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Hydrodynamic turbulence and diffusion-controlled reactions. Simulation of the effect of stirring on the oscillating Belousov-Zhabotinsky reaction with the radicalator model
Abstract
Different stirring effects of the Belousov-Zhabotinsky (BZ) reaction observed by previous authors and also reported here can be explained and modeled semiquantitatively by a diffusion-controlled radical-radical reaction step of the Radicalator. It is shown that hydrodynamic turbulence can accelerate the rate of a diffusion-controlled reaction considerably provided that both reactants of the diffusion-controlled step in the mechanism of other (non-BZ) reactions as well. Finally, it is found that uniform ultrasonic stirring can substitute for the less uniform mechanical stirring in the BZ reaction.
... Hence, one expects that such a system should be well approximated by a set of differential equations that describe the temporal dynamics of the mean concentrations (inde-Proceedings of the ASME 2015 International Mechanical Engineering Congress and Exposition IMECE2015 November 13-19, 2015, Houston, Texas pendently of the stirring rate). However, it is well-known from experiments that significant non-uniformities in the concentration field persist even at high stirring rates, resulting in stirring effects [7,8]. Such effects cannot be captured by simple models that assume spatially uniform concentrations [1]. ...
Advection-controlled and diffusion-controlled oscillatory chemical reactions appear in various areas of life sciences, hydrogeological systems, and contaminant transport. In this conference paper, we analyze whether the existing numerical formulations and commercial packages provide physically meaningful values for concentration of the chemical species for two popular oscillatory chemical kinetic schemes. The first one corresponds to the chlorine dioxide-iodine-malonic acid reaction while the second one is a simplified version of Belousov-Zhabotinsky reaction of a non-linear chemical oscillator. The governing equations for species balance are presented based on the theory of interacting continua. This results in a set of coupled non-linear partial differential equations. Obtaining analytical solutions is not practically viable. Moreover, it is well-known in literature that if the local dynamics becomes complex, the range of possible dynamic behavior in the presence of diffusion and advection becomes practically unlimited. We resort to numerical solutions, which are obtained using two popular stabilized formulations: Streamline Upwind/Petrov Galerkin and Galerkin/Least Squares. In order to make the computational analysis tractable, an estimate on the range of system-dependent parameters is obtained based on model reduction performed on the strong-form of the governing equations. Finally, we quantify the errors in satisfying the local and global species balance for various realistic benchmark problems. Through these representative numerical examples, we shall demonstrate the need and importance of developing locally conservative non-negative numerical formulations for chaotic and oscillatory chemically reacting systems.
... Like all precipitation processes, this reaction is influenced by mixing. Mixing liquids to precipitate solid particles is a common multiphase chemical process that comprises several complex phenomena [47][48][49][50][51][52][53][54][55][56][57]. ...
Despite two decades of intensive laboratory investigations, several aspects of contaminant removal from aqueous solutions by elemental iron materials (e.g., in Fe0/H2O systems) are not really understood. One of the main reasons for this is the lack of a unified procedure for conducting batch removal experiments. This study gives a qualitative and semi-quantitative characterization of the effect of the mixing intensity on the oxidative dissolution of iron from two Fe0-materials (material A and B) in a diluted aqueous ethylenediaminetetraacetic solution (2 mM EDTA). Material A (fillings) was a scrap iron and material B (spherical) a commercial material. The Fe0/H2O/EDTA systems were shaken on a rotational shaker at shaking intensities between 0 and 250 min-1 and the time dependence evolution of the iron concentration was recorded. The systems were characterized by the initial iron dissolution rate (kEDTA). The results showed an increased rate of iron dissolution with increasing shaking intensity for both materials. The increased corrosion through shaking was also evidenced through the characterization of the effects of pre-shaking time on kEDTA from material A. Altogether, the results disprove the popular assumption that mixing batch experiments is a tool to limit or eliminate diffusion as dominant transport process of contaminant to the Fe0 surface.
... Like all precipitation processes, this reaction is influenced by mixing. Mixing liquids to precipitate solid particles is a common multiphase chemical process that comprises several complex phenomena4748495051525354555657. The reaction between Fe 3+ and OH − initially forms soluble Fe(OH) 3 , but in a supersaturated, metastable state relative to its equilibrium solubility product. ...
Despite two decades of intensive laboratory investigations, several aspects of contaminant removal from aqueous solutions by elemental iron materials (e.g., in Fe(0)/H2O systems) are not really understood. One of the main reasons for this is the lack of a unified procedure for conducting batch removal experiments. This study gives a qualitative and semi-quantitative characterization of the effect of the mixing intensity on the oxidative dissolution of iron from two Fe(0)-materials (materials A and B) in a diluted aqueous ethylenediaminetetraacetic solution (2 mM EDTA). Material A (fillings) was a scrap iron and material B (spherical) a commercial material. The Fe(0)/H2O/EDTA systems were shaken on a rotational shaker at shaking intensities between 0 and 250 min(-1) and the time dependence evolution of the iron concentration was recorded. The systems were characterized by the initial iron dissolution rate (k(EDTA)). The results showed an increased rate of iron dissolution with increasing shaking intensity for both materials. The increased corrosion through shaking was also evidenced through the characterization of the effects of pre-shaking time on k(EDTA) from material A. Altogether, the results disprove the popular assumption that mixing batch experiments is a tool to limit or eliminate diffusion as dominant transport process of contaminant to the Fe(0) surface.
A programmable chemical computer with memory that can perform pattern recognition using a reaction-diffusion reaction is demonstrated
Ruthenium-functionalized poly(N-isopropyl acrylamide)-based chemically oscillating microgels with diameters between 1 and 6 µm are synthesized by a modified precipitation polymerization approach. It is found that the initial amount of N-isopropyl acrylamide (NIPAAm) can significantly affect the final sizes of the microgels. 2.5 g of initial NIPAAm results in microgels with maximum average diameter of ≈6 ± 0.5 µm. Making use of their fluorescence due to their ruthenium contents and their larger sizes compared to microgels prepared using other traditional methods, the impact of changes in the NaBrO3 concentrations on their microscopic behavior is studied using a combination of fluorescence microscopy and dynamic light scattering techniques. When increasing the concentration of NaBrO3 in a solution, the microgels first experience a decrease in size followed by aggregation that leads to the loss of colloidal stability. Finally, the redox potential behavior and optical performance of the Belousov-Zhabotinsky reaction catalyzed by these microgels are studied by electrochemical and spectroscopic means.
