Skip to main content

Isothermal Autocatalysis in the CSTR: Exotic Stationary-State Patterns (Isolas and Mushrooms)and Sustained Oscillations

  • Chapter
Chemical Instabilities

Part of the book series: NATO ASI Series ((ASIC,volume 120))

  • 142 Accesses

Abstract

The prototype, cubic autocatalytic reaction (A + 2B → 3B) forms the basis of a simple homogeneous system displaying a rich variety of complex behaviour. Even under well-stirred, isothermal open conditions (the CSTR) we may find multistability, hysteresis, extinction and ignition. Allowing for the finite lifetime of the catalyst (B inert products) adds another dimension. The dependence of the stationary-states on residence-time now yields isolas and mushrooms. Sustained oscillations (stable limit cycles) are also possible. There are strong analogies between this simple system and the exothermic, first-order reaction in a CSTR.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Zeldovich, Ya. B. 1941 Zh. Tekh. Fiz. 11, pp. 493–508;

    Google Scholar 

  2. Zeldovich, Ya. B. and Zysin, Y.A. B. 1941 Zh. Tekh. Fiz. 11, pp. 509–524.

    Google Scholar 

  3. van Heerden, C. 1953 Ind. Engng. Chem. 45, pp. 12422–1247.

    Google Scholar 

  4. Uppal, A., Ray, W.H. and Poore, A.B. 1974 Chem. Engng. Sci. 29, pp. 967–985;

    Article  CAS  Google Scholar 

  5. Ray, W.H. 1976 Chem. Engng. Sci. 31, pp. 205–214.

    Google Scholar 

  6. Vaganov, D.A., Samoilenko, N.G. and Abramov, V.G. 1978 Chem. Engng. Sci. 33, pp. 1133–1140.

    Article  CAS  Google Scholar 

  7. Balakotaiah, V. and Luss, D. 1982 Chem. Engng. Sci. 37, pp. 1611–1623.

    Article  CAS  Google Scholar 

  8. Aarons, L.J. and Gray, B.F. 1976 Chem. Soc. Rev. 5, pp. 359–375.

    Article  CAS  Google Scholar 

  9. Prigogine, I. and Lefever, R. 1968 J. Chem. Phys. 48, pp. 1695–1700.

    Article  Google Scholar 

  10. Field, R.J. and Noyes, R.M. 1974 J. Chem. Phys. 60, pp. 1877–1884.

    Article  CAS  Google Scholar 

  11. Lin, K.F. 1979 Can. J. Chem. Engng. 54, pp. 476–480;

    Article  Google Scholar 

  12. Lin, K.F. 1981 Chem. Engng. Sci. 36, pp. 1447–1452.

    Google Scholar 

  13. Heinrichs, M. and Schneider, F.W. 1981 J. Phys. Chem. 85, pp. 2112–2116;

    Article  CAS  Google Scholar 

  14. Heinrichs, M. and Schneider, F.W. 1980 Ber. dts. Bunsenges. phys. Chem. 84, pp. 857–865.

    Google Scholar 

  15. Gray, P. and Scott, S.K. 1983 Chem. Engng. Sci. 38, pp. 29–43.

    Article  CAS  Google Scholar 

  16. Scott, S.K. 1983 Chem. Engng. Sci. 38

    Google Scholar 

  17. Gray, P. and Scott, S.K. 1983 J. phys. Chem.

    Google Scholar 

  18. Gray, P. and Scott, S.K. 1983 Ber. dts. Bunsenges. phys. Chem.

    Google Scholar 

  19. Gray, P. and Scott, S.K. 1983 Chem. Engng. Sci.

    Google Scholar 

  20. Hassard, B.D., Kazarinoff, N.D. and Wan, Y.-H. 1981 Theory and Applications of Hoph Bifurcation (London Mathematical Society Lecture Note Series no. 41, I.M. James ed. ), Cambridge University Press.

    Google Scholar 

  21. Papsin, G.A. Hanna, A. and Showalter, K. 1981 J. Phys. Chem. 85, pp. 2575–2582.

    Article  CAS  Google Scholar 

  22. Reckley, J.S. and Showalter, K. 1981 J. Amer. Chem. Soc. 103, pp. 7012–3.

    Article  CAS  Google Scholar 

  23. Noyes, R.M. 1981 Proc. Natl. Sci. USA 78, pp. 7248–7250.

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1984 D.Reidel Publishing Company

About this chapter

Cite this chapter

Gray, P., Scott, S.K. (1984). Isothermal Autocatalysis in the CSTR: Exotic Stationary-State Patterns (Isolas and Mushrooms)and Sustained Oscillations. In: Nicolis, G., Baras, F. (eds) Chemical Instabilities. NATO ASI Series, vol 120. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-7254-4_5

Download citation

  • DOI: https://doi.org/10.1007/978-94-009-7254-4_5

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-009-7256-8

  • Online ISBN: 978-94-009-7254-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics