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Simple Expression for the Tortuosity of Porous Media

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Abstract

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.

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References

  • Adler P.M.: Porous Media. Geometry and Transport. Butterworths-Heinemann Series in Chemical Engineering, London (1992)

    Google Scholar 

  • Carman P.: Fluid f low through granular beds. Trans. Inst. Chem. Eng. 15, 150–166 (1937)

    Google Scholar 

  • Carman P.: Flow of Gases through Porous Media. Butterworths Scientific Publication, London (1956)

    Google Scholar 

  • 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 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • Koponen A., Kataja M., Timonen J.: Permeability and effective porosity of porous media. Phys. Rev. E 56, 3319–3325 (1997)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • Kubik J.: A macroscopic description of geometrical pore structure of porous solids. Int. J. Eng. Sci. 24, 971–980 (1986)

    Article  Google Scholar 

  • Mackie J.S., Meares P.: The diffusion of electrolytes in a cation-exchange resin membrane. Proc. R. Soc. A 232, 498–509 (1955)

    Article  Google Scholar 

  • Matyka M., Khalili A., Koza Z.: Tortuosity–porosity relation in the porous media flow. Phys. Rev. E 78, 026306 (2008)

    Article  Google Scholar 

  • 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 

  • Pisani L.: The limits of proton conductivity in polymeric sulfonated membranes: a modelling study. J. Power Sour 194, 451–455 (2009)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • Prager S.: Diffusion in inhomogeneous media. J. Chem. Phys. 33, 122–127 (1960)

    Article  Google Scholar 

  • Shen L., Chen Z.: Critical review of the impact of tortuosity on diffusion. Chem. Eng. Sci. 62, 3748–3755 (2007)

    Article  Google Scholar 

  • Stauffer D., Aharony A.: Introduction to Percolation Theory. CRC Press, Boca Raton (1994)

    Google Scholar 

  • 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)

    Article  Google Scholar 

  • Weissberg H.L.: Effective diffusion coefficients in porous media. J. Appl. Phys. 34, 2636–2639 (1963)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

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Pisani, L. Simple Expression for the Tortuosity of Porous Media. Transp Porous Med 88, 193–203 (2011). https://doi.org/10.1007/s11242-011-9734-9

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  • DOI: https://doi.org/10.1007/s11242-011-9734-9

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