Diffusion-controlled instabilities and stationary structures in a model for a ferroin-catalyzed Belousov-Zhabotinskii reaction

A model for the bromate-ferroin-bromomalonic acid reaction has been used to examine the conditions under which the homogeneous state loses stability as a result of Turing bifurcation. Stationary periodic structures with small or large amplitudes can exist. There is also a structure modification effect.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 24, No. 4, pp. 440–449, July–August, 1988.I am indebted to A. M. Zhabotinskii and Yu. A. Kuznetsov for useful discussions, and also to I. I. Goryanin for providing access to his software suite for defining a curve in n-dimensional space.     

Bifurcation of irregular oscillatory regimes in the Belousov-Zhabotinskii reaction in a closed reactor

We describe the bifurcation diagram for irregular oscillatory regimes in the Belousov-Zhabotinskii reaction in a closed reactor upon variation of the initial concentrations of ferroin and potassium bromate. We formulate rules for transition from one regime to another.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol, 28, No. 5–6, pp. 474–478, September–December, 1993.     

Effect of temperature on bifurcation of self-oscillating modes in the Belousov-Zhabotinskii reaction in a continuous-flow stirred-tank reactor

The effect of the temperature on self-oscillating modes in the Belousov-Zhabotinskii reaction in a continuous-flow stirred-tank reactor (CSTR) at T=288–333 K was investigated. It was found that changing the temperature leads to a cascade of different bifurcations: the steady state changes into sinusoidal oscillations, then chaotic and complex periodic oscillations appear in the system and turn into regular oscillations with a further increase in the temperature. The regular oscillations disappear at T=329 K as a result of a degenerate supercritical Hopf bifurcation.Translated from Teoreticheskaya i Eksperimental'naya Khimiya, Vol. 31, No. 2, pp. 69–75, March–April, 1995.     

Period-doubling and chaotic oscillations the ferroin-catalyzed Belousov-Zhabotinsky reaction in a CSTR

The ferroin-catalyzed Belousov-Zhabotinsky (BZ) reaction, the oxidation of malonic acid by acidic bromate, is the most commonly investigated chemical system for understanding spatial pattern formation. Various oscillatory behaviors were found from such as mixed-mode and simple period-doubling oscillations and chaos on both Pt electrode and Br-ISE at high flow rates to mixed-mode oscillations on Br-ISE only at Iow flow rates. The complex dynamic behaviors were qualitatively reproduced with a two-cycle coupling model proposed initially by Gy(o)rgyi and Field. This investigation offered a proper medium for studying pattern formation under complex temporal dynamics. In addition, it also shows that complex oscillations and chaos in the BZ reaction can be extended to other bromate-driven nonlinear reaction systems with different metal catalysts.     

Period-doubling and chaotic oscillations in the ferroin-catalyzed Belousov-Zhabotinsky reaction in a CSTR

The ferroin-catalyzed Belousov-Zhabotinsky(BZ) reaction,the oxidation of malonic acid by acidic bromate,is the most commonly investigated chemical system for understanding spatial pattern forma-tion. Various oscillatory behaviors were found from such as mixed-mode and simple period-doubling oscillations and chaos on both Pt electrode and Br-ISE at high flow rates to mixed-mode oscillations on Br-ISE only at low flow rates. The complex dynamic behaviors were qualitatively reproduced with a two-cycle coupling model proposed initially by Gy?rgyi and Field. This investigation offered a proper medium for studying pattern formation under complex temporal dynamics. In addition,it also shows that complex oscillations and chaos in the BZ reaction can be extended to other bromate-driven nonlinear reaction systems with different metal catalysts.     

Coexistence of two bifurcation regimes in a closed ferroin-catalyzed Belousov-Zhabotinsky reaction

The ferroin-catalyzed Belousov-Zhabotinsky (BZ) reaction was studied in a batch reactor under anaerobic conditions and was found to evolve through two separated regimes of complex oscillations. Significantly, the two bifurcation regimes exhibited qualitatively different dependence on compositions of the reaction mixture, i.e., initial concentrations of bromate, sulfuric acid, malonic acid, and ferroin. The reaction temperature also showed opposite effects on the two bifurcation regimes, in which complexities of the first bifurcation regime were enhanced while oscillations in the second bifurcation regime became simpler as a result of decreasing temperature. Numerical simulations with a 12-variable model developed specifically for the ferroin-BZ system were able to reproduce transient complex oscillations observed in experiments. These calculations further illustrated that reactions such as ferroin and HOBr, ferroin and HBrO2, and ferriin and Br- were not essential in describing complex dynamics of the ferroin-BZ reaction.     

Oscillations and waves in the Belousov-Zhabotinskii reaction in a finite medium

Travelling reaction-diffusion waves are considered in a finite medium. The model considered is a simplified model of the Belousov-Zhabotinskii reaction, described mathematically by the two-variable Oregonator. A one-dimensional problem consisting of three regions is considered. Regions I (x 0) and III (x 1) act as reservoirs with fixed concentrations of the reactant X (the autocatalyst, hypobromous acid (HBrO₂)), where the concentration of X in regions I and III may be different. Region II represents a catalyst-loaded membrane, within which species X can diffuse while species Z (the oxidized form of the metal-ion catalyst (Ce(IV))) is fixed spatially. The large time behaviour of the system is considered and both stable steady states and periodic spatio-temporal structures are seen.     

