{"title":"The short-time transient of diffusion outside a conducting body","authors":"C. G. Phillips, Kalvis M. Jansons","doi":"10.1098/rspa.1990.0042","DOIUrl":null,"url":null,"abstract":"We consider the short-time transient of the diffusion of mass (or heat) to a body whose surface is held at zero concentration, with the space outside initially at unit concentration. The problem is expressed in terms of the probability that a brownian path of short duration intersects the body. A three-term asymptotic series for the absorption rate is derived for an arbitrary smooth body, together with the leading corrections due to edges and lines of contact with insulating surfaces. A three-term series is also derived for a plane laminar conductor with a smooth boundary, or equivalently a conducting film mounted on an insulating plane. These results are used to derive short-time absorption rates for shapes such as discs, rings and cylinders, commonly used for microelectrodes and hot-film devices.","PeriodicalId":20605,"journal":{"name":"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"1990-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"41","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1098/rspa.1990.0042","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 41
Abstract
We consider the short-time transient of the diffusion of mass (or heat) to a body whose surface is held at zero concentration, with the space outside initially at unit concentration. The problem is expressed in terms of the probability that a brownian path of short duration intersects the body. A three-term asymptotic series for the absorption rate is derived for an arbitrary smooth body, together with the leading corrections due to edges and lines of contact with insulating surfaces. A three-term series is also derived for a plane laminar conductor with a smooth boundary, or equivalently a conducting film mounted on an insulating plane. These results are used to derive short-time absorption rates for shapes such as discs, rings and cylinders, commonly used for microelectrodes and hot-film devices.