Two-dimensional Numerical Simulation Method for Convective Flow Structure Induced by Chemical Concentration Waves

Atsushi Nomura, Tatsunari Sakurai, Hidetoshi Miike

2014

Abstract

This paper presents a two-dimensional numerical simulation method for modeling a convective flow structure induced by chemical concentration waves of Belousov-Zhabotinsky (BZ) reaction in a two-dimensional rectangular domain of horizontal space and vertical depth. The method assumes a scenario in which an air-liquid interface of the BZ chemical solution has an elastic property and the Marangoni effect drives the surface motion of the interface. As a result of the surface motion, a convective flow is organized in the bulk of the chemical solution. The bulk flow of the chemical solution is described with the Navier-Stokes equations, and the chemical reaction is described with the Oregonator model. Thus, we couple the three systems of the bulk flow, the chemical reaction and the surface motion described with an elastic equation in the numerical simulation method. Results of several numerical simulations performed with the method show that a single chemical concentration wave propagates with a broad convective flow structure and a chemical concentration wave train propagates with a global flow structure. These flow structures are similar to those observed in real laboratory experiments.

References

  1. Diewald, M., Matthiessen, K., Müller, S. C., and Brand, H. R. (1996). Oscillatory hydrodynamic flow due to concentration dependence of surface tension. Physical Review Letters, 77:4466-4469.
  2. Field, R. J., Koros, E., and Noyes, R. M. (1972). Oscillations in chemical systems. II. Thorough analysis of temporal oscillation in the bromate-cerium-malonic acid system. Journal of American Chemical Society, 94:8649-8664.
  3. Inomoto, O., Abe, K., Amemiya, T., Yamaguchi, T., and Kai, S. (2000). Bromomalonic-acid-induced transition from trigger wave to big wave in the BelousovZhabotinsky reaction. Physical Review E, 61:5326- 5329.
  4. Jahnke, W., Skaggs, W. E., and Winfree, A. T. (1989). Chemical vortex dynamics in the BelousovZhabotinskii reaction and in the two-variable oregonator model. Journal of Physical Chemistry, 93:740- 749.
  5. Keener, J. P. and Tyson, J. J. (1986). Spiral waves in the Belousov-Zhabotinskii reaction. Physica D, 21:307- 324.
  6. Matthiessen, K. and Müller, S. C. (1995). Global flow waves in chemically induced convection. Physical Review E, 52:492-495.
  7. Matthiessen, K., Wilke, H., and Müller, S. C. (1996). Influence of surface tension changes on hydrodynamic flow induced by traveling chemical waves. Physical Review E, 53:6056-6060.
  8. Miike, H., Miura, K., Nomura, A., and Sakurai, T. (2010). Flow waves of hierarchical pattern formation induced by chemical waves: The birth, growth and death of hydrodynamic structures. Physica D, 239:808-818.
  9. Miike, H., Müller, S. C., and Hess, B. (1988). Oscillatory deformation of chemical waves induced by surface flow. Physical Review Letters, 61:2109-2112.
  10. Miike, H., Yamamoto, H., Kai, S., and Müller, S. C. (1993). Accelerating chemical waves accompanied by traveling hydrodynamic motion and surface deformation. Physical Review E, 48:R1627-R1630.
  11. Nomura, A., Sakurai, T., Miike, H., and Hano, M. (2004). Model for the Belousov-Zhabotinsky reaction and surface flow structure induced by chemical concentration gradients. In Proceedings of 2004 International Symposium on Nonlinear Theory and its Applications, pages 363-366, Fukuoka, Japan.
  12. Rongy, L. and De Wit, A. (2007). Marangoni flow around chemical fronts traveling in thin solution layers: influence of the liquid depth. Journal of Engineering Mathematics, 59(2):221-227.
  13. Rossi, F., Budroni, M. A., Marchettini, N., and CarballidoLandeira, J. (2012). Segmented waves in a reactiondiffusion-convection system. Chaos, 22(3):037109 (11 pages).
  14. Rossi, F. and Liveri, M. L. T. (2009). Chemical selforganization in self-assembling biomimetic systems. Ecological Modelling, 220:1857-1864.
  15. Sakurai, T., Inomoto, O., Miike, H., and Kai, S. (2004). Structure of surface deformation waves induced in spiral pattern in the Belousov-Zhabotinsky reaction. Journal of the Physical Society of Japan, 73:485-490.
  16. Sakurai, T., Miike, H., Okada, K., and Müller, S. C. (2003). Spiral flow wave in a reaction-diffusion-convection system. Journal of the Physical Society of Japan, 72:2177-2180.
  17. Sakurai, T., Miike, H., Yokoyama, E., and Müller, S. C. (1997). Initiation front and annihilation center of convection waves developing in spiral structures of Belousov-Zhabotinsky reaction. Journal of the Physical Society of Japan, 66:518-521.
  18. Yoshikawa, K., Kusumi, T., Ukitsu, M., and Nakata, S. (1993). Generation of periodic force with oscillating chemical reaction. Chemical Physics Letters, 211:211-213.
  19. Zaikin, A. N. and Zhabotinsky, A. M. (1970). Concentration wave propagation in two-dimensional liquidphase self-oscillating system. Nature, 225:535-537.
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Paper Citation


in Harvard Style

Nomura A., Sakurai T. and Miike H. (2014). Two-dimensional Numerical Simulation Method for Convective Flow Structure Induced by Chemical Concentration Waves . In Proceedings of the 4th International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH, ISBN 978-989-758-038-3, pages 613-618. DOI: 10.5220/0005108506130618


in Bibtex Style

@conference{simultech14,
author={Atsushi Nomura and Tatsunari Sakurai and Hidetoshi Miike},
title={Two-dimensional Numerical Simulation Method for Convective Flow Structure Induced by Chemical Concentration Waves},
booktitle={Proceedings of the 4th International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH,},
year={2014},
pages={613-618},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005108506130618},
isbn={978-989-758-038-3},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 4th International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH,
TI - Two-dimensional Numerical Simulation Method for Convective Flow Structure Induced by Chemical Concentration Waves
SN - 978-989-758-038-3
AU - Nomura A.
AU - Sakurai T.
AU - Miike H.
PY - 2014
SP - 613
EP - 618
DO - 10.5220/0005108506130618