Limit cycle behaviour in the Belousov-Zhabotinskii oscillatory reaction

Oscillations in the bromate-Mn(II)-organic substrate system are studied by following the concentrations of Mn(III) and Br₂ spectrophotometrically, apart from monitoring the concentration of Br^- by potentiometry. Limit cycles for the Mn(III)-Br₂ combination are constructed experimentally and theoretically. The experimental results agree with the theoretical expectations based on a suggested mechanism.     

Deuteration effect in auto-oscillation chemiluminescence of the Belousov-Zhabotinskii reaction

It has been established that substitution of H₂O by D₂O in the auto-oscillation system of malonic acid+bromate+catalyst (Ce^{3+ 4+}, Ru(bipy) ₃ ^{2+, 3+} ) not only changes the parameters of oscillations recorded according to the chemiluminescence intensity, but can also lead to their complete disappearance. The step that is responsible for the D₂O effect on chemiluminescent oscillation reactions is the deuteration of the methylene group of malonic acid.

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, H₂O D₂O — — (Ce^3+,4+, Mn^2+,3+, Ru(bipy) ₃ ^2+,3+ ) , , . , D₂O , .

     

Chemiluminescence and free-radical stages of the Belousov-Zhabotinskii reaction

The profound effect of stirring on chemiluminescence of the system: bromate-malonic acid-ruthenium complexes with low (10^–5 M) catalyst concentrations indicates the significant contribution of organic radicals R^. to the oscillation mechanism. Critical radical concentration for this oscillation is [R^.]_C<7×10^–10 M.

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: - - (10^–5 M) . R^. : [R^.]_C<7×10^–10M.

     

effect of initial reagent concentrations on the oscillatory behavior of the BZ reaction in a batch reactor

A detailed investigation on resorcinol as the Belousov–Zhabotinsky (BZ) oscillator in manganese(II) ion catalyzed reaction system with inorganic bromate (oxidant) and acetone (cosubstrate) was carried out in aqueous sulfuric acid medium (1.3 M). The aforesaid reagents were mixed with various concentrations to evolve the effective concentrations at which the reaction system exhibited better oscillations. The various oscillatory parameters such as time period (t_p), induction period (t_in), frequency (v), amplitude (A), and number of oscillations (n) were derived, and the dependence of concentration of the reacting species on these oscillatory parameters was interpreted on the basis of the Field–Koros–Noyes mechanism. © 2009 Wiley Periodicals, Inc. Int J Chem Kinet 41: 650–657, 2009     

Experimental study of the bifurcation diagram in the Belousov-Zhabotinskii reaction

In the citric acid-Mn²⁺–H₂SO₄–KBrO₃ system a hysteresis phenomenon in the switching on and off of the oscillations has been observed. The possible bifurcation diagrams of the system are discussed.

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-Mn⁺²–H₂SO₄–KBrO₃ . .

     

Effect of metal ions forming bromide complexes on the Belousov-Zhabotinskii reaction

Metal ions forming stable complexes with bromide ions greatly influence both the amplitude and frequency of the Belousov-Zhabotinskii reaction. In case of thallium(I), redox reactions involving the metal ion should also be considered beside complex formation.

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, , , -. (I), , .

     

Preliminary biomass characterization in a sequencing batch biofilm reactor

The paper reports the results of an investigation aimed to evaluate the influence of hydrodynamic conditions on physical and biochemical characteristics of granular sludge obtained in a SBBR system. Biomass density resulted very high, i.e. 70-125 gTSS/L(biomass), and this permitted to achieve a biomass concentration such high as 17-45 gTSS/L(bed). An appropriate equation proved that the pressure loss, an easily measurable parameter, can be used for biomass porosity measurement and indirect assessment of biomass concentration in the biofilter. As for biomass biochemical characterisation, the EPS (Extracellular Polymeric Substances) content was rather low (5-7% of the total organic matter) and mostly made up of proteins whereas the cellular protein content, a parameter frequently used as an indicator of microorganisms activity, was high (30-60% of total organic matter).     

Temperature dependence of quantitative characteristics of chaotic regime in Belousov-Zhabotinskii reaction

In a Ferroin-catalyzed oscillatory Belousov-Zhabotinskii reaction, the temperature dependences of the largest Lyapunov exponent (LLE) and the induction period for a chaotic regime to appear are linear in the 285–308 interval when plotted on Arrhenius coordinates. For the LLE, the activation energies calculated for different concentrations of the catalyst are in the 82–126 kJ/mole interval, and for the induction period in the 61–95 kJ/mole interval. On the basis of the experimental data, it has been concluded that this autooscillatory chemical system, within a narrow range of catalyst concentrations, is relatively insensitive to random, small, external perturbations.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 29, No. 2, pp. 186–190, March–April, 1993.The authors wish to thank K. B. Yatsimirskii, Academician of the Academy of Sciences of Ukraine, for discussing the data obtain in this work.