A sufficient stream of nitrogen or oxygen bubbled into the oscillating Bray-Liebhafsky (BL) reaction system can suppress oscillations at ambient pressure. A significant stirring effect is observed, and it is confirmed that rapid stirring can cause the oscillatory state to be inhibited. It is shown that the rate of interphase transport of 12 can be greatly influenced by both bubbling and stirring changes. The total iodine concentration in the solution can be significantly depleted in such a way, and the value of the pseudo rate constant k(obs) = 3.2 x 10(-4) s(-1) for the It removal is determined to be crucial in our set up at 50 degrees C. This critical value of the rate constant corresponds to the mass-transfer coefficient k(tr) 1.60 x 10(-3) cm s(-1). We suggest that the rate of transport of volatile iodine from the BL solution to the gas phase may be a significant component of the overall mechanism of the BL oscillations.
The new character of non-linear chemical reaction of the AA(acetacetic ether)-BrO3-Mn2+-H2SO4 system was studied. The best reaction condition and the concentration ranges for starting oscillation of each reactant were determined. The oscillatory phase and life period shortened remarkably with rising temperature, ln(1/tp) had a good linear relationship with (1/T), viz. ln(1/tp)=-E p/RT+Ap. The apparent activation parameter of oscillatory period was obtained to be 41.94 kJ·mol-1. The effects of many factors on oscillation reaction were investigated, such as reactant initial concentration, Ag+, scorbutanin, Glucose, H2O2, C2H5OH, free radical inhibitor and temperature. In addition, there would be an induction period, even inhibition of the oscillation reaction when the acidic aqueous solution was taken to participate in the oscillation reaction after standing for 120-720 min, and this shows that the hydrolyzation of AA may have some effect on the oscillation reaction. Together with the FKN mechanism, the oscillating mechanism of the oscillating reaction in the present system was discussed briefly.
Sustained oscillations were observed in the BrO3--fructose-Mn2+-H2SO4 system. Unlike the classical BZ oscillations, the present oscillations might be considered as radical-controlled rather than bromide-controlled since no substance subjected to bromination was present. Addition of acetone induced dual-frequency oscillations comprised of both the radical-controlled and the bromide-controlled oscillations.
A novel Belousov-Zhabotinskii(BZ) type oscillating reaction was observed in a closed serine(Ser)-BrO3--Mn2+-H 2SO4 system(Ser-BZ system), which exhibited the following characteristics: (1) Although Ser is unable to be brominated, the sustained oscillations could still be observed in the above system under batch-reactor conditions even in the absence of either acetone or inert gas flow. (2) The present oscillations displayed extremely short induction period(0) and very few oscillation number(<11). (3) Cl-, acrylonitrile, or Br- could effectively inhibit the oscillations. However, in the case when enough Ag+ was added into the system to completely inhibit the oscillations in [Br-], the oscillations on the Pt-electrode could still be observed. Based on the above oscillation characteristics and the product analysis, it was concluded that the present oscillations in Ser-BZ system may be radical-controlled rather than Br--controlled. Addition of suitable amount of acetone could induce the sequential oscillations owing to the coexistence of these two types of controlling models. According to the kinetic studies on the reactions of Mn3+-Ser and BrO3--Mn2+, together with the FKN mechanism, the oscillating mechanism in the present system was discussed briefly.
We present a novel reaction-diffusion system that exhibits three-dimensional superdiffusive traveling waves without external forcing. These waves include single circular targets, spirals, and ripples as well as phase-like waves. The system is based on the interplay of the precipitation reaction of mercuric iodide in a gel medium, its polymorphic transformation to a different crystalline form, and its redissolution in excess iodide. A phase diagram is constructed as function of the initial concentrations of the reagents. The spatiotemporal evolution of these waves is thoroughly analyzed and seems to be a consequence of an anomalous dispersion relation. Pattern selection and wavelengths of propagating waves are found to depend on initial concentrations of the reactants. The breakup of the waves is also investigated. While the breakdown of ripples and spirals are shown to be a consequence of a Doppler-like instability in conjunction with anomalous dispersion, the targets undergo a boundary defect-mediated breakup.
We have studied the stirring effect on the time-delayed bifurcations of transient oscillations in the Belousov-Zhabotinsky (BZ) oscillating chemical reaction in a closed system. Experiments show that oscillations disappear through the time-delayed Hopf bifurcations, whose parameters depend on the stirring rate. The explanation of the stirring effect is based on the theories of diffusion-controlled reactions and hydrodynamic turbulence. We show that an increase of the stirring rate leads to an increase of the rate constant for the diffusion-controlled reaction. We propose a kinetic scheme that describes the effect observed in the experiments. A good agreement between the experimental data and the simulations is obtained.
Formation of precipitation patterns and wave propagation in excitable media have attracted considerable scientific interest in the context of nonlinear chemical kinetics because of a new approach to micro and nanofabrication, in addition to some biological aspects. All precipitation patterns share common morphological characteristics, namely the formed patterns are stationary and no dynamical patterns can be observed in these classical precipitation systems (e.g., Liesegang phenomenon). However, it has been recently shown that in several circumstances dynamic patterns (chemical waves) can exist in purely inorganic precipitation systems similar to the well-known and studied (excitable) waves in Belousov-Zhabotinsky reaction. In this study, we show how to fine-tune the pattern characteristics in precipitation systems, such as the wavelength and the pattern morphology by changing the concentrations of the reagents, and we demonstrate chemical waves on a moving 3D spherical precipitation layer. We show that such precipitation waves have anomalous transport property, specifically superdiffusive nature, and it can be controlled by the initial concentration of the inner electrolyte. Moreover, we present several precipitation systems in which chemical wave propagation inside a moving precipitation layer can emerge. This observation points out the generality and robustness of similar behavior in diffusion-precipitation systems.
We report novel results on self-organized three-dimensional spiral and target patterns exhibiting anomalous superdiffusive behaviour in a reaction-diffusion system with simultaneous precipitation and polymorphic transformation of mercuric iodide without external forcing. The superdiffusive dynamics of propagation of the targets/spirals and their breakup is presented.
The behaviour of a system composed of malonic acid (MA), KBrO 3 , H 2 SO 4 , and ferroin was investigated in batch experiments at various concentrations of oxygen above the chemical mixture when changing the concentration of MA. We could observe that at 10% of oxygen or more and for initial concentrations of malonic acid [MA] 0 between 0.15 M and 0.6 M the system attains an equilibrium by some of mixed mode oscillations. Such a behaviour of the system could be described by a model used lately. Additionally for [MA] 0 = 0.1 M or less at 0 – 20% of oxygen a region of sequential oscillations was discovered (observed for the first time in the system with ferroin) and a trial of understanding of the event is suggested. For rather small [MA] 0 ca. 0.025 M no mixed mode oscillations, no sequential ones but the so-called relaxation oscillations were observed.
