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Diffusion in Porous Media: Phenomena and Mechanisms

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Abstract

Two distinct but interconnected approaches can be used to model diffusion in fluids; the first focuses on dynamics of an individual particle, while the second deals with collective (effective) motion of (infinitely many) particles. We review both modeling strategies, starting with Langevin’s approach to a mechanistic description of the Brownian motion in free fluid of a point-size inert particle and establishing its relation to Fick’s diffusion equation. Next, we discuss its generalizations which account for a finite number of finite-size particles, particle’s electric charge, and chemical interactions between diffusing particles. That is followed by introduction of models of molecular diffusion in the presence of geometric constraints (e.g., the Knudsen and Fick–Jacobs diffusion); when these constraints are imposed by the solid matrix of a porous medium, the resulting equations provide a pore-scale representation of diffusion. Next, we discuss phenomenological Darcy-scale descriptors of pore-scale diffusion and provide a few examples of other processes whose Darcy-scale models take the form of linear or nonlinear diffusion equations. Our review is concluded with a discussion of field-scale models of non-Fickian diffusion.

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Acknowledgements

This research was supported in part by US National Science Foundation (NSF) under Award Number CBET-1606192 issued to DMT, and by the European Research Council (ERC) through the Project MHetScale (617511) issued to MD.

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  1. Department of Energy Resources Engineering, Stanford University, 367 Panama Street, Stanford, CA, 94305, USA

    Daniel M. Tartakovsky

  2. Institute of Environmental Assessment and Water Research, Spanish National Research Council (CSIC), 08034, Barcelona, Spain

    Marco Dentz

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Tartakovsky, D.M., Dentz, M. Diffusion in Porous Media: Phenomena and Mechanisms. Transp Porous Med 130, 105–127 (2019). https://doi.org/10.1007/s11242-019-01262-6

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