Skip to main content
SpringerLink
Log in

Nucleation, Growth, and Scaling in Slow Combustion

  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

We study the nucleation and growth of flame fronts in slow combustion. This is modeled by a set of reaction-diffusion equations for the temperature field, coupled to a background of reactants and augmented by a term describing random temperature fluctuations for ignition. We establish connections between this model and the classical theories of nucleation and growth of droplets from a metastable phase. Our results are in good agreement with theoretical predictions.

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. For a review see J. D. Gunton, M. San Miguel, and P. S. Sahni, in Phase Transitions and Critical Phenomena, C. Domb and J. L. Lebowitz, eds. (Academic Press, London, 1983), Vol. 8.

    Google Scholar 

  2. Y. Yamada, N. Hamaya, J. D. Axe, and S. M. Shapiro, Phys. Rev. Lett. 53:1665 (1984).

    Google Scholar 

  3. N. Metoki, H. Suematsu, Y. Murakami, Y. Ohishi, and Y. Fujii, Phys. Rev. Lett. 64:657 (1990).

    Google Scholar 

  4. R. Kapral, R. Livi, G.-L. Oppo, and A. Politi, Phys. Rev. E 49:2009 (1994).

    Google Scholar 

  5. H. M. Duiker and P. D. Beale, Phys. Rev. B 41:490 (1990).

    Google Scholar 

  6. R. Becker and W. Döring, Ann. Phys. (Leipzig) 24:719 (1935). For a review see F. F. Abraham, Homogeneous Nucleation Theory(Academic Press, NY, 1974). For the modern theory of nucleation see J. S. Langer, Ann. Phys. 54:258 (1969).

    Google Scholar 

  7. N. Provatas, T. Ala-Nissila, L. Piché, and M. Grant, Phys. Rev. E 51:4232 (1995).

    Google Scholar 

  8. N. Provatas, T. Ala-Nissila, L. Piché, and M. Grant, J. Stat. Phys. 81:737 (1995).

    Google Scholar 

  9. M. Kardar, G. Parisi, and Y. C. Zhang, Phys. Rev. Lett. 56:889 (1986).

    PubMed  Google Scholar 

  10. J. Maunuksela, O. Myllys, O.-P. Kähkönen, J. Timonen, N. Provatas, M. J. Alava, and T. Ala-Nissila, Phys. Rev. Lett. 79:1515 (1997).

    Google Scholar 

  11. A. N. Kolmogorov, Bull. Acad. Sci. USSR, Mat. Ser. 1:335 (1937).

    Google Scholar 

  12. M. Avrami, J. Chem. Phys. 7:1103 (1939).

    Google Scholar 

  13. W. A. Johnson and A. Mehl, Trans. Am. Inst. Min. Eng. 135:416, (1939).

    Google Scholar 

  14. R. M. Bradley and P. N. Strenski, Phys. Rev. B 40:8967 (1989).

    Google Scholar 

  15. Y. Ishibashi and Y. Takagi, J. Phys. Soc. Jpn. 31:506 (1971).

    Google Scholar 

  16. K. Sekimoto, Physica A 135:328 (1986). The exponent of yin front of the logarithmic term should vs be 3 instead of 2 in Eq. (3.14) of this paper.

    Google Scholar 

  17. B. Grossmann, H. Guo, and M. Grant, Phys. Rev. A 43:1727 (1991).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics and the Centre for the Physics of Materials, McGill University, Montréal (, Qué.), Canada, H3A 2T8

    Mikko Karttunen & Martin Grant

  2. Loomis Laboratory of Physics, Department of Physics and Mechanical Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois, 61801-3080

    Nikolas Provatas

  3. Helsinki Institute of Physics, University of Helsinki, P.O. Box 9, FIN-00014, Helsinki, Finland

    Nikolas Provatas & Tapio Ala-Nissila

  4. Department of Physics, Brown University, Providence, Rhode Island, 02912

    Tapio Ala-Nissila

Authors
  1. Mikko Karttunen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nikolas Provatas
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Tapio Ala-Nissila
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Martin Grant
    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

Karttunen, M., Provatas, N., Ala-Nissila, T. et al. Nucleation, Growth, and Scaling in Slow Combustion. Journal of Statistical Physics 90, 1401–1411 (1998). https://doi.org/10.1023/A:1023243831128

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1023243831128

Search

Navigation