Math. Model. Nat. Phenom.
Volume 6, Number 1, 2011Instability and patterns. Issue dedicated to the memory of A. Golovin
|Page(s)||226 - 242|
|Published online||09 June 2010|
On the Origin of Chaos in the Belousov-Zhabotinsky Reaction in Closed and Unstirred Reactors
Dipartimento di Chimica Università di Siena,
Via della Diana 2a, 53100 Siena,
2 Dipartimento di Chimica Università di Sassari and INSTM, Via Vienna 2, 07100 Sassari, Italy
* Corresponding author. E-mail: firstname.lastname@example.org
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.
Mathematics Subject Classification: 37G35 / 35B36 / 35Q35
Key words: chemical chaos / spatial–temporal chaos / reaction–diffusion–convection system / Belousov–Zhabotinsky reaction
© EDP Sciences, 2010
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