Transport in Porous Media

, Volume 88, Issue 2, pp 193–203 | Cite as

Simple Expression for the Tortuosity of Porous Media

  • L. PisaniEmail author


In this article, we derive a simple expression for the tortuosity of porous media as a function of porosity and of a single parameter characterizing the shape of the porous medium components. Following its value, a very large range of porous materials is described, from non-tortuous to high tortuosity ones with percolation limits. The proposed relation is compared with a widely used expression derived from percolation theory, and its predictive power is demonstrated through comparison with numerical simulations of diffusion phenomena. Application to the tortuosity of hydrated polymeric membranes is shown.


Tortuosity Porosity Porous media Diffusion 


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  1. Adler P.M.: Porous Media. Geometry and Transport. Butterworths-Heinemann Series in Chemical Engineering, London (1992)Google Scholar
  2. Carman P.: Fluid f low through granular beds. Trans. Inst. Chem. Eng. 15, 150–166 (1937)Google Scholar
  3. Carman P.: Flow of Gases through Porous Media. Butterworths Scientific Publication, London (1956)Google Scholar
  4. Cieszko M.: Description of anisotropic pore space structure of permeable materials based on Minkowski metric space. Arch. Mech. 61(6), 425–444 (2009)Google Scholar
  5. Edmondson C.A., Stallworth P.E., Chapman M.E., Fontanella J.J., Wintersgill M.C., Chung S.H., Greenbaum S.G.: Complex impedance studies of proton conducting membranes. Solid State Ion 135, 419–423 (2000)CrossRefGoogle Scholar
  6. Fimrite J., Carnes B., Struchtrup H., Djilali N.: Transport phenomena in polymer electrolyte membranes. II. Binary friction membrane model. J. Electrochem. Soc. 152, A1815–A1823 (2005)CrossRefGoogle Scholar
  7. Koponen A., Kataja M., Timonen J.: Permeability and effective porosity of porous media. Phys. Rev. E 56, 3319–3325 (1997)CrossRefGoogle Scholar
  8. Kreuer K.D., Paddison S.J., Spohr E., Schuster M.: Transport in proton conductors for fuel cell applications: simulation, elementary reactions, and phenomenology. Chem. Rev. 104, 4637–4678 (2004)CrossRefGoogle Scholar
  9. Kubik J.: A macroscopic description of geometrical pore structure of porous solids. Int. J. Eng. Sci. 24, 971–980 (1986)CrossRefGoogle Scholar
  10. Mackie J.S., Meares P.: The diffusion of electrolytes in a cation-exchange resin membrane. Proc. R. Soc. A 232, 498–509 (1955)CrossRefGoogle Scholar
  11. Matyka M., Khalili A., Koza Z.: Tortuosity–porosity relation in the porous media flow. Phys. Rev. E 78, 026306 (2008)CrossRefGoogle Scholar
  12. Meredith R.E., Tobias C.W.: Conduction in heterogeneous systems. In: Tobias, C.W. (ed.) Advances in Electrochemistry and Electrochemical Engineering 2., Interscience Publishers, New York (1962)Google Scholar
  13. Pisani L.: The limits of proton conductivity in polymeric sulfonated membranes: a modelling study. J. Power Sour 194, 451–455 (2009)CrossRefGoogle Scholar
  14. Pisani L., Valentini M., Hofmann D.H., Kuleshova L.N., D’Aguanno B.: An analytical model for the conductivity of sulfonated membranes. Solid State Ion 179, 465–476 (2008)CrossRefGoogle Scholar
  15. Prager S.: Diffusion in inhomogeneous media. J. Chem. Phys. 33, 122–127 (1960)CrossRefGoogle Scholar
  16. Shen L., Chen Z.: Critical review of the impact of tortuosity on diffusion. Chem. Eng. Sci. 62, 3748–3755 (2007)CrossRefGoogle Scholar
  17. Stauffer D., Aharony A.: Introduction to Percolation Theory. CRC Press, Boca Raton (1994)Google Scholar
  18. Thampan T., Malhotra S., Tang T., Datta R.: Modeling of conductive transport in proton-exchange membranes for fuel cells. J. Electrochem. Soc. 147, 3242–3250 (2000)CrossRefGoogle Scholar
  19. Weissberg H.L.: Effective diffusion coefficients in porous media. J. Appl. Phys. 34, 2636–2639 (1963)CrossRefGoogle Scholar
  20. Zawodzinsky T.A., Springer T.E., Davey J., Jestel R., Lopez C., Valerio J., Gottesfeld S.: A comparative study of water uptake by and transport trough ionomeric fuel cell membranes. J. Electrochem. Soc. 140, 1981–1985 (1993)CrossRefGoogle Scholar

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© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Center for Advanced Studies, Research and Development in Sardinia (CRS4), Parco Scientifico e Tecnologico, POLARISPulaItaly

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