Trigger wave fronts of rapid consumption in a Belousov-Zhabotinskii system

John Rinzel, G. Bard Ermentrout

Research output: Contribution to journalArticle

Abstract

Showalter (J. Phys. Chem. 1981, 85, 440) observed front-type trigger waves in the acidic bromate oxidation of ferroin, a BZ system without malonic acid. To model these waves of autocatalytic growth of X and consumption of Y, we consider an Oregonator model with two species, X = [HBrO2], Y = [Br-], in which the consumption rate of Y rapidly increases as Y falls below Yc. Such waves and models have also been used to describe the leading edge of pulse-like trigger waves in the full BZ system. For an appropriate parameter range (notably, when [H+] is small), we exploit a pseudo-steady-state assumption on X to reduce the two-variable model to a single nonlinear reaction-diffusion equation for Y. Our approximate one-variable model admits a traveling front solution which corresponds to the total consumption of Br- from Y, [Br-] ahead of the wave, down to Y = 0. Propagation speed as a function of Y is easily computed for this model. We also show analytically that for large Y speed is inversely proportional to Y. We have considered two other simplified consumption models which are analytically solvable. The speed dependence on Y is compared for all the models (Figure 3). Our theoretical results are also compared to the experimental dependence of speed on initial reactant concentrations. Our study has considered parameter ranges which complement those of previous theoretical treatments.

Original languageEnglish (US)
Pages (from-to)2954-2958
Number of pages5
JournalJournal of Physical Chemistry
Volume86
Issue number15
StatePublished - 1982

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wave fronts
actuators
Bromates
bromates
reaction-diffusion equations
leading edges
complement
Oxidation
oxidation
acids
propagation
Acids
pulses

ASJC Scopus subject areas

  • Physical and Theoretical Chemistry

Cite this

Trigger wave fronts of rapid consumption in a Belousov-Zhabotinskii system. / Rinzel, John; Ermentrout, G. Bard.

In: Journal of Physical Chemistry, Vol. 86, No. 15, 1982, p. 2954-2958.

Research output: Contribution to journalArticle

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