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Journal of Engineering Mathematics

, Volume 56, Issue 2, pp 129–142 | Cite as

Thermal explosion in a hot gas mixture with organic gel fuel droplets

  • Igor Goldfarb
  • Vladimir Gol’dshtein
  • J. Barry. Greenberg
  • Ann Zinoviev
Original Paper

Abstract

Recent experimental evidence has uncovered the peculiar behavior of certain gel droplets which, under appropriate ambient thermal conditions, evaporate and burn in an oscillatory fashion. In this work a preliminary foray is made into the theoretical analysis of the nature of the evolution of a hot gas mixture containing organic gel fuel droplets with oscillatory evaporation within the context of thermal-explosion theory. The problem is modeled as a system of highly nonlinear singularly perturbed ordinary differential equations. Non-dimensionalization of the equations enables identification of the parameters that play a major role in determining the dynamical regimes of the system of equations. The method of integral manifolds is exploited for the analysis and it is found, that for certain parametric regions, the system exhibits new dynamical behavior that is quite different from that found for conventional liquid droplets.

Keywords

Gel fuel droplets Singularly perturbed system of equations Theory of integral manifolds Thermal explosion 

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Copyright information

© Springer Science + Business Media B.V. 2006

Authors and Affiliations

  • Igor Goldfarb
    • 1
  • Vladimir Gol’dshtein
    • 1
  • J. Barry. Greenberg
    • 2
  • Ann Zinoviev
    • 3
  1. 1.Department of Mathematics and Computer SciencesBen-Gurion University of the NegevBeer-ShevaIsrael
  2. 2.Faculty of Aerospace EngineeringTechnion – Israel Institute of TechnologyHaifaIsrael
  3. 3.Department of MathematicsSami Shamoon College of EngineeringBeer-ShevaIsrael

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