The short-time transient of diffusion outside a conducting body

C. G. Phillips, Kalvis M. Jansons
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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.
传导体外扩散的短时瞬态
我们考虑质量(或热)扩散到一个物体的短时瞬态,其表面保持在零浓度,外部空间初始为单位浓度。这个问题是用短时间的布朗路径与物体相交的概率来表示的。对于任意光滑体,导出了吸收率的三项渐近级数,以及由于与绝缘表面接触的边缘和线引起的主要修正。对于具有光滑边界的平面层流导体,或等效地安装在绝缘平面上的导电膜,也导出了一个三项级数。这些结果可用于推导圆盘、圆环和圆柱体等形状的短期吸收率,这些形状通常用于微电极和热膜装置。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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