Diffusion through ordered force fields: a case-study problem. The classical Fick or Einstein model for diffusion is based on the assumption that the diffusing molecule is exposed to a random force field arising from molecular motion. The assumption is reasonable and predicts phenomena such as Knudsen diffusion for small-sized pores but might not be true for nanopores, where there may be a directional force field. This variation is due to local concentration differences, the presence of surface charge, etc. Such systems can be simulated by using the Fokker–Planck equation and the Smoluchowski equation, and an illustrative study has been presented by Wang et al. (2009). Your goal is to review this paper, write a computational model that permits incorporation of a prescribed force field, and calculate the additional contribution to diffusion arising from such ordered force fields. Diffusion in zeolites is an example in chemical reaction engineering where such effects can become important.
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