{"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":1,"journal":{"name":"Accounts of Chemical Research","volume":" 41","pages":""},"PeriodicalIF":17.7000,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"92","ListUrlMain":"https://doi.org/10.1080/00268976.2024.2378116","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","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：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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