Ion Flow Through Narrow Membrane Channels: Part I

This paper is devoted to the study of the electrostatic potential in a composite dielectric medium. The geometry consists of a membrane-like layer with one dielectric constant, perforated by a hole filled with a material with a different dielectric constant. The field is due to a known, but otherwis...

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Bibliographic Details
Published in:SIAM journal on applied mathematics 1992-10, Vol.52 (5), p.1391-1404
Main Author: Barcilon, Victor
Format: Article
Language:English
Subjects:
Applied mathematics
Aqueous solutions
Boundary conditions
Charge density
Coordinate systems
Dielectric materials
Electric fields
Fourier series
Geometry
Greens function
Integral equations
Ion channels
Permittivity
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Summary:This paper is devoted to the study of the electrostatic potential in a composite dielectric medium. The geometry consists of a membrane-like layer with one dielectric constant, perforated by a hole filled with a material with a different dielectric constant. The field is due to a known, but otherwise arbitrary, distribution f(z) of charges in the hole, where z is the coordinate along the axis of the hole. The induced surface charge at the interface between the two media is found as an asymptotic series in the small aspect ratio α of the hole, for the case in which f(z) vanishes at the endpoints and is C1. This analysis reveals the existence of a distinguished limit in which the small ratio of the permittivities ε is proportional to -α2ln α.
ISSN:0036-1399
1095-712X
DOI:10.1137/0152080