MENU
  • Scitation Home
SUBMIT YOUR ARTICLE

Thank you

For your interest in Chaos: An Interdisciplinary Journal of Nonlinear Science

Check for updates on crossmark
Prev Next
No Access Submitted: 07 February 2019 Accepted: 03 July 2019 Published Online: 30 August 2019

  • Convective instabilities derived from dissipation of chemical energy

Chaos 29, 083136 (2019); https://doi.org/10.1063/1.5092137
Reuben H. Simoyi1,2,a)
more...View Affiliations
View Contributors
  • Reuben H. Simoyi
  • Correction: Chaos 31, 019901 (2021)
    • ABSTRACT
    Oxidation reactions of a series of organosulfur compounds by chlorite are excitable, autocatalytic, and exothermic and generate a lateral instability upon being triggered by the autocatalyst. This article reports on the convective instabilities derived from the reaction of chlorite and thiourea in a Hele-Shaw cell. Reagent concentrations used for the development of convective instabilities delivered a temperature jump at the wave front of 2.1 K. The reaction zone was 2 mm and due to normal cooling after the wave front, this induced a spike rather than the standard well-studied front propagation. Localized spatiotemporal patterns develop around the wave front. This exothermic autocatalytic reaction has solutal and thermal contributions to density changes that act in opposite directions due to the existence of a positive isothermal density change in the reaction. The competition between these effects generates thermal plumes. The fascinating feature of this system is the coexistence of plumes and fingering in the same solution as the front propagates through the Hele-Shaw cell. Wave velocities of descending and ascending fronts are oscillatory. Fingers and plumes are generated in alternating frequency as the front propagates. This generates hot and cold spots within the Hele-Shaw cell, and subsequently spatiotemporal inhomogeneities. The small ΔT at the wave front generated thermocapillary convection which competed effectively with thermogravitational forces at low Eötvös numbers. A simplified reaction-diffusion-convection model was derived for the system. Plume formation is heavily dependent on boundary effects from the cell dimensions.

    ACKNOWLEDGMENTS

    Several people were involved in this work that is meant to honor Kenneth Showalter. I would like to acknowledge the work of Dr. Marcus Hauser of Otto-von-Guericke University in Magdeburg for calculating Marangoni factors and thermogravitational effects. Professor Bice Martincigh of the University of KwaZulu-Natal did the work shown in Fig. 5. Professor Tony Howes of the University of Queensland in St. Lucia worked on the data shown in Fig. 1. Special thanks and acknowledgements go to Matthew Eskew of Portland State University who did a lot of the experimental work that goes with Figs. 6–9. He also sketched Fig. 1. This work was supported by Research Grant No. CHE-1056366 from the National Science Foundation (NSF) and a Research Professor Grant from the University of KwaZulu-Natal, Cost Center No. P565.