We report a 2D reaction-diffusion system that exhibits superdiffusive propagating wave with anomalous cusp-like contours. This wave results from a leading precipitation reaction (wavefront) and a trailing redissolution (waveback) between initially separated mercuric chloride and potassium iodide to produce mercuric iodide precipitate (HgI2) in a thin sheet of a solid hydrogel (agar) medium. The propagation dynamics is accompanied by continuous polymorphic transformations between the metastable yellow crystals and the stable red crystals of HgI2. We study the dynamics of wavefront and waveback propagation that reveals interesting anomalous superdiffusive behavior without the influence of external enhancement. We find that a transition from superdiffusive to diffusive dynamics occurs as a function of outer iodide concentration. Inner mercuric concentrations lead to the transition from the anomalous cusp-like to cusp-free regular bands. While gel concentration affects the speed of propagation of the wave, it has no effect on its shape or on its superdiffusive dynamics. Microscopically, we show that the macroscopic wave propagation and polymorphic transformations are accompanied by an Ostwald ripening mechanism in which larger red HgI2 crystals are formed at the expense of smaller yellow HgI2 crystals.
The Linear-Eddy Model has been applied to simulations of stirring effects on the decay of concentration fluctuations in the chemical system A → X, 2X → P in a batch reactor. The reactor size and the size of the stirrer are the same as in experiments with the Belousov-Zhabotinskii reaction with oxalic acid in which oscillations appear when the stirring rate is between 50 and 150 rpm but are suppressed above 200 rpm. An interesting coincidence has been found between our simulations and experimental observations. The results support the idea that stirring affects especially rapid chemical reactions with reactants in low concentrations. Simulations show that the combination of concentration fluctuations, turbulent mixing and chemical kinetics may be the key to understanding this stirring effect.
The stirring effect in the BZ reaction with oxalic acid in a closed batch reactor was simulated in good agreement with experiments. Oscillations, lowering of the number of oscillations and the absence of oscillations under strong stirring were all reproduced using a simple qualitative consideration of the influence of concentration fluctuations on the rates of fast reactions.
The Belousov–Zhabotinskii reaction with oxalic acid in a closed, stirred batch reactor has been investigated in H2SO4–NaHSO4, H2SO4–SO2–4(cations Na+ or Mg2+) and H2SO4–MClO4(M+= Na+ or Li+) mixtures. While the addition of sulphate ions has little effect on the oscillating reaction, perchlorate ions can inhibit it or increase the number of oscillations.
A novel kind of oscillations was observed in the Ser-BrO3--Mn2+-H2SO4 system. Unlike other BZ oscillations, this kind of oscillations might be considered as radical-controlled rather than bromide-controlled because no substance subjected to bromination was present. The addition of acetone induced the dual-frequency oscillations, in which the radical-controlled oscillations appeared first following the bromide-controlled oscillations.
Under batch-reactor conditions, the BrO(3)(-)glucose-Mn2+-H2SO4 system exhibits several types of oscillations, depending on the concentrations of the reactants. In certain cases, dual-frequency oscillations are observed owing to a sequential appearance of different types of oscillations. Since glucose is not subject to bromination, these oscillations may be considered as being typically radical-controlled, and can be distinguished from bromide-controlled oscillations by adding acetone, which also results in dual-frequency oscillations due to the presence of both radical-controlled and bromide-controlled oscillations. Further experimental results demonstrate that the different types of oscillations observed in the absence of acetone can be possibly attributed to the Mn2+ -catalyzed reactions between bromate and glucose, or various intermediates produced from the oxidative degradation of glucose. The effects of the [BrO3-]/[glucose] ratio and [H2SO4] on the oscillatory behaviors are discussed on the basis of their effects on either the depth of oxidative degradation of glucose or the oxidizing ability of bromate.
When acrylonitrile is added to the Belousov-Zhabotinsky reaction, periodic polymerization is observed. (Pojman, J. A.; Leard, D. C.; West, W. W. J. Am. Chem. Sec. 1992, 114, 8298). The polymer's structure and the amount of bromine in the polymer sample were determined by C-13 NMR and elemental analysis, respectively. Carbon-13-labeled malonic acid indicates that polymerization of acrylonitrile is initiated by malonyl radical. The bromous radicals are believed to terminate the polymer leaving an alcohol group on the polymer end. Further analysis of the polymer sample confirms that the sample is partially brominated. Numerical simulations based on a modified FKN mechanism are found to be in good agreement with experimental findings. Simulations indicate that periodic termination of the polymer chain by bromine dioxide, not the periodic initiation by malonyl radical, is the dominant cause of the periodic polymerization. Similar results were found in the malonyl-controlled variant of the BZ reaction.
The oscillatory features of a novel type B–Z type oscillator, fructose [F]+oxalic acid [OA]+Ce4++BrO3−+H2SO4 has been investigated. The induction time is found to be usually small or negligible. Both single frequency oscillations and two oscillatory states separated by a time-pause are observed. Oscillations occur between two critical limits of [F] and [OA]. A tentative mechanism has been suggested which involves both Br− ion control and free radical control. Computer simulation correctly predicts some of the oscillatory features such as (i) time of initiation, (ii) critical limits of [OA] and (iii) stoppage of oscillations by higher [Br−], confirming the primary role of Br− control mechanism.
Under batch-reactor conditions, 7 amino acids were employed as organic substrates in Belousov–Zhabotinskii (BZ) oscillations. These amino acids displayed different types of oscillations. Aspartic acid exhibited the classical BZ oscillations owing to the formation of oxalacetic acid (an intermediate of Aspartic acid oxidation) which is easily brominated. Tyrosine exhibited the uncatalyzed BZ oscillations where the metal ion catalyst is not necessary. Cystine, alanine, glycine, and glutamic acid could give rise to sustained oscillations only in the presence of acetone as a coupled organic substrate to remove bromine via bromination, known as the mixed-substrate BZ oscillations. Serine showed oscillations even in the absence of acetone though serine is not subjected to bromination. Obviously, this is a new kind of BZ type oscillations since no bromination occurred at all. The excess bromine is possibly removed through the reduction by serine and/or its intermediates. Addition of acetone induces the dual-frequency oscillations. © 2002 Wiley Periodicals, Inc. Int J Chem Kinet 34: 405–410, 2002
The stirring-induced bifurcation at low stirring rate S0 = 23 rpm of the reaction volume has been observed for the chaotic regime in the Belousov—Zhabotinsky oscillating chemical reaction (malonic acidbromatecerium(III)sulfuric acid) in a continuously stirred tank reactor in premixing mode. This bifurcation is characterized by a stepwise growth of the macroscopic spatial concentration gradients that is shown by the use of the time dependencies of the potential difference between two platinum electrodes.
A numerical investigation of the macromixing effect on the bistable ClO−2+I− reaction based on the global fluid flow field was undertaken in this work. Results obtained in this study indicated that the mixing intensity has a significant effect on the location and transition point of the thermodynamic branch, but has nearly no effect on the flow branch.
