The Short-Time Transient of Diffusion Outside a Conducting Body
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 th...
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| Veröffentlicht in: | Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences Mathematical and physical sciences, 1990-04, Vol.428 (1875), p.431-449 |
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| container_end_page | 449 |
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| container_issue | 1875 |
| container_start_page | 431 |
| container_title | Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences |
| container_volume | 428 |
| creator | Phillips, Charles Garrett Jansons, Kalvis M. |
| description | 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. |
| doi_str_mv | 10.1098/rspa.1990.0042 |
| format | Article |
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A</addtitle><date>1990-04-09</date><risdate>1990</risdate><volume>428</volume><issue>1875</issue><spage>431</spage><epage>449</epage><pages>431-449</pages><issn>1364-5021</issn><issn>0080-4630</issn><eissn>1471-2946</eissn><eissn>2053-9169</eissn><coden>PRLAAZ</coden><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. 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| ispartof | Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences, 1990-04, Vol.428 (1875), p.431-449 |
| issn | 1364-5021 0080-4630 1471-2946 2053-9169 |
| language | eng |
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| source | JSTOR Mathematics & Statistics; Jstor Complete Legacy |
| subjects | Asymptotic series Boundary conditions Coefficients Curvature Cylinders Differential equations Electrodes Exact sciences and technology Geometric planes Physics Solutes Statistical physics, thermodynamics, and nonlinear dynamical systems Tangent planes Transport processes |
| title | The Short-Time Transient of Diffusion Outside a Conducting Body |
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