{"title":"Kinetic theory of diffusion in a channel of varying cross section","authors":"J. Brey, M. I. G. D. Soria, P. Maynar","doi":"10.1080/00268976.2024.2378116","DOIUrl":null,"url":null,"abstract":"Self-diffusion along the longitudinal coordinate in a channel of varying cross section is considered. The starting point is the two-dimensional Enskog-Boltzmann-Lorentz kinetic equation with appropriated boundary conditions. It is integrated over the transversal coordinate to get an approximated one-dimensional kinetic equation, keeping the relevant properties of the original one. Then, a macroscopic equation for the time evolution of the longitudinal density is derived, by means of a modified Chapman-Enskog expansion method, that takes into account the inhomogeneity of the equilibrium longitudinal density. This transport equation has the form of the phenomenological Ficks-Jacobs equation, but with an effective diffusion coefficient that contains corrections associated to the variation of the slope of the equilibrium longitudinal density profile.","PeriodicalId":18817,"journal":{"name":"Molecular Physics","volume":null,"pages":null},"PeriodicalIF":1.6000,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Molecular Physics","FirstCategoryId":"92","ListUrlMain":"https://doi.org/10.1080/00268976.2024.2378116","RegionNum":4,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"CHEMISTRY, PHYSICAL","Score":null,"Total":0}
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Abstract
Self-diffusion along the longitudinal coordinate in a channel of varying cross section is considered. The starting point is the two-dimensional Enskog-Boltzmann-Lorentz kinetic equation with appropriated boundary conditions. It is integrated over the transversal coordinate to get an approximated one-dimensional kinetic equation, keeping the relevant properties of the original one. Then, a macroscopic equation for the time evolution of the longitudinal density is derived, by means of a modified Chapman-Enskog expansion method, that takes into account the inhomogeneity of the equilibrium longitudinal density. This transport equation has the form of the phenomenological Ficks-Jacobs equation, but with an effective diffusion coefficient that contains corrections associated to the variation of the slope of the equilibrium longitudinal density profile.
期刊介绍：
Molecular Physics is a well-established international journal publishing original high quality papers in chemical physics and physical chemistry. The journal covers all experimental and theoretical aspects of molecular science, from electronic structure, molecular dynamics, spectroscopy and reaction kinetics to condensed matter, surface science, and statistical mechanics of simple and complex fluids. Contributions include full papers, preliminary communications, research notes and invited topical review articles.
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