The imperfect mixing of reactants in a continuously fed stirred tank reactor generates inhomogeneous perturbations that are responsible for stirring and mixing effects. Using a cellular mixing model and a kinetic model of the Belousov−Zhabotinsky reaction, we studied the statistical properties and dynamical consequences of the reactor inhomogeneities during limit cycle oscillations. Our key resultthe time-dependent probability distributiondepends dramatically on oscillation phase: it is sharply peaked during the slow phase and broadens during the rapid phase of oscillation, where reaction is fast compared to mixing, and inhomogeneities and fluctuations are prominent. Observables are obtained from the probability distribution by appropriate averaging. We studied the stirring dependence of fluctuations and of the average oscillation amplitude and period, as well as the variance of these oscillation attributes.
A probability cellular automaton (PCA) is suggested. With its aid, the molecular diffusion, Belousov−Zhabotinsky (BZ) chemical reaction, and turbulent stirring are simulated by the Monte Carlo method. The Oregonator model was taken as the simplest model for the BZ reaction. Lattice maps vividly demonstrate the emergence of nuclei (microheterogeneities) at the autocatalytic step of the BZ reaction. The dependence of the nucleus size on stirring rate and on the molecular diffusion coefficient D0 are shown. S-wise dependencies of the induction period Tind of the autocatalytic step on stirring rate are obtained. The dependencies of the stirring effect magnitude on (1) volume Vm of the PCA elementary cell, (2) coefficient D0, (3) the total number of cells in the PCA lattice, and (4) the rate of the BZ system approach to the critical point are studied. The results of computer simulation are in good agreement with the experimental data.
This study illustrates a new role played by stirring in a reaction system subjected to a constant inhomogeneous external forcing. The studied model system is an excitable photosensitive Belousov−Zhabotinsky (BZ) reaction, where the inhomogeneous forcing is implemented via a spatially inhomogeneous global illumination or a homogeneous local light illumination. Because illumination reduces the excitability of the BZ system via producing an additional amount of bromide, the above stirred system is expected to stay at a stationary state regardless of the mixing rate. In contrast, our numerical calculations show that under moderate stirring rates global oscillations of simple and complex modes are obtained in this otherwise nonoscillatory chemical system. The onset of oscillatory behavior is due to stirring-induced fluctuations in the bromide concentration, which is known to be capable of inducing excitations at the vicinity of a Hopf-bifurcation point. Counterintuitively, our calculations further illustrate that having a large inhomogeneity in the external forcing does not necessarily favor the occurrence of stirring-induced oscillatory behavior.
We present an overview and extend previous results on the effects of large scale oceanic transport processes on plankton population dynamics, considering different types of ecosystem models. We find that increasing stirring rate in an environment where the carrying capacity is non-uniformly distributed leads to an overall decrease of the effective carrying capacity of the system. This may lead to sharp regime shifts induced by stirring in systems with multiple steady states. In prey-predator type systems, stirring leads to resonant response of the population dynamics to fluctuations enhancing the spatial variability-patchiness-in a certain range of stirring rates. Oscillatory population models produce strongly heterogeneous patchy distribution of plankton blooms when the stirring is weak, while strong stirring may either synchronise the oscillatory dynamics, when the inhomogeneity is relatively weak, or suppress oscillations completely (oscillator death) by reducing the effective carrying capacity below the bifurcation point.
Past experiments on Turing patterns have all been conducted using the chlorite-iodide-malonic acid (CIMA) reaction with Thiodene from Prolabo as an indicator. In this work two other indicators have been examined and found to yield Turing patterns similar to those obtained with Thiodene: soluble starch and poly(vinyl alcohol) (PVA). The present work shows that Thiodene is not simply a soluble starch, as previously assumed, but is probably made by mixing about 7% starch with 93% molten urea. To determine whether the indicators might also effect the chemical kinetics, the effect of the indicators was examined in batch studies of two CIMA systems: the minimal CIMA system (chlorine dioxide-iodine-malonic acid) and the CIMA-Cl system (chlorine dioxide-iodomalonic acid-chloride). It was found that starch and poly(vinyl alcohol) affect the dynamics of the minimal CIMA oscillator but they have no effect on the CIMA-Cl system. On the other hand, in the same or even larger weight/volume concentration glucose and 2-propanol has no effect on the minimal CIMA system. These finding prove that starch and poly(vinyl alcohol) participate exclusively in triiodide complex-forming reactions: they react with an enzyme-like selectivity. Thiodene, however, has an effect on the CIMA-Cl reaction because of its urea content. 19 refs., 6 figs.
To illustrate the dynamical consequences of inhomogeneities due to incomplete mixing in a continuous stirred tank reactor (CSTR), a coupled reactor model of the autocatalator reaction is studied as a function of the degree of inhomogeneity. On the basis of results and data from the literature, a classification sceme of stirring effects in CSTR's is proposed.
Past experiments and simulations on the Belousov-Zhabotinsky (BZ) reaction clearly demonstrated the existence of chaos in stirred flow reactors at low flow rates. However, the existence of chaos at high flow rates has remained the subject of controversy. The controversy is resolved by the present experiments at high flow rates, which accurately reproduce the complex sequence of periodic, complex periodic, and chaotic states observed by Hudson and co-workers; the flow rates observed here for the different dynamical regimes agree with those of Hudson et al. within a few percent. This striking reproducibility of the complex periodic and chaotic dynamics is found to be insensitive to stirring rate, size of the reactor, purity of the reagents, temperature, and type of pumping (peristaltic or piston pumps, premixed or nonpremixed feeds). Moreover, the observed sequence is reproduced qualitatively by a four-variable model of the BZ reaction. Thus, this work provides definitive evidence for the existence of deterministic chaos in the BZ reaction at high flow rates. The authors conclude that past descriptions of aperiodic behavior at high flow rates in terms of various stochastic mechanisms including incomplete mixing or switching between adjacent periodic states, are inappropriate for the conditions of the Hudson`s experiments. 24 refs., 5 figs., 2 tabs.
In this paper, the effect of stirring and the appearance of chaotic oscillations in closed oxygen-free Belousov-Zhabotinsky systems are explained in terms of fluctuation-mediated excitations.
The effect of stirring on the autocatalytic bromate-bromide-catalyst reaction has been studied at various initial concentrations of bromate, [BrO3-](0), bromide, [Br-](0), and catalyst, [C](0), in a batch closed reactor. As catalysts, ferroin and Ce-III were used. An enhancement of the stirring rate was found to lead to a longer induction period T-ind of the autocatalytic reaction. A hypothesis has been substantiated that the magnitude of the stirring effect, expressed as T-ind(max)/T-ind(min), is determined by the rate of [Br-] approaching the critical concentration [Br-](cr) and by the amplitude of asymmetrical nonequilibrium fluctuations. When this rate decreases in response to larger [Br-](0) or smaller [BrO3-](0), as well as when the fluctuation amplitude grows in response to larger [C](0), the magnitude of T-ind(max)/T-ind(min) increases. The role of nuclei has been discussed. The stirring effect in the oscillatory Belousov-Zhabotinsky reaction and in the autocatalytic bromate-bromide-catalyst reaction was shown to have the same origin.
