### 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 = [HBrO_{2}], Y = [Br^{-}], in which the consumption rate of Y rapidly increases as Y falls below Y_{c}. 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 language | English (US) |
---|---|

Pages (from-to) | 2954-2958 |

Number of pages | 5 |

Journal | Journal of Physical Chemistry |

Volume | 86 |

Issue number | 15 |

State | Published - 1982 |

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### ASJC Scopus subject areas

- Physical and Theoretical Chemistry

### Cite this

*Journal of Physical Chemistry*,

*86*(15), 2954-2958.

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

Research output: Contribution to journal › Article

*Journal of Physical Chemistry*, vol. 86, no. 15, pp. 2954-2958.

}

TY - JOUR

T1 - Trigger wave fronts of rapid consumption in a Belousov-Zhabotinskii system

AU - Rinzel, John

AU - Ermentrout, G. Bard

PY - 1982

Y1 - 1982

N2 - 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.

AB - 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.

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M3 - Article

VL - 86

SP - 2954

EP - 2958

JO - Journal of Physical Chemistry

JF - Journal of Physical Chemistry

SN - 0022-3654

IS - 15

ER -