Skip to main content
SpringerLink
Log in

Extinction Threshold in Random Heterogeneous Condensed Mixtures with an Extremely Small Amount of a Combustible

  • Published:
Journal of Engineering Physics and Thermophysics Aims and scope

Abstract

A mathematical model describing the process of combustion of heterogeneous condensed mixtures with account for the randomness of the distribution of combustible particles over the system is proposed. The step dependence of the reaction rate on the temperature is used as a model of chemical kinetics. The case where the concentration of the particles is extremely low but the heat energy released in their combustion is high has been investigated. It is shown that for an adiabatic system there exists a concentration limit of combustion. The relation of this combustion limit to the geometric phase transition occurring in a heterogeneous condensed mixture with rare combustion inclusions has been demonstrated. An analytical approach to the evaluation of the threshold concentration of the combustible in such systems, based on the continual theory of percolation, is proposed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. A. S. Rogachev and A. G. Merzhanov, Dokl. Ross. Akad. Nauk, 365, No. 6, 788-791 (1999).

    Google Scholar 

  2. A. Varma, A. S. Mukasyan, and S. Hwang, Chem. Eng. Sci., 56, 1459-1466 (2001).

    Google Scholar 

  3. E. Shafirovich, A. S. Mukasyan, and A. Varma, Combust. Flame, 128, No. 1/2, 133-144 (2002).

    Google Scholar 

  4. G. S. Kshirsagar, J. C. Cannon, and Yu. Zhang, U.S. Patent No. 6030583 (2000).

  5. Yu. Zhang and J. C. Cannon, U.S. Patent No. 6231816 B1 (2001).

  6. Yu. Zhang and J. C. Cannon, U.S. Patent No. 6352652 B2 (2002).

  7. D. Kunii and J. M. Smith, AIChE J., 6, No. 1, 71-78 (1960).

    Google Scholar 

  8. L. D. Landau and E. M. Lifshits, Statistical Physics[in Russian], Pt. 1, Moscow (1976).

  9. R. Balescu, Equilibrium and Nonequilibrium Statistical Mechanics, Vol. 1, New York (1978).

  10. L. I. Kheifets and A. V. Neimark, Multiphase Processes in Porous Media[in Russian], Moscow (1982).

  11. B. I. Shklovskii and A. L. Efros, Electronic Properties of Doped Semiconductors, Berlin (1984).

  12. J. Quintanilla, S. Torquato, and R. M. Ziff, J. Phys. A, 33, No. 42, L399-L407 (2000).

    Google Scholar 

  13. B. I. Shklovskii and A. L. Efros, Usp. Fiz. Nauk, 117, No. 3, 401-435 (1975).

    Google Scholar 

  14. M. K. Phani and D. Dhar, J. Phys. A, 17, No. 12, L645-L649 (1984).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. National Academy of Sciences of Belarus, A. V. Luikov Heat and Mass Transfer Institute, Minsk, Belarus

    O. S. Rabinovich & P. S. Grinchuk

Authors
  1. O. S. Rabinovich
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. S. Grinchuk
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rabinovich, O.S., Grinchuk, P.S. Extinction Threshold in Random Heterogeneous Condensed Mixtures with an Extremely Small Amount of a Combustible. Journal of Engineering Physics and Thermophysics 76, 325–334 (2003). https://doi.org/10.1023/A:1023653201567

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1023653201567

Keywords

Search

Navigation