We built a true alternating current (a.c.) battery that periodically reverses value and sign of its electromotive force (e.m.f.). This a.c. battery is an electrochemical concentration cell that consists of two coupled half cells in which identical oscillating Belousov-Zhabotinskii (BZ) reactions take place isothermally at 28.0°. The homogeneous BZ oscillations are phase shifted in order to create a potential difference between both half cells. With an increasing load the phase shift between the two half cells decreases (i.e. both oscillations tend to synchronize), consequently the amplitude of the alternating current decreases while the amplitudes of the individual BZ-oscillators remain unaffected. The e.m.f.-current diagram of the a.c. battery is analogous to that of direct current batteries. Although the present frequency (period of ∼58 s), current (∼±2.5 μA), e.m.f. (∼±50 mV) and maximum power produced (∼10−7 W) are low it should be possible to construct a.c. batteries with improved performances by the use of other chemical oscillators.
In order to elucidate the mechanism of Ce4++BrO3−+H2SO4+fructose [F] oscillatory reaction which has no apparent bromine removal mechanism, detailed experimental studies have been undertaken to investigate (i) [Br−] at different time intervals during oscillations, (ii) effect of addition of (a) Br− during oscillations, (b) fructose and BrO3− after stoppage of oscillations and (c) tartaric acid [TA], below the lower critical limit of [F] for oscillations. A reaction mechanism has been suggested which involves active participation of free radicals and which also correctly predicts most of the observed oscillatory features.
New experimental results on the oscillatory dynamics of the radical-controlled Belousov-Zhabotinsky reaction (the Racz system) in a batch reactor are reported. The system exhibits oscillations with no induction period, a typical feature of the radical-controlled mechanism. However, in the presence of acetylacetone (CH2(COCH3)(2)), an induction period is observed before oscillations start, which increases with increasing acetylacetone concentration. There is a critical concentration of acetylacetone at which no oscillations occur. Quenching of radical-controlled oscillations is also observed at low and high malonic acid concentrations as well as at low and high sulfuric acid concentrations. An induction period is observed before the onset of radical-controlled oscillations at sulfuric acid concentrations greater than or equal to 5.5 M. The duration of radical-controlled oscillations reaches a maximum at an intermediate sulfuric acid concentration. Numerical simulations based on the Radicalator model predict limits of malonic acid and sulfuric acid concentration within which oscillations are observed. The Radicalator model with additional reactions involving (i) CH2(COCH3)(2) + Ce4+ --> (CH)-C-.(COCH3)(2), (ii) (CH)-C-.(COCH3)(2) + BrO2. --> products, and (iii) (CH)-C-.(COCH3)(2) + (CH)-C-.(COCH3)(2) --> products also predicts lengthening of induction period with the increase of acetylacetone concentration and suppression of oscillations at high acetylacetone concentration. Inclusion of the reaction between acetylacetone and HOBr had no effect.
A decrease in pressure from 101.3 to 26 kPa or less results in a dramatic change in the oscillation parameters in the batch Bray-Liebhafsky (BL) oscillatory system in an N2 or O2 atmosphere. It was confirmed that at 101.3 kPa the oscillations can be suppressed by rapid stirring. The experiments show that the rate of interphase transport of I2 is not negligible at 50°C and can be influenced by both stirring and pressure changes. It is indicated that the escape of I2 from the BL solution to the phase above it can significantly deplete the total concentration of iodine. We conclude that external pressure can be considered to be the bifurcation parameter which is associated with stability of the BL system.
Macromixing effects on the oscillating Belousov—Zhabotinsky reaction based on the global fluid field have been investigated. The three-variable irreversible Oregonator and the networks-of-zones model with 2 × N × N zones were chosen for describing the chemical kinetics and the flow field, respectively. With high stirring rate, all zones in the tank will oscillate synchronously and the tank can be taken as an ideally well-mixing continuous-flow stirred-tank reactor. When stirring rate is decreased, locally simple oscillation patterns were found to be sustained, and the oscillation period was decreased accordingly. It is proposed that the output zone acts as an excitable nucleus which determines the overall oscillations. When stirring rate is reduced further, many local zones can be excited as nuclei, and apparent complex oscillations can result.
The uncatalyzed system BrO<sub>3</sub><sup>-</sup>-phenol-H<sub>2</sub>SO<sub>4</sub> exhibits an astonishing variety of dynamic behaviour, including sequential oscillations in a closed, stirred batch reactor. The effect of initial addition of chloride and bromide ions on a sequential oscillating system has been studied. Various results were obtained, depending on the initial chloride and bromide concentrations. Increasing the concentration of chloride ions (from 5 × 10<sup>-5</sup> to 6 × 10<sup>-4</sup> mol dm<sup>-3</sup>), the parameters of sequential oscillations changed. The number of first oscillations increased from 4 to 21 and their amplitude decreased. The duration of the non-oscillatory period and the number of second oscillations decreased from 96 to 26 min and from 8 to 1, respectively. In the concentration range 3.5 mmol dm<sup>-3</sup> < [Br<sup>-</sup>]<sub>o</sub> < 8.0 mmol dm<sup>-3</sup>, the system displays a dual-frequency, dual-amplitude and aperiodic oscillations with a transition period between high- and low-frequency oscillations. The induced oscillations were also observed when the system was perturbed by chloride or bromide ions. The oxidation of pyrocatechol with bromate is an autocatalytic reaction; the rate constants corresponding to the uncatalyzed and catalyzed reactions were evaluated and used in numerical simulations.
A high-precision batch-mode technique of gasometric measurement, employing weighing of liquid displaced by the gas, is proposed and supported by a detailed protocol for correct evaluation of the experimental data acquired. Results of measuring the gas production in the Briggs-Rauscher reaction with acetone, recorded following the procedures suggested, and precautions to be taken to enhance their reproducibility are discussed, and a previously undetected structure of the gas evolution rate peaks is reported.
The effect of stirring in an inhomogeneous oscillatory medium is investigated. We show that the stirring rate can control the macroscopic behavior of the system producing collective oscillations (synchronization) or complete quenching of the oscillations (oscillator death). We interpret the homogenization rate due to mixing as a measure of global coupling and compare the phase diagrams of stirred oscillatory media and of populations of globally coupled oscillators.
