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Journal Article

Theory of electrochemical pattern formation

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Christoph,  Jan
Physical Chemistry, Fritz Haber Institute, Max Planck Society;

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Eiswirth,  Markus
Physical Chemistry, Fritz Haber Institute, Max Planck Society;

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Citation

Christoph, J., & Eiswirth, M. (2002). Theory of electrochemical pattern formation. Chaos, 12(1), 215-230. doi:10.1063/1.1449956.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0011-15D9-5
Abstract
The spatial coupling in electrochemical systems is mediated by ion migration under the influence of the electric field. Since field effects spread very rapidly, every point of an electrode can communicate with every other one practically instantaneously through migration coupling. Based on mathematical potential theory we present the derivation of a generally applicable reaction-migration equation, which describes the coupling via an integral over the whole electrode area. The corresponding coupling function depends only on the geometry of the electrode setup and has been computed for commonly used electrode shapes (such as ring, disk, ribbon or rectangle). The pattern formation observed in electrochemical systems in the bistable, excitable and oscillatory regime can be reproduced in computer simulations, and the types of patterns occurring under different geometries can be rationalized.