Diffusion in Porous Media: Phenomena and Mechanisms

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 bothmodeling strategies, starting with Langevin's approach to amechanistic 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.