Involutes: the geometry of chemical waves rotating in annular membranes

Chaos
Attila LazarHorst-Dieter Forsterling

Abstract

According to earlier theories certain parts of a chemical wave front propagating in a 2-D excitable medium with a convex obstacle should be involutes of that obstacle. The present paper discusses a special case where self-sustained chemical waves are rotating around a central obstacle in an annular 2-D excitable region. A simple geometrical model of wave propagation based on the Fermat principle (minimum propagation time) is suggested. Applying this model it is shown that the wave fronts in the case of an annular excitable region should be purely involutes of the central obstacle in the asymptotic state. This theory is supported by experiments in a novel membrane reactor where a catalyst of the Belousov-Zhabotinsky reaction is fixed on a porous membrane combined with a gel medium. Involutes of circular and triangular obstacles are observed experimentally. Deviations from the ideal involute geometry are explained by inhomogeneities in the membrane. (c) 1995 American Institute of Physics.

Citations

Jun 5, 2003·Chaos·Xiujiang LiHarm Hinrich Rotermund
Jul 13, 2004·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Xiaonan WangQi Ouyang
Apr 24, 2002·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·P KettunenT Yamaguchi
Apr 24, 2002·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·S Sieniutycz
Sep 21, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Hongyu GuoQi Ouyang
Mar 11, 2006·The Journal of Physical Chemistry. a·Satoshi NakataHiroyuki Kitahata
Jul 13, 2006·The Journal of Physical Chemistry. a·Hiroyuki KitahataTakatoshi Ichino
Jun 9, 2007·The Journal of Physical Chemistry. a·Mariko MatsushitaHiroyuki Kitahata

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