Diffusion in Porous Media: Phenomena and Mechanisms

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 to 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.

Unexpected Performance of Inkjet‐Printed Membrane Electrode Assemblies for Proton Exchange Membrane Fuel Cells

“…Energy dispersive X-ray spectroscopy (EDS) confirms that the platinum catalyst does not penetrate the membrane ( Figure S2, Supporting Information). [17] Thus, while the printed Pt/C catalyst forms a dense superficial layer on the Nafion membrane, on the carbon substrate, it forms a diffuse interfacial layer that penetrates up to %20 μm into the MPL. The value of 21.4 wt% platinum is somewhat below the expected value (40 wt%) if the deposited material contains only carbon, platinum, and Nafion.…”

“…The quantity of platinum detected as a function of depth decreases exponentially, consonant with a diffusive mass transport process occurring in competition with the drying of the printed layer. [17] Thus, while the printed Pt/C catalyst forms a dense superficial layer on the Nafion membrane, on the carbon substrate, it forms a diffuse interfacial layer that penetrates up to %20 μm into the MPL. Within this diffuse interfacial layer, the concentration of the platinum catalyst is naturally graded as a result of the printing process.…”

Taste of time: A porous-medium model for human tongue surface with implications for early taste perception

“…D eff is the effective diffusivity within the porous media. A commonly used estimation of effective diffusivity 42,43 is…”

“…The diffusion-dominant transport during sip and hold was simulated by a 1-D diffusion equation in porous media 42,43 :…”

Editorial for Special Issue in Honor of InterPore’s 10th Anniversary

“…The articles within this issue are here to help provide a "big picture" of many aspects of porous material research. Some of the articles address modeling: at the macroscale, where the multiple phases are indistinguishable (Battiato et al 2019), to the pore scale or microscale (Ramstad et al 2019); modeling of diffusion/dispersion of particles on the order of 10 microns and larger (Tartakovsky and Dentz 2019) and of colloids on the order of a micrometer to nanometers (Molnar et al 2019); modeling of reactions within porous materials that are limited by lack of mixing of the components (diffusion limited) (Valocchi et al 2018;Tartakovsky and Dentz 2019); modeling charged porous materials (Joekar-Niasar et al 2019), fractures (Berre et al 2018), and heat transfer (Nield and Simmons 2018). Other articles address experimental issues-at the macroscale (Falzone et al 2018) and fluid displacement at the pore scale (Gerami et al 2018), while Armstrong et al (2018) demonstrates how one can go from X-ray microcomputed tomography to characterizing porous media for modeling.…”