Oscillations in a Belousov-Zhabotinskii (B-Z) system having oxalic acid (OA) and glucose (G) as a mixed organic substrate, neither of which acts as a bromine scavenger, have been investigated. Studies have been performed for (i) varying the concentration of G while keeping the OA concentration fixed and (ii) varying OA but keeping G fixed in a batch reactor. In both cases upper and lower critical limits occur, between which oscillations are observed. Both single and double frequency oscillations have been observed in a wide range of concentrations of G as well as of OA. The induction period in most of the cases was <1 min. When G is fixed and OA is varied, the time pause between the sequential oscillations increases with an increase in OA. On the other hand when OA is fixed and G is varied, the time-pause decreases with an increase in G. The first type of oscillation is Br(-)-controlled, whereas the second is non-Br(-)-controlled. The order of addition of G and OA in the last has no influence on the induction period. It influences, however, the oscillatory characteristics. Br(2) evolution in the G + OA + Ce(4+) + BrO(3)(-) + H(2)SO(4) reaction system has been investigated spectrophotometrically. ESR and polymerization studies indicate the important role of free radicals in influencing the reaction mechanism. A tentative dual control mechanism has been suggested involving autocatalysis of HBrO(2) and BrO2*.
We report the experimental observation that stirring in a closed 1,4-cyclohexanedione-bromate reaction can induce transitions not only between oscillatory and nonoscillatory states but also between simple and period-doubled oscillations. Notably, the transition from simple to complex oscillations occurs as a result of increasing stirring rate. When illumination was employed to characterize the importance of microfluctuations of concentrations, the threshold stirring rate for inducing a bifurcation was found to increase proportionally to the intensity of the applied light. Numerical simulations with an existing model illustrate that the experimental phenomena could be qualitatively reproduced by considering effects of mixing on diffusion-limited radical reactions, namely, the disproportion reaction of hydroquinone radicals.
Oscillations in the platinum redox potential during the reaction of bromate ions with acetonedicarboxylic acid catalyzed by Mn(II) ions were observed. The volume of gaseous carbon dioxide produced was measured. A nonoscillatory course was found both at the slow and rapid stirring rates for carbon dioxide evolution. The perturbation experiments suggest supersaturation during the Belousov-Zhabotinsky reaction with acetonedicarboxylic acid. Possible reasons for such observations are discussed.
Nonlinear evolution of a reaction--super-diffusion system near a Hopf bifurcation is studied. Fractional analogues of complex Ginzburg-Landau equation and Kuramoto-Sivashinsky equation are derived, and some of their analytical and numerical solutions are studied.
The autocatalytic reaction between chlorite and iodide ions exhibits a remarkable range of dynamical behavior. In a stirred tank reactor it shows bistability between steady states and between a steady and an oscillatory state. It forms the core of a large family of systematically designed chemical oscillators. The chlorite-iodide system has served as the prototype reaction in the discovery and investigation of mixing effects in stirred tank reactors, in studies of coupled oscillators, and in new experimental approaches to spatiotemporal bifurcation behavior. Mechanistic studies of the system have resulted in an eight-step mechanism that gives excellent agreement with nearly all the above observations.
The bistability hysteresis of the inorganic subsystem of the BZ reaction was studied in a CSTR as a function of stirring rate and mixing mode with the flow rate as the control parameter. We found that premixing (PM) of the feedstreams stabilizes the thermodynamic branch, while enhanced stirring in the nonpremixed (NPM) mode destabilizes the same branch. Furthermore, decreased stirring of the NPM system broadens the hysteresis and can, for sufficiently large changes of stirring rate, shift the loop to a domain that does not overlap that obtained at high stirring rate. These counterintuitive and surprising results demonstrate the different dynamical roles played by stirring and by the reactant premixing, and they show the importance of heterogeneous-noise-induced effects
Recent experiments have shown that the stirring rate strongly affects the bistable region exhibited by certain chemical systems in continuous stirred tank reactors. An interpretation of these results is presented in terms of the competition between turbulent mixing and the inhomogeneities generated by the feeding of the reactor.
In a closed stirred batch Belousov-Zhabotinskii system the parameters for the oscillating reaction depend on the rate of stirring even in an oxygen-free atmosphere.
The authors have found that impurities on the ppm level in malonic acid are sufficient to alter dramatically a sequence of bifurcations in the Belousov-Zhabotinskii (BZ) reaction. Samples of malonic acid from 15 vendors were tested, and each was found in contain one or more of the following impurities that affect the reaction dynamics: iron, paraformaldehyde, ethanol, methanol, ethyl ester, and methyl ester. The authors describe a straightforward procedure for purifying malonic acid. Reproducible bifurcation structures can only be observed with the highly purified malonic acid. Measurements with varying amounts of the above-mentioned impurities added to purified malonic acid show the striking effect of impurities on the dynamics of the BZ reaction.
Various chemical reagents were fed continuously into a continuously stirred tank reactor to perturb the Belousov-Zhabotinskii system. The resulting bifurcation diagrams each contain multiple curves separating regions with different types of dynamical behavior. These very complex diagrams can be used as fingerprints of the perturbing chemical mechanism. Essentially the same bifurcation structures were observed under the addition of formaldehyde and sodium bromite, indicating the same mechanism. The effect of bromomalonic and hypobromous acids was also found to be nearly identical; the slight differences between their fingerprints is explained by the effect of bromine, which contaminates the HOBr. Finally, the effect of added bromide is shown in another bifurcation diagram.
The periodic reaction between malonic acid, sulphuric acid, potassium bromate, and a catalyst is inhibited by molecular oxygen, hydrogen peroxide, and acrylonitrile, and hence has a free-radical mechanism.
Using a coalescence–dispersion model of the continuous flow-stirred tank reactor (CSTR), we study the effect of premixed vs nonpremixed reactant flows on chemical bistability. The region of bistability is smaller for segregated feed streams than for a fully premixed feed stream. The transition from flow branch to thermodynamic branch is particularly sensitive to the feed stream configuration.
A new theory of the Belousov-Zhabotinsky (BZ) reaction, the Radicalator model, is presented. This model is based on a negative feedback loop involving a fast reaction between malonyl and bromine dioxide radicals. Experimental evidence for the validity of the model is given for BZ systems in 3 M and 1 M sulfuric acid solution.
It is probable that different phenomena attributed to mechanical stirring during the Belousov-Zhabotinskii (BZ) reaction are caused by atmospheric oxygen and, as far as our experiments show, they have nothing to do with dissipative structures or with the turbulence of the reacting mixture.
We have performed experiments on the Belousov-Zhabotinskii reaction perturbed by ultraviolet light and by silver ions, and over a range of sulfuric acid concentrations, the reaction shows a large sensitivity to these perturbations. Our results support Foersterling and Noszticzius' theory of malonyl radicals as a second control intermediate. Results of perturbation by both ultraviolet light and silver ions at the same time, however, are not adequately explained by either malonyl radical control or bromide control (or both) and suggest a third control intermediate such as bromomalonyl radicals.
