Starting from Fick’s train of thought, which led to the formulation of his law governing diffusion in a solid or liquid medium, we first consider the limits of applicability of this law to solid medium-single penetrant systems. We then take up the question of proper formulation, in combination with simple but physically meaningful modeling, of diffusion behavior deviating from this law, because of (i) concentration dependence (ii) time dependence or (iii) space dependence, of the relevant transport parameters (which include the sorption, no less than the diffusion, coefficient). Examples of application to real systems are offered in each case. We conclude that progress in such studies depends on following Fick’s mode of thinking rather than on adhering to the formalism of his law.

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This paper considers permeation through microporous or nanoporous inorganic membranes under the influence of an applied pressure gradient. In general membrane permeation may be considered as a diffusive process, driven by the gradient of chemical potential (which depends on both composition and pressure). The relative importance of these two factors varies greatly for different types of system. The general features of such processes are reviewed and the diffusional behavior of selected systems is examined. (membrane permeation, osmosis, diffusion, zeolite membrane, DDR-3, SAPO-34)

The diffusion mechanism of pure component Ar and binary mixtures of Ar/Kr and Ar/Ne confined in single-walled carbon nanotubes (SWNTs) and bundles was investigated by a combined Grand Canonical Monte Carlo and molecular dynamics study. For Ar confined in SWNTs, a crossover from single-file to Fickian diffusion existed when the density of Ar was a minimum as a function of the SWNT diameter. Argon diffused by a single-file mechanism in SWNTs smaller than an accessible diameter of 1.76σAr, corresponding to (7,7), (12,0) and (8,6) SWNTs but by a Fickian mechanism for SWNTs larger in diameter. Both components in Ar/Kr mixtures had a single-file diffusional mechanism in (6,6) and (7,7) SWNTs and a Fickain mechanism for SWNTs larger in diameter. Likewise, both components in a Ar/Ne mixtures had a single-file diffusional mechanism in a (6,6) CNT, and Ar had a single-file diffusional mechanism in a (7,7) SWCNT. However, Ne in the Ar/Ne mixture exhibited Fickian diffusion in the (7,7) SWNT , which indicated bi-modal diffusion. Larger diameters of SWNTs provided Fickian diffusion for both components in an Ar/Ne mixture. Argon diffused in a (25,0) SWNT bundle (with a bimodal pore size distribution) in a bimodal mechanism, with Ar diffusing in single-file in interstitial sites and in a Fickian mechanism in inner nanotube channels. In all cases of single-file diffusion the mean-squared displacement (MSD) of the fluid molecules had a square root of time dependence, while molecules diffusing by a Fickian mechanism had a MSD with a linear time dependence.