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.
Similar content being viewed by others
References
Adler P.M.: Porous Media. Geometry and Transport. Butterworths-Heinemann Series in Chemical Engineering, London (1992)
Carman P.: Fluid f low through granular beds. Trans. Inst. Chem. Eng. 15, 150–166 (1937)
Carman P.: Flow of Gases through Porous Media. Butterworths Scientific Publication, London (1956)
Cieszko M.: Description of anisotropic pore space structure of permeable materials based on Minkowski metric space. Arch. Mech. 61(6), 425–444 (2009)
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)
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)
Koponen A., Kataja M., Timonen J.: Permeability and effective porosity of porous media. Phys. Rev. E 56, 3319–3325 (1997)
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)
Kubik J.: A macroscopic description of geometrical pore structure of porous solids. Int. J. Eng. Sci. 24, 971–980 (1986)
Mackie J.S., Meares P.: The diffusion of electrolytes in a cation-exchange resin membrane. Proc. R. Soc. A 232, 498–509 (1955)
Matyka M., Khalili A., Koza Z.: Tortuosity–porosity relation in the porous media flow. Phys. Rev. E 78, 026306 (2008)
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)
Pisani L.: The limits of proton conductivity in polymeric sulfonated membranes: a modelling study. J. Power Sour 194, 451–455 (2009)
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)
Prager S.: Diffusion in inhomogeneous media. J. Chem. Phys. 33, 122–127 (1960)
Shen L., Chen Z.: Critical review of the impact of tortuosity on diffusion. Chem. Eng. Sci. 62, 3748–3755 (2007)
Stauffer D., Aharony A.: Introduction to Percolation Theory. CRC Press, Boca Raton (1994)
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)
Weissberg H.L.: Effective diffusion coefficients in porous media. J. Appl. Phys. 34, 2636–2639 (1963)
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)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11242-011-9734-9