. Elsevier, New York (1948)Google Scholar
  38. Wijmans J.G., Baker R.W.: The solution-diffusion model: a review. J. Membr. Sci. 107, 1–21 (1995)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Department of Mathematical and Statistical SciencesUniversity of Colorado DenverDenverUSA

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