    REFERENCES
    Section:
    Previous sectionNext section

    1. 1. J. Buceta and K. Lindenberg, “Switching-induced Turing instability,” Phys. Rev. E 66, 046202 (2002). https://doi.org/10.1103/PhysRevE.66.046202, Google ScholarCrossref
    2. 2. A. M. Turing, “Chemical basis for morphogenesis,” Trans. R. Soc. Lond. B 327, 37–72 (1952). Google Scholar
    3. 3. M. A. Budroni, L. Lemaigre, D. M. Escala, A. P. Munuzuri, and W. A. De, “Spatially localized chemical patterns around an A + B → oscillator front,” J. Phys. Chem. A 120, 851–860 (2016). https://doi.org/10.1021/acs.jpca.5b10802, Google ScholarCrossref
    4. 4. V. K. Vanag and I. R. Epstein, “Design and control of patterns in reaction-diffusion systems,” Chaos 18, 026107 (2008). https://doi.org/10.1063/1.2900555, Google ScholarScitation
    5. 5. I. L’Heureux, “Self-organized rhythmic patterns in geochemical systems,” Philos. Trans. A Math. Phys. Eng. Sci. 371, 20120356 (2013). https://doi.org/10.1098/rsta.2012.0356, Google ScholarCrossref
    6. 6. A. A. Mansour and M. Al-Ghoul, “Band propagation, scaling laws, and phase transition in a precipitate system. 2. Computational study,” J. Phys. Chem. A 119, 9201–9209 (2015). https://doi.org/10.1021/acs.jpca.5b05069, Google ScholarCrossref
    7. 7. S. H. Hejazi, P. M. J. Trevelyan, J. Azaiez, and A. De Wit, “Viscous fingering of a miscible reactive A + B → C interface: A linear stability analysis,” J. Fluid Mech. 652, 501–528 (2010). https://doi.org/10.1017/S0022112010000327, Google ScholarCrossref
    8. 8. K. Eckert, M. Acker, R. Tadmouri, and V. Pimienta, “Chemo-Marangoni convection driven by an interfacial reaction: Pattern formation and kinetics,” Chaos 22, 037112 (2012). https://doi.org/10.1063/1.4742844, Google ScholarScitation
    9. 9. W. A. De, K. Eckert, and S. Kalliadasis, “Introduction to the focus issue: Chemo-hydrodynamic patterns and instabilities,” Chaos 22, 037101 (2012). https://doi.org/10.1063/1.4756930, Google ScholarScitation
    10. 10. M. A. Budroni, L. A. Riolfo, L. Lemaigre, F. Rossi, M. Rustici, and W. A. De, “Chemical control of hydrodynamic instabilities in partially miscible two-layer systems,” J. Phys. Chem. Lett. 5, 875–881 (2014). https://doi.org/10.1021/jz5000403, Google ScholarCrossref
    11. 11. C. R. Chinake and R. H. Simoyi, “Complex reaction dynamics derived from an autocatalytic exothermic chemical reaction,” S. Afr. J. Chem. 50, 220–226 (1997); https://hdl.handle.net/10520/AJA03794350_1317, Google Scholar
    12. 12. C. R. Chinake and R. H. Simoyi, “New experimental-data on the chlorite-thiourea reaction,” J. Phys. Chem. 97, 11569–11570 (1993). https://doi.org/10.1021/j100146a035, Google ScholarCrossref
    13. 13. J. B. Jones, C. R. Chinake, and R. H. Simoyi, “Oxyhalogen sulfur chemistry: Oligooscillations in the formamidinesulfinic acid chlorite reaction,” J. Phys. Chem. 99, 1523–1529 (1995). https://doi.org/10.1021/j100005a024, Google ScholarCrossref
    14. 14. C. R. Chinake and R. H. Simoyi, “Fingering patterns and other interesting dynamics in the chemical waves generated by the chlorite-thiourea reaction,” J. Phys. Chem. 98, 4012–4019 (1994). https://doi.org/10.1021/j100066a019, Google ScholarCrossref
    15. 15. T. Gerard, T. Toth, P. Grosfils, D. Horvath, W. A. De, and A. Toth, “Hot spots in density fingering of exothermic autocatalytic chemical fronts,” Phys. Rev. E 86, 016322 (2012). https://doi.org/10.1103/PhysRevE.86.016322, Google ScholarCrossref
    16. 16. L. Sebestikova and M. J. Hauser, “Buoyancy-driven convection may switch between reactive states in three-dimensional chemical waves,” Phys. Rev. E 85, 036303 (2012). https://doi.org/10.1103/PhysRevE.85.036303, Google ScholarCrossref