The potential response of silver halide membrane electrodes to the corrosive bromous, bromic, iodous, and iodic acids is investigated in sulfuric acid solutions ([H2SO4] = 0.15 and 1.5 M), typical media for several well-known oscillating reactions. The syntheses of the materials (bromide-free NaBrO2 and HIO2) needed for the experiments are described. The potentials recorded as a function of time were used for the determination or estimation of several rate constants at 24 ± 1°C: the disproportionation rate constant of HBrO2 is kB1 = (1.4 ± 0.2) × 103 M-1 s-1 (in 0.15 M H2SO4) and (3.8 ± 1.0) × 103 M-1 s-1 (in 1.5 M H2SO4); the corresponding value for HIO2 is kI1 < 5.4 M-1 s-1 (in 0.05-0.15 M H2SO4); the disproportionation of HIO2 is autocatalytic, the rate-determining step is a reaction of HIO2 with H2OI+, the rate constant of which is kI5 = 130 ± 5 M-1 s-1 (in 0.15 M H2SO4); the rate constants of the reactions of HBrO2 with Br- and H+, and HIO2 with I- and H+ are 106 < kB2 < 4 × 106 M-2 s-1 (in 1.5 M H2SO4) and 106 < kI2 < 4 × 107 M-2 s-1 (in 0.15 M H2SO4), respectively. The corrosive reactions of the halous and halic acids with halide ions are much slower than those of hypohalous acids, which fact required the development of the theory for slow corrosive reactions. Criteria for the definitions of "slow" and "fast" corrosive reactions are given. The possibility of a second autocatalytic process in the halate driven oscillating reactions is demonstrated. On the basis of these results, a generalized Lotka-Volterra scheme is proposed for the BZ, BL, and BR oscillators.
When a turbulent binary fluid mixture is quenched below its consolute point, turbulent mixing competes with an instability toward phase separation. A linear stability analysis in the viscous-convective range of concentration fluctuations shows that spinodal decomposition can be suppressed entirely by sufficiently strong stirring. An instability reappears, however, for deep quenches, when the injection rate of concentration fluctuations exceeds the rate of turbulent mixing. The growing concentration fluctuations which result appear to be confined to the viscous-convective range.
We present a stochastic model for stirred chemical reactors. In the limiting case of practical interest, i.e., fast stirring, we solve for the characteristic function in steady state and derive expressions for the stationary moments through a perturbation expansion. Moments are explicitly calculated for a generic model of bistable behavior. We find that stirring decreases the area of the bistable region essentially by changing the point of transition from the high reaction rate state to the low reaction rate state. This is in remarkable agreement with the experimental findings of Roux, et al. Our results indicate that stirring should not be considered simply as an ‘‘enhanced diffusion’’ process and that nucleation plays only a minor role in transitions between multiple steady states in a continuous flow stirred tank reactor (CSTR).
The reaction between chlorite and iodide has been studied in a CSTR at different stirring rates with and without premixing of the input reagents. Most of the experiments have been conducted under oscillatory conditions. Three steady states are found in the premixing configuration. With the state of mixing as the bifurcation parameter, phase portraits are obtained showing the disappearance of oscillations through various types of bifurcation. The mixing dependence of the system’s dynamical behavior is discussed in terms of the elementary steps in a recently proposed mechanism. The significant enrichment in the dynamical behavior observed on varying the mixing requires revision of the mechanism.
We propose an interpretation of mixing effects on temporal dissipative structures in CSTR in terms of micromixing. The bistability of the ClO−2 –I− reaction is extensively discussed. The micromixing process is successively represented by a mean field model and a coalescence redispersion model, together with a realistic kinetic scheme of the reaction. The latter was found more suited to the problem. The results are in good agreement with experimental observations previously reported, accounting for shifts in the transitions from thermodynamic branch to flow branch both in premixed and nonpremixed mode. It also accounts for dynamical behavior in the vicinity of the transition, including oscillatory fluctuations. It is finally suggested that micromixing processes could induce oscillations in otherwise nonoscillating conditions if the system was perfectly homogeneous.
The appearance of full blown oscillations at the end of the induction period in the classical BZ reaction (substrate: malonic acid) is usually explained by a subcritical Hopf bifurcation. Our perturbation experiments have revealed that the classical BZ reaction is excitable in its induction period and the threshold of excitability is decreasing gradually to zero during that period. Thus the sudden appearance of limit cycle oscillations at the end of the induction period can be explained by a saddle‐node infinite period (SNIPER) bifurcation as well.
A stiffly‐coupled Oregonator model based on the two independent variables Y and Z has been examined in detail with the use of the stoichiometric factor as a single disposable parameter. The trajectories and periods of the stable limit cycles can be generated with unanticipated accuracy from simple linear differential equations. Transitions between stable limit cycles and stable steady states takes place by means of subcritical Hopf bifurcations. Unstable limit cycles and thresholds of excitability can be recovered by integrating the equations of motion backward in time; such procedures cannot be applied so easily for models based on more than two independent variables. We have examined claims of experimental evidence for saddle‐node infinite period (SNIPER) bifurcations and have concluded that all currently available evidence is equivocal. Until unambiguous criteria can be established for identifying SNIPER bifurcations in real systems, and until chemical mechanisms have been proposed which generate such bifurcations, observations should be interpreted by existing models based on Hopf bifurcations. Experimental behaviors are listed which can and cannot be simulated in terms of two independent composition variables.
Using the theory of normal forms, we investigate the effects of mixing in a continuous flow stirred tank reactor (CSTR) for a reaction model exhibiting oscillatory behavior in the vicinity of a degenerated bifurcation point (here, a Takens–Bogdanov point). In addition we show without specification of a particular reaction system that, as long as reaction rates remain much slower than the inverse mixing time, incomplete mixing introduces a new bifurcation parameter for nonpremixed feeding conditions, whereas premixed feeding conditions merely lead to a renormalization of flow rate.
Use is made of literature data on the Hammett acidity function, the activity of water, and Raman spectral results for sulfuric acid solutions to construct a hydration model which will account quantitatively for the observed acidity in the 0-99% acid range. No activity coefficient corrections are applied. Calculations are not extended to higher concentrations because of complications due to the self-ionization of sulfuric acid. The results indicate that above 50 mole % sulfuric acid, the species H3O+, H5O2+, H7O3+, and H9O4+ can account for the observed acidity, whereas at lower concentrations of acid more highly hydrated proton hydrates coexist in the same solution. The largest hydrate postulated to exist is H21O10+. The average apparent hydration number of the proton as a function of acid concentration is predicted to pass through a maximum at about 2 M sulfuric acid. This is interpreted to result from a shift in the balance between the tendency of ions to hydrate and the tendency of water molecules to form clusters. No water clusters are believed to exist above 2 ± 1 M sulfuric acid.
