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Homogeneous branched-chain explosion: Initiation to completion

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Summary

This paper traces the complete time history of a spatially homogeneous model of a branched-chain reaction through asymptotic methods and develops (i) a subcritical solution (fizzle) where the state variables change by small amounts, and (ii) a supercritical solution (explosion) where extremely rapid transients occur. Three distinct time scales are seen to govern the explosion: a long induction period exhibiting a very slow change of state (as in a thermal explosion), a very brief period characterized by a rapid increase in the chain-carrier concentration but a small increase in temperature (unlike a thermal explosion), followed by a longer period in which most of the chemical heat is released.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Rensselaer Polytechnic Institute, 12181, Troy, New York, USA

    A. K. Kapila

Authors
  1. A. K. Kapila
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Additional information

This research was supported by the U. S. Army Research Office, Durham under Grant DAAG 29-76-G-0253.

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Kapila, A.K. Homogeneous branched-chain explosion: Initiation to completion. J Eng Math 12, 221–235 (1978). https://doi.org/10.1007/BF00036460

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  • DOI: https://doi.org/10.1007/BF00036460

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