    17. 17. B. S. Martincigh and R. H. Simoyi, “Pattern formation fueled by dissipation of chemical energy: Conclusive evidence for the formation of a convective torus,” J. Phys. Chem. A 106, 482–489 (2002). https://doi.org/10.1021/jp012502k, Google ScholarCrossref
    18. 18. B. S. Martincigh, C. R. Chinake, T. Howes, and R. H. Simoyi, “Self-organization with traveling waves: A case for a convective torus,” Phys. Rev. 55, 7299–7303 (1997). https://doi.org/10.1103/PhysRevB.55.R7299, Google ScholarCrossref
    19. 19. B. S. Martincigh, M. J. Hauser, and R. H. Simoyi, “Formation of thermal plumes in an autocatalytic exothermic chemical reaction,” Phys. Rev. E 52, 6146–6153 (1995). https://doi.org/10.1103/PhysRevE.52.6146, Google ScholarCrossref
    20. 20. F. Rossi, M. A. Budroni, N. Marchettini, and J. Carballido-Landeira, “Segmented waves in a reaction-diffusion-convection system,” Chaos 22, 037109 (2012). https://doi.org/10.1063/1.4752194, Google ScholarScitation, ISI
    21. 21. P. M. Vilela and D. A. Vasquez, “Rayleigh-Taylor instability of steady fronts described by the Kuramoto-Sivashinsky equation,” Chaos 24, 023135 (2014). https://doi.org/10.1063/1.4883500, Google ScholarScitation
    22. 22. B. Rollin and M. J. Andrews, “Mathematical model of Rayleigh-Taylor and Richtmyer-Meshkov instabilities for viscoelastic fluids,” Phys. Rev. E 83, 046317 (2011). https://doi.org/10.1103/PhysRevE.83.046317, Google ScholarCrossref
    23. 23. A. K. Horvath, I. Nagypal, G. Peintler, and I. R. Epstein, “Autocatalysis and self-inhibition: Coupled kinetic phenomena in the chlorite-tetrathionate reaction,” J. Am. Chem. Soc. 126, 6246–6247 (2004). https://doi.org/10.1021/ja048982l, Google ScholarCrossref
    24. 24. A. K. Horvath, I. Nagypal, and I. R. Epstein, “Oscillatory photochemical decomposition of tetrathionate ion,” J. Am. Chem. Soc. 124, 10956–10957 (2002). https://doi.org/10.1021/ja0269441, Google ScholarCrossref
    25. 25. A. K. Horvath and I. Nagypal, “Kinetics and mechanism of the reaction between hypochlorous acid and tetrathionate ion,” Int. J. Chem. Kinet. 32, 395–402 (2000). https://doi.org/10.1002/(SICI)1097-4601(2000)32:7<395::AID-KIN1>3.0.CO;2-G, Google ScholarCrossref
    26. 26. E. Popity-Toth, D. Horvath, and A. Toth, “Horizontally propagating three-dimensional chemo-hydrodynamic patterns in the chlorite-tetrathionate reaction,” Chaos 22, 037105 (2012). https://doi.org/10.1063/1.4740464, Google ScholarScitation
    27. 27. C. R. Chinake and R. H. Simoyi, “Experimental studies of spatial patterns produced by diffusion-convection-reaction systems,” J. Chem. Soc. Faraday Trans. 93, 1345–1350 (1997). https://doi.org/10.1039/a607541j, Google ScholarCrossref
    28. 28. G. Rabai and M. Orban, “General-model for the chlorite ion based chemical oscillators,” J. Phys. Chem. 97, 5935–5939 (1993). https://doi.org/10.1021/j100124a026, Google ScholarCrossref
    29. 29. M. J. B. Hauser, C. R. Chinake, and R. H. Simoyi, “Breakdown of symmetry, spatio-temporal patterns and travelling waves in oxyhalogen-sulfur systems,” S. Afr. J. Chem. 48, 135–141 (1995); https://hdl.handle.net/10520/AJA03794350_932. Google Scholar
    30. 30. K. Eckert, L. Rongy, and W. A. De, “A +  B → C reaction fronts in Hele-Shaw cells under modulated gravitational acceleration,” Phys. Chem. Chem. Phys. 14, 7337–7345 (2012). https://doi.org/10.1039/c2cp40132k, Google ScholarCrossref
    31. 31. M. J. B. Hauser and R. H. Simoyi, “Inhomogeneous precipitation patterns in a chemical wave. Part 7,” Phys. Lett. A 191, 31–38 (1994). https://doi.org/10.1016/0375-9601(94)90556-8, Google ScholarCrossref
    32. 32. A. Indelli, “Kinetic study on the reaction of sodium chlorite with potassium iodide,” J. Phys. Chem. 68, 3027–3031 (1964). https://doi.org/10.1021/j100792a050, Google ScholarCrossref
