Journal
JOURNAL OF PHYSICS-CONDENSED MATTER
Volume 30, Issue 19, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1361-648X/aaba0d
Keywords
diffusion; confined systems; effective diffusivity
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Axial diffusion in channels and tubes of smoothly-varying geometry can be approximately described as one-dimensional diffusion in the entropy potential with a position-dependent effective diffusion coefficient, by means of the modified Fick-Jacobs equation. In this work, we derive analytical expressions for the position-dependent effective diffusivity for two-dimensional asymmetric varying-width channels, and for three-dimensional curved midline tubes, formed by straight walls. To this end, we use a recently developed theoretical framework using the Frenet-Serret moving frame as the coordinate system (2016 J. Chem. Phys. 145 074105). For narrow tubes and channels, an effective one-dimensional description reducing the diffusion equation to a Fick-Jacobs-like equation in general coordinates is used. From this last equation, one can calculate the effective diffusion coefficient applying Neumann boundary conditions.
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