Role of the Reactor Geometry in the Onset of Transient Chaos in an Unstirred Belousov−Zhabotinsky System

Liveri, Maria Liria Turco; Lombardo, Renato; Masia, Marco; Calvaruso, Giuseppe; Rustici, Mauro

doi:10.1021/jp027213q

Cited by 13 publications

(16 citation statements)

References 28 publications

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“…Nevertheless, this number is known to be correlated with experimental parameters such as the medium viscosity or the reactor geometry. According to such relation, our simulation results agree with previous experiments 19,20 and explain the observed behavior, i.e., that the transition to chaos is related with the onset of convection.…”

Section: ͑5͒supporting

confidence: 91%

“…They are written in a dimensionless form using the time scale defined above t 0 = 21 s and the space scale x 0 = 0.06 cm, arbitrarily imposed to be equal to the entire space domain explored, just greater than the value 0.05 cm ͑the minimal dimension for which in the real experiment chaos is observed 19 ͒. The set of dimensionless equations was formulated in the − form and in the Boussinesq approximation 25…”

Section: ͑5͒mentioning

confidence: 99%

“…This coupling is expected in particular for the BZ reaction in closed unstirred reactors 14,15 by the strict experimental dependence in the onset of chaos on ͑i͒ the percent in volume of initial reactants concentrations, 16 ͑ii͒ the system viscosity, 17 ͑iii͒ the temperature, 18 and ͑iv͒ the reactor geometry. 19 A suitable choice of starting values for these parameters results in a RTN transition to chaos when the system is far from equilibrium and the inverse RTN scenario as the reaction drifts to the ultimate state. 20 Taking into account the combination of the parameters controlling the fluid dynamics and the chemistry of the system would be useful to understand the instabilities occurring in the BZ reaction in a close unstirred reactor.…”

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confidence: 99%

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Ruelle–Takens–Newhouse scenario in reaction-diffusion-convection system

Budroni

Masia

Rustici

et al. 2008

The Journal of Chemical Physics

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Direct numerical simulations of the transition process from periodic to chaotic dynamics are presented for two variable Oregonator-diffusion model coupled with convection. Numerical solutions to the corresponding reaction-diffusion-convection system of equations show that natural convection can change in a qualitative way, the evolution of concentration distribution, as compared with convectionless conditions. The numerical experiments reveal distinct bifurcations as the Grashof number is increased. A transition to chaos similar to Ruelle- Takens The process by which a laminar viscous flow undergoes transition to turbulence is a topic of notable fluid-dynamical interest. Experiments 1 and numerical simulations 2 of closed system flows like Rayleigh-Bernard convection 3-5 have pointed out how the evolution to turbulence follows a specific route and well-definite sequence of transition on the basis of flow features. 6 In particular it was observed 7 that transitions to chaos in self-sustained oscillatory flows are consistent with the well-known Ruelle-Takens-Newhouse ͑RTN͒ scenario. 8 The onset of convection in self-sustained oscillating chemical reactions such as the BelousovZhabotinsky ͑BZ͒ reaction 9 had been extensively studied 10,11 proving an effective coupling between kinetic and hydrodynamic of the system. On the other hand, it was shown 12,13 how autocatalytic systems exhibit aperiodic and chaotic dynamics by the coupling of reaction kinetics to transport phenomena. This coupling is expected in particular for the BZ reaction in closed unstirred reactors 14,15 by the strict experimental dependence in the onset of chaos on ͑i͒ the percent in volume of initial reactants concentrations, 16 ͑ii͒ the system viscosity, 17 ͑iii͒ the temperature, 18 and ͑iv͒ the reactor geometry. 19 A suitable choice of starting values for these parameters results in a RTN transition to chaos when the system is far from equilibrium and the inverse RTN scenario as the reaction drifts to the ultimate state. 20 Taking into account the combination of the parameters controlling the fluid dynamics and the chemistry of the system would be useful to understand the instabilities occurring in the BZ reaction in a close unstirred reactor. The model used to simulate the system is a two-dimensional vertical slab which had been demonstrated to be a good approximation to the three-dimensional problem. 10 A set of reactiondiffusion-convection partial derivative equations is solved by means of numerical integration over a suitable grid. This model allows one to focus on the contribution of convection and to neglect the consumption of reactants. Chemical kinetics is formulated using the well-known two-variables Oregonator model [21][22][23] proposed for the first time by Fields-Köros-Noyes. They defined two nonlinear coupled differential equations,where c 1 and c 2 are, respectively, the nondimensional concentrations of the intermediate species HBrO 2 and Ce 4+ derived by the dimensional ones C 1 and C 2 as follows:A , B being the starting reactant...

