Skip to main content
SpringerLink
Log in

Fractal structure and features of energy-release (combustion) processes in heterogeneous condensed systems

  • Published:
Combustion, Explosion and Shock Waves Aims and scope

Abstract

In this work, the theory of fractals has been used to describe the structure of heterogeneous condensed systems (HCS). Features of energy-release processes with variation of the initial structure parameters have been investigated. The microstructure of HCS and the dynamics of its change have been studied as functions of the proportion and properties of their components. It is shown that particles of the components form fractal structures, which are characterized by fractional dimensions. The obtained images of the microstructure reflect the presence of the geometric phase transition “fractal cluster-percolation cluster.” Regularities of reaction-front propagation are determined. It is found that the concentration limits of energy release and combustion are associated with the evolution of fractal structures and the formation (disruption) of a continuous reaction surface. The electrical conductivity of the starting compositions is measured as an indicator of the formation of fractal structures of one or another configuration. Electrical and thermal-physics properties of the samples and energy-release (combustion) parameters are analyzed. The systems exhibit similar behavior in different processes. Near the critical point, the dependence of the parameters studied on concentration has an exponential character. The exponent is close to that determined in percolation theory. A computational algorithm for the contact surface of the components is developed and implemented. The computation results allow one to distinguish the “base block” that influences the combustion rate and to determine the critical concentrations of the components. The study of HCS in the context of the new direction in the geometry of disordered systems—the theory of fractals—is promising for generalization of available experimental data and for predicting the parameters of energy release in HCS with variation in the structural parameters.

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. Ya. B. Zel'dovich, “On combustion theory for powders and explosives,”Zh. Éksp. Teor. Fiz.,12, No. 1, 498 (1942).

    Google Scholar 

  2. A. F. Belyaev, “On combustion of explosives,”Zh. Fiz. Khim.,12, No. 1, 93 (1938).

    Google Scholar 

  3. O. I. Leipunskii and Yu. V. Frolov (eds.),Theory of Combustion of Powders and Explosives [in Russian], Nauka, Moscow (1982).

    Google Scholar 

  4. A. F. Belyaev, Yu. V. Frolov, and F. I. Dubovitskii, “Combustion rate in condensed composite systems with various degrees of component mixing,”Fiz. Goreniya Vzryva,4, No. 1, 1–10 (1968).

    Google Scholar 

  5. B. S. Ermolaev, A. I. Korotkov, and Yu. V. Frolov, “Combustion in layered condensed systems,”Fiz Goreniya Vzryva,6, No. 3, 277–284 (1970).

    Google Scholar 

  6. V. B. Librovich, “On the characteristic combustion rate of composite powders,”Prikl. Mekh. Tekh. Fiz., No. 4, 33–39 (1962).

    Google Scholar 

  7. Ya. B. Zel'dovich, G. I. Barenblatt, V. B. Librovich, and G. M. Makhviladze,Mathematical Theory of Combustion and Explosion [in Russian], Nauka, Moscow (1980).

    Google Scholar 

  8. P. F. Pokhil, A. F. Belyaev, Yu. V. Frolov, et al.,Combustion of Powder Metals in Active Media [in Russian], Nauka, Moscow (1972).

    Google Scholar 

  9. Yu. V. Frolov and B. E. Nikol'skii, “Spatial structure and concentration limits of combustion of gasless systems,”Dokl. Akad. Nauk SSSR,305, No. 2, 386 (1989).

    Google Scholar 

  10. B. B. Mandelbrot,Fractal Geometry of Nature, Freeman, San Francisco (1982).

    MATH  Google Scholar 

  11. H. Gould and J. Tobochnik,An Introduction to Computer Simulation Methods. Applications to Physics, Addison-Wesley Publ., New York (1988).

    Google Scholar 

  12. J. P. Fitzpatrick, R. B. Malt, and F. Spaepen, “Percolation theory of conductivity of random close packed mixtures of hard spheres,”Phys. Lett.,A47, 207 (1974).

    Article  Google Scholar 

  13. F. C. Gouldin, “An application of fractals to modeling premixed turbulent flames,”Combust. Flame,68, 249 (1987).

    Article  Google Scholar 

  14. N. S. Cohen, “A pocket model for aluminum agglomeration in composite propellants,”AIAA J.,21, No. 5, 720–725 (1983).

    Article  Google Scholar 

  15. W. C. Strahle, “Some statistical considerations in the burning of composite solid propellants,”AIAA J.,16, No. 8, 843–847 (1978).

    Google Scholar 

  16. U. Wendtland,Thermal Methods of Analysis [Russian translation], Mir, Moscow (1978).

    Google Scholar 

  17. Yu. V. Frolov, A. N. Pivkina, and F. Kh. Varenykh, “Fractal structure and properties of combustion of heterogeneous condensed systems,” in:Chemical Physics of Combustion and Explosion [in Russian], Chernogolovka (1992).

  18. A. J. Katz and A. H. Thompson, “Fractal sandstone pores: implication for conductivity and pore formation,”Phys. Lett.,54, 1325–1328 (1985).

    Article  Google Scholar 

  19. Yu. Frolov, A. Pivkina, and B. Nickolsky, “Concentration limits of the combustion wave spreading in reactive heterogeneous systems,” in: Proc. 14th Int. Pyrotechnics Seminar (UK, Jersey, Channel Island, Sept. 18–22, 1989).

  20. R. Zallen,Physics of Amorphous Solids, Henry Ling, Ltd., Dorset Press, New York (1983).

    Google Scholar 

  21. W. Haller, “Rearrangement kinetics of the liquid-liquid immiscible microphases in alkali borosilicate melts,”J. Chem. Phys.,42, 2 (1965).

    Google Scholar 

  22. C. F. Wenzel,Lehr von der Verwandtschaft der Korper, Dresden (1777).

  23. Yu. Frolov and A. Pivkina, “Combustion of boron-containing compositions,” in: Proc. 25th Int. Annual Conf. of ICT (Karlsruhe, Germany, June 28–July 1, 1994).

  24. Yu. V. Frolov, A. N. Pivkina, and B. E. Nikol'skii, “Concentration limits of combustion-wave propagation in heterogeneous systems,” in:Chemical Physics of Combustion and Explosion Processes [in Russian], Chernogolovka (1989).

  25. Yu. V. Frolov, A. N. Pivkina, and F. Kh. Varenykh, “Fractal structure and combustion properties of a HC,” in:an Xth Symposium on Combustion and Explosion (Chernogolovka, 1992), Moscow (1992).

  26. Yu. Frolov and A. Pivkina, “Fractal structure and combustion characteristics of heterogeneous condensed systems,” in: Proc. 23rd Int. Conf. of ICT (June 30–July 3, 1992), Karlsruhe, Germany (1992).

  27. Yu. Frolov and A. Pivkina, “Combustion of heterogeneous condensed systems: influence of structure,” in: Proc. Int. Conf. on Combustion (Moscow, Sept., 1994), Moscow (1994).

Download references

Authors
  1. Y. V. Frolov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. N. Pivkina
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Institute of Chemical Physics, Russian Academy of Sciences, Moscow 117977. Translated from Fizika Goreniya i Vzryva, Vol. 33, No. 5, pp. 3–19, September–October, 1997.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Frolov, Y.V., Pivkina, A.N. Fractal structure and features of energy-release (combustion) processes in heterogeneous condensed systems. Combust Explos Shock Waves 33, 513–527 (1997). https://doi.org/10.1007/BF02672736

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02672736

Keywords

Search

Navigation