    33. 33. D. Villers and J. K. Platten, “Coupled buoyancy and Marangoni convection in acetone: Experiments and comparison with numerical simulations,” J. Fluid Mech. 234, 487–510 (1992). https://doi.org/10.1017/S0022112092000880, Google ScholarCrossref
    34. 34. K. M. S. Bajaj, D. S. Cannell, and G. Ahlers, “Competition between spiral-defect chaos and rolls in Rayleigh-Benard convection,” Phys. Rev. E 55, R4869–R4872 (1997). https://doi.org/10.1103/PhysRevE.55.R4869, Google ScholarCrossref
    35. 35. M. Larranaga, M. M. Bou-Ali, D. A. de Mezquia, D. A. Rees, J. A. Madariaga, C. Santamaria, and J. K. Platten, “Contribution to the benchmark for ternary mixtures: Determination of Soret coefficients by the thermogravitational and the sliding symmetric tubes techniques,” Eur. Phys. J. E 38, 28 (2015). https://doi.org/10.1140/epje/i2015-15028-1, Google ScholarCrossref
    36. 36. M. J. Andrews and S. B. Dalziel, “Small Atwood number Rayleigh-Taylor experiments,” Philos. Trans. A Math. Phys. Eng. Sci. 368, 1663–1679 (2010). https://doi.org/10.1098/rsta.2010.0007, Google ScholarCrossref
    37. 37. S. Slavtchev, G. Simeonov, S. Van Vaerenbergh, and J. C. Legros, “Marangoni instability of a layer of binary liquid in the presence of nonlinear Soret effect,” Int. J. Heat Mass Transf. 42, 3007–3011 (1999). https://doi.org/10.1016/S0017-9310(98)00353-6, Google ScholarCrossref
    38. 38. C. Karcher and U. Muller, “Onset of oscillatory convection in binary-mixtures with Soret effects and solidification,” Int. J. Heat Mass Transf. 37, 2517–2523 (1994). https://doi.org/10.1016/0017-9310(94)90289-5, Google ScholarCrossref
    39. 39. C. Karcher, “Bifurcation behavior of Benard convection in binary-fluid mixtures with non-Boussinesq properties,” Z. Angew. Math. Mech. 74, T437–T439 (1994). Google Scholar
    40. 40. J. K. Platten, M. M. Bou-Ali, P. Blanco, J. A. Madariaga, and C. Santamaria, “Soret coefficients in some water-methanol, water-ethanol, and water-isopropanol systems,” J. Phys. Chem. B 111, 11524–11530 (2007). https://doi.org/10.1021/jp074206z, Google ScholarCrossref
    41. 41. P. Costeseque, T. Pollak, J. K. Platten, and M. Marcoux, “Transient-state method for coupled evaluation of Soret and Fick coefficients, and related tortuosity factors, using free and porous packed thermodiffusion cells: Application to CuSO4 aqueous solution (0.25 M),” Eur. Phys. J. E 15, 249–253 (2004). https://doi.org/10.1140/epje/i2004-10064-6, Google ScholarCrossref
    42. 42. E. Michel, A. Baglin, M. Auvergne, C. Catala, R. Samadi, F. Baudin, T. Appourchaux, C. Barban, W. W. Weiss, G. Berthomieu, P. Boumier, M. A. Dupret, R. A. Garcia, M. Fridlund, R. Garrido, M. J. Goupil, H. Kjeldsen, Y. Lebreton, B. Mosser, A. Grotsch-Noels, E. Janot-Pacheco, J. Provost, I. W. Roxburgh, A. Thoul, T. Toutain, D. Tiphene, S. Turck-Chieze, S. D. Vauclair, G. P. Vauclair, C. Aerts, G. Alecian, J. Ballot, S. Charpinet, A. M. Hubert, F. Lignieres, P. Mathias, M. J. Monteiro, C. Neiner, E. Poretti, J. R. de Medeiros, I. Ribas, M. L. Rieutord, T. R. Cortes, and K. Zwintz, “Corot measures solar-like oscillations and granulation in stars hotter than the Sun,” Science 322, 558–560 (2008). https://doi.org/10.1126/science.1163004, Google ScholarCrossref
    43. 43. V. M. Canuto, “Semiconvection and overshooting Schwarzschild and Ledoux criteria revisited,” Astrophys. J. 534, L113–L115 (2000). https://doi.org/10.1086/312654, Google ScholarCrossref
    1. © 2019 Author(s). Published under license by AIP Publishing.

    Article Metrics

    Views
    256
    Citations
    Crossref 2
    Web of Science
    ISI 0

    Altmetric

    Please Note: The number of views represents the full text views from December 2016 to date. Article views prior to December 2016 are not included.