A revised set of rate constants at 20°C and in 1 M H2SO4 is developed for the Field-Körös-Noyes mechanism of the 4Ce(III) + BrO3- + 5H+ ⇌ 4Ce(IV) + HOBr + 2H2O component of the oscillatory Belousov-Zhabotinskii reaction. The mechanism involves 10 species and 8 reversible reactions. Our results are based on the recognition that the reaction HBrO2 + BrO3- + H+ ⇌ 2BrO2• + H2O is strongly reversible and is in fact close to equilibrium under normal Belousov-Zhabotinskii conditions where [Ce(III)] ≪ [BrO3-]. This is not true if Fe(phen)32+ is substituted for Ce(III). We find the equilibrium constant to be about 1 × 10-6 M-1. This value leads to ΔGf°(HBrO2) ≅ -0.4 ± 1 kJ/mol and pKa(HBrO2) ≅ 4.9. The species HBrO2 is thus considerably more stable than has been assumed previously. This value of ΔGf° (HBrO2) is combined with other thermodynamic data, several recent determinations of the rate constants of individual component reactions, and data on the overall process to yield a complete set of rate constants that is thermodynamically consistent and in essential agreement with all known direct kinetic measurements. The resulting values are very close to the "Lo" values derived by Tyson except that k for HBrO2 + BrO3- + H+ → 2BrO2• + H2O is somewhat higher than proposed by him. They are able to simulate very accurately simultaneous data on [Ce(IV)] and [BrO2•] in the overall reaction of Ce(III) with bromate even when the reactant concentrations are varied over factors of several hundred. This agreement supports both the essential form of the mechanism and the derived rate constant values, which we believe to be accurate to within a factor of 2. Propagation of the revised rate constants into the Oregonator reduction of the Field-Körös-Noyes mechanism is discussed.
The rate constant of the bromide/bromous acid reaction Br- + HBrO2 + H+ → 2HOBr has been measured at various sulfuric acid concentrations by using a bromide-selective electrode. The second-order rate constant at [H2SO4] = 0.5 M and T = 24°C was found to be k2′ = 4.2 × 105 M-1 s-1. Spectrophotometric measurements led to similar results. This value is 3 orders of magnitude smaller than the one calculated by Field, Körös, and Noyes and provides further support for the recently developed "LO" set of rate constants for the Belousov-Zhabotinskii reaction scheme.
Spatially distributed concentration fluctuations are found, using micro- and macroelectrodes, to occur over a wide range of reactant concentrations in a stirred-batch-reactor study of the Belusov-Zhabotinsky reaction. The noise spectrum as well as the period of the limit cycle depend sensitively on the rate of stirring. This is explained by the hydrodynamic control of the fluctuations and by noise-induced transitions (NIT) mediated through exchange at the gas/liquid interface.
The reactions constituting the mechanism of the oscillatory Belousov-Zhabotinskii (BZ) reaction may be divided into an inorganic and an organic subset. The former is well established and generally accepted, but the latter remains under development. There has been considerable work on component reactions of the organic subset over the past few years, but little effort has been made to incorporate the results of this work into an improved BZ mechanism. We do so and present a BZ mechanism containing 80 elementary reactions and 26 variable species concentrations and which implements recent experimental results and suggestions concerning the complicated organic chemistry involved. The possible role of organic radicals as a second control intermediate is explored. The rate constants of the inorganic subset also are adjusted for acidity effects. The performance of the model in simulating either quantitatively or semiquantitatively a number of recent BZ experiments is substantially better than that of previous models. Several areas in need of further work are identified.
Concentration heterogeneities and stirring effects on the oscillations of the ferroin-catalyzed BZ reaction have been studied in a batch reactor that is open to the atmosphere. The concentration fluctuations, arising from gas exchange at the liquid-gas interface, were characterized, using microelectrodes, by measuring the spatial correlation function C(d\S) = (E(r) E(r+d)) and studying its dependence on stirring speed S. The S dependence of the correlation le1ngth L(S) varies as L(S) ≈ S-n, where n = 1.36. This agrees well with theory which predicts n = 1.2-1.5 for macroscale eddies.
Deterministic chaos is undoubtedly a part of the wide variety of phenomena exhibited by the oscillatory Belousov-Zhabotinskii (BZ) reaction in a continuous-flow stirred tank reactor (CSTR). Even though BZ-CSTR chaos is well-characterized phenomenologically, there is still no convincing explanation for its occurrence in the chemical dynamics of the BZ reaction as presently understood. Models capable of simulating all other behaviors of the BZ reaction are not able to satisfactorily reproduce the robust experimental aperiodicity. We suggest that BZ-CSTR chaos results not from the chemical dynamics of the BZ reaction itself but instead from coupling among regions of somewhat different chemical composition developing in different parts of the CSTR as a result of imperfect mixing of the feedstreams into the bulk of the reaction mixture. The particular model presented here emphasizes interaction between the bulk reaction mixture and reagents in the tips of the CSTR inlet ports. It simulates well several features of the experimental aperiodicity including wave forms, the route from periodicity to chaos, and the relatively wide flow rate range over which chaos occurs.
The stoichiometry, kinetics, and mechanism of the reaction between chlorite and thiosulfate have been studied at 25°C and pH 6-9. In excess thiosulfate, the stoichiometry is 4S2O32- + ClO2- + 2H2O = 2S4O62- + 4OH- + Cl-. In excess chlorite, sulfate is produced as well, the stoichiometry being a mixture of the above reaction and S2O3 + 2ClO2- + H2O = 2SO42- + 2Cl- + 2H+. The rate of production of OH- is d(δ[OH-])/dt = kexpt[S2O32-] [ClO2-][H+], but the rate constant kexpt varies with the [ClO2-]/[S2O32-] ratio, being about twice as large in excess S2O32- as in excess ClO2-. A mechanism is proposed involving the complex intermediates S2O3ClO- and S2O3Cl-, a key reaction between the simpler intermediates SO32- and ClO- and the "supercatalytic" chlorite-tetrathionate reaction. At pH ≈ 11 in unbuffered solution, the reaction behaves as a "clock" reaction, with an initial rise in pH followed by an abrupt drop. The reaction time, however, varies irreproducibly, even in identically prepared samples. Careful analysis of the reaction time distribution and its variation with temperature, volume reactant concentrations, and stirring rate leads to the conclusion that the switch from net OH- production to net H+ generation is induced by random fluctuations within the solution. The implications of this interpretation are discussed.
Substantial differences exist in the stirring dependence of the ClO2- + I- bistability transitions when premixed and nonpremixed reactant feedstreams are used. This demonstrates clearly the dynamical importance of residual spatial inhomogeneities. A qualitative interpretation based on a micromixing type approach is proposed.
The BZ reaction with oxalic acid substrate is one of the simplest BZ oscillator which oscillates only if the produced bromine is removed by an inert carrier gas. In the present study an electrochemical method is reported to determine kBR, the "rate constant" for bromine removal. Oscillations can be found within a certain interval of the kBR parameter values only. Outside of that range two different excitable states were discovered. Transitions from the oscillatory to the excitable states go via saddle-node infinite period bifurcations. Different