Advertisement

Mosaic Patterns in Reaction-Diffusion Systems

  • Dalia Ezzeddine
  • Rabih SultanEmail author
Conference paper
  • 13 Downloads
Part of the Springer Proceedings in Complexity book series (SPCOM)

Abstract

We study a variety of reaction-diffusion processes that lead to the formation of exotic patterns. 1. We carry out precipitation reactions in gel media, wherein the interdiffusion of the co-precipitates takes place from multiple diffusion sources arranged in a symmetric framework. The precipitation zones are delimited by clear polygonal boundaries in congruence with the spatial distribution of the diffusion pools. 2. A displacement reaction in a solid-gel medium is conducted as a carbonic acid diffusion front invades an agar-calcium hydroxide gel putty. The formation of calcium carbonate yields a diversity of patterns, ranging from mosaic structures to Liesegang bands. 3. A Liesegang experiment precipitating lead chromate from the interdiffusion of lead and chromate ions in 2D yields a pattern of rings exhibiting revert spacing. When the diffusion comes from a constantly fed unstirred source (or reactor, CFUR), the patterns transit to a chaotic regime which is sensitive to the concentrations used and the flow rate.

Keywords

Patterns Chaos Liesegang Portlandite Polygons Reaction-diffusion 

Notes

Acknowledgements

This study was supported by a University Research Board (URB) grant of the American University of Beirut (AUB). X-ray diffraction, IR spectroscopy, freeze drying and SEM were performed at the Central Research Science Lab (CRSL) of the AUB.

References

  1. 1.
    P. Ball, The Self-Made Tapestry: Pattern Formation in Nature (Oxford University Press, Oxford, 1999)zbMATHGoogle Scholar
  2. 2.
    I. Lagzi (ed.), Precipitation Patterns in Reaction-Diffusion Systems (Research Signpost publications, Trivandrum, Kerala, 2011)Google Scholar
  3. 3.
    R.E. Liesegang, Chemische Fernwirkung, Lieseg. Photograph. Arch. 37, 305 (1896); continued in 37, 331 (1896)Google Scholar
  4. 4.
    R.E. Liesegang, Geologische Diffusionen (Steinkopff, Dresden, 1913)Google Scholar
  5. 5.
    R.E. Liesegang, Die Achate (Steinkopf, Dresden-Leipsig, 1915)Google Scholar
  6. 6.
    B. Jamtveit, P. Meakin (eds.), Growth, Dissolution and Pattern Formation in Geosystems (Kluwer, Dordrecht, 1999)Google Scholar
  7. 7.
    P. Ortoleva, Geochemical Self-Organization (Oxford University Press, New York, 1994)Google Scholar
  8. 8.
    A.D. Fowler, I. L’Heureux, Self-organized banded sphalerite and branching galena in the Pine Point ore deposit Northwest Territories. Can. Miner. 34, 1211–1222 (1996)Google Scholar
  9. 9.
    J.H. Kruhl (ed.), Fractals, and Dynamic Systems in Geoscience (Springer, Berlin, 1994)Google Scholar
  10. 10.
    C. Rodriguez-Navarro, O. Cazalla, K. Elert, E. Sebastian, Liesegang pattern development in carbonating traditional lime mortars. Proc. R. Soc. Lond. A 458, 2261–2273 (2002)ADSCrossRefGoogle Scholar
  11. 11.
    R. Sultan, A. Abdel-Rahman, On dynamic self-organization: examples from magmatic and other geochemical systems. Latin Am. J. Solids Struct. (LAJSS) 10, 59–73 (2013)CrossRefGoogle Scholar
  12. 12.
    M. Msharrafieh, M. Al-Ghoul, F. Zaknoun, H. El-Rassy, S. El-Joubeily, R. Sultan, Simulation of geochemical banding I: acidization-precipitation experiments in a ferruginous limestone rock. Chem. Geol. 440, 42–49 (2016)ADSCrossRefGoogle Scholar
  13. 13.
    H. Batlouni, H. El-Rassy, M. Al-Ghoul, Cosynthesis, coexistence, and self-organization of α-and β-Cobalt hydroxide based on diffusion and reaction in organic gels. J. Phys. Chem. A 112(34), 7755–7757 (2008)CrossRefGoogle Scholar
  14. 14.
    T. Karam, H. El-Rassy, F. Zaknoun, Z. Moussa, R. Sultan, Liesegang banding and multiple precipitate formation in cobalt phosphate systems. Chem. Phys. Lett. 525–526, 54–59 (2012)ADSCrossRefGoogle Scholar
  15. 15.
    C.K. Jablczynski, Mémoires présentes à la société chimique. Les anneaux de Liesegang. Bull. Soc. Chim. France 33, 1592–1602 (1923)Google Scholar
  16. 16.
    M. Droz, J. Magnin, M. Zrinyi, Liesegang patterns: studies on the width law. J. Chem. Phys. 110(19), 9618–9622 (1999)ADSCrossRefGoogle Scholar
  17. 17.
    T. Karam, H. El-Rassy, R. Sultan, Mechanism of revert spacing in a PbCrO4 Liesegang system. J. Phys. Chem. A 115(14), 2994–2998 (2011)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of ChemistryAmerican University of BeirutBeirutLebanon

Personalised recommendations