### Abstract

The propagation of a premixed laminar flame supported by an exothermic chemical reaction under adiabatic conditions but subject to inhibition through parallel endothermic chemical processes is considered. These consist of the endothermic decomposition of an inhibitor W leading to the formation of a 'radical scavenger' S, which acts as a catalyst for the removal of active radicals X through an additional termination step. The heat loss through the endothermic reaction and the action of the radical scavenger, represented by the parameters α and ρ, both have a strong quenching effect on wave propagation. The dependence of the flame velocity c on α and ρ is determined by numerical integration of the flame equations for a range of values of the other parameters. The (ρ ,c) curve can have at least one turning point, the (α,c) curve can be monotone or it can have one or three turning points, depending on the values of the parameters β, representing the rate at which inhibitor is consumed, μ, the ratio of the activation energies of the reactants and the Lewis numbers. The additional feature caused by the scavenger is that the (α, c) curve has a turning point for any (μ, β) parameter pair if ρ is sufficiently large. A new feature of the model is that, for non-zero values of ρ, there can be four solutions below critical values of α. This behaviour is confirmed by a high activation energy analysis, which also reveals some additional features of the flame structure resulting from the presence of the radical scavenger.

Original language | English |
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Pages (from-to) | 203-231 |

Number of pages | 29 |

Journal | Journal of Mathematical Chemistry |

Volume | 38 |

Issue number | 2 |

DOIs | |

Publication status | Published - Aug 1 2005 |

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### Keywords

- Flame quenching
- Multiple solutions
- Radical scavenger
- Travelling waves

### ASJC Scopus subject areas

- Chemistry(all)
- Applied Mathematics

### Cite this

*Journal of Mathematical Chemistry*,

*38*(2), 203-231. https://doi.org/10.1007/s10910-005-5409-5