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Section: ͑5͒supporting

confidence: 91%

Section: ͑5͒mentioning

confidence: 99%

mentioning

confidence: 99%

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Ruelle–Takens–Newhouse scenario in reaction-diffusion-convection system

Budroni

Masia

Rustici

et al. 2008

The Journal of Chemical Physics

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“…Among the model systems that have attracted the attention of researchers, the oscillating reaction of Belousov-Zhabotinsky (BZ) is one of the most extensively studied. [1][2][3][4][5][6][7] In fact, the first study was undertaken in order to mimic the Krebs cycle. In its "classic" version, the BZ reaction consists of the bromuration and oxidation of an organic substrate (the malonic acid) in strongly acidic medium, in the presence of a catalyst (one electron redox couple, usually the system Ce(IV)/Ce(III) or Ferroin/Ferriin).…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Response of a Batch BZ Oscillator to the Addition of the Anionic Surfactant Sodium Dodecyl Sulfate

2007

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The response of the Belousov-Zhabotinsy (BZ) system to the addition of increasing amounts of the anionic surfactant sodium dodecyl sulfate (SDS) was monitored at 25.0°C in stirred batch conditions. The presence of SDS in the reaction mixture influences the oscillatory parameters, i.e., induction period and oscillation period, to an extent that depends on the surfactant concentration. The experimental results have shown that the induction period increases slightly on increasing surfactant concentration and, then, a further increase in the [SDS] leads to an enhancement while the oscillation period increases monotonously on increasing SDS concentration. It has been proposed that the response of the oscillatory BZ system to the addition of SDS is due to the peculiar capability of the organized surfactant assemblies to affect the reactivity by selectively sequestering some key reacting species. Indeed, explanations of the experimental results have been given on the basis of the role played by the micellar shape, which in turn dictates the hydrophobic nature. The suggested perturbation effects have been supported by performing viscosity measurements on the aqueous SDS solutions and by the spectrophotometric estimation of the binding constant of the bromine species to the micellar aggregates. This study has indirectly corroborated the existence of two kind of micelles and unambiguously revealed that the bromine species show a different affinity toward the spherical and rod-like micelles.

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“…After experimental evidence, the interplay of the kinetics with transport phenomena has been also invoked to explain the onset of chemical chaos. This hypothesis was confirmed by the strict dependence of the transition on (i) stirring [5], (ii) viscosity [12,13], (iii) the temperature [4] and (iv) the reactor geometry [14]. We aim to fill a literature blank existing between the temporal and spatial-temporal approaches to these systems.…”

Section: Introductionmentioning

confidence: 89%

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

Budroni

Rustici

Tiezzi

2010

Math. Model. Nat. Phenom.

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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.

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Role of the Reactor Geometry in the Onset of Transient Chaos in an Unstirred Belousov−Zhabotinsky System

Cited by 13 publications

References 28 publications

Ruelle–Takens–Newhouse scenario in reaction-diffusion-convection system

Ruelle–Takens–Newhouse scenario in reaction-diffusion-convection system

Nonlinear Response of a Batch BZ Oscillator to the Addition of the Anionic Surfactant Sodium Dodecyl Sulfate

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

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