Involutes: The geometry of chemical waves rotating in annular membranes

Attila Lázár, Zoltán Noszticzius, Henrik Farkas, Horst Dieter Försterling

Research output: Contribution to journalArticle

38 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)443-447
Number of pages5
Issue number2
Publication statusPublished - Jan 1 1995

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

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