On the Origin of Chaos in the Belousov-Zhabotinsky Reaction in Closed and Unstirred Reactors

M. A. Budroni; M. Rustici; E. Tiezzi

Mathematical Modelling of Natural Phenomena (2010)

  • Volume: 6, Issue: 1, page 226-242
  • ISSN: 0973-5348

Abstract

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We investigate the origin of deterministic chaos in the Belousov–Zhabotinsky (BZ) reaction carried out in closed and unstirred reactors (CURs). In detail, we develop a model on the idea that hydrodynamic instabilities play a driving role in the transition to chaotic dynamics. A set of partial differential equations were derived by coupling the two variable Oregonator–diffusion system to the Navier–Stokes equations. This approach allows us to shed light on the correlation between chemical oscillations and spatial–temporal dynamics. In particular, numerical solutions to the corresponding reaction-diffusion-convection (RDC) problem show that natural convection can change the evolution of the concentration distribution as well as oscillation patterns. The results suggest a new way of perceiving the BZ reaction when it is conducted in CURs. In conflict with the common experience, chemical oscillations are no longer a mere chemical process. Within this framework the evolution of all dynamical observables are demonstrated to converge to the regime imposed by the RDC coupling: chemical and spatial–temporal chaos are genuine manifestations of the same phenomenon.

How to cite

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Budroni, M. A., Rustici, M., and Tiezzi, E.. "On the Origin of Chaos in the Belousov-Zhabotinsky Reaction in Closed and Unstirred Reactors." Mathematical Modelling of Natural Phenomena 6.1 (2010): 226-242. <http://eudml.org/doc/197646>.

@article{Budroni2010,
abstract = {We investigate the origin of deterministic chaos in the Belousov–Zhabotinsky (BZ) reaction carried out in closed and unstirred reactors (CURs). In detail, we develop a model on the idea that hydrodynamic instabilities play a driving role in the transition to chaotic dynamics. A set of partial differential equations were derived by coupling the two variable Oregonator–diffusion system to the Navier–Stokes equations. This approach allows us to shed light on the correlation between chemical oscillations and spatial–temporal dynamics. In particular, numerical solutions to the corresponding reaction-diffusion-convection (RDC) problem show that natural convection can change the evolution of the concentration distribution as well as oscillation patterns. The results suggest a new way of perceiving the BZ reaction when it is conducted in CURs. In conflict with the common experience, chemical oscillations are no longer a mere chemical process. Within this framework the evolution of all dynamical observables are demonstrated to converge to the regime imposed by the RDC coupling: chemical and spatial–temporal chaos are genuine manifestations of the same phenomenon.},
author = {Budroni, M. A., Rustici, M., Tiezzi, E.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {chemical chaos; spatial–temporal chaos; reaction–diffusion–convection system; Belousov–Zhabotinsky reaction; spatial-temporal chaos; reaction-diffusion-convection system; Belousov-Zhabotinsky reaction},
language = {eng},
month = {6},
number = {1},
pages = {226-242},
publisher = {EDP Sciences},
title = {On the Origin of Chaos in the Belousov-Zhabotinsky Reaction in Closed and Unstirred Reactors},
url = {http://eudml.org/doc/197646},
volume = {6},
year = {2010},
}

TY - JOUR
AU - Budroni, M. A.
AU - Rustici, M.
AU - Tiezzi, E.
TI - On the Origin of Chaos in the Belousov-Zhabotinsky Reaction in Closed and Unstirred Reactors
JO - Mathematical Modelling of Natural Phenomena
DA - 2010/6//
PB - EDP Sciences
VL - 6
IS - 1
SP - 226
EP - 242
AB - We investigate the origin of deterministic chaos in the Belousov–Zhabotinsky (BZ) reaction carried out in closed and unstirred reactors (CURs). In detail, we develop a model on the idea that hydrodynamic instabilities play a driving role in the transition to chaotic dynamics. A set of partial differential equations were derived by coupling the two variable Oregonator–diffusion system to the Navier–Stokes equations. This approach allows us to shed light on the correlation between chemical oscillations and spatial–temporal dynamics. In particular, numerical solutions to the corresponding reaction-diffusion-convection (RDC) problem show that natural convection can change the evolution of the concentration distribution as well as oscillation patterns. The results suggest a new way of perceiving the BZ reaction when it is conducted in CURs. In conflict with the common experience, chemical oscillations are no longer a mere chemical process. Within this framework the evolution of all dynamical observables are demonstrated to converge to the regime imposed by the RDC coupling: chemical and spatial–temporal chaos are genuine manifestations of the same phenomenon.
LA - eng
KW - chemical chaos; spatial–temporal chaos; reaction–diffusion–convection system; Belousov–Zhabotinsky reaction; spatial-temporal chaos; reaction-diffusion-convection system; Belousov-Zhabotinsky reaction
UR - http://eudml.org/doc/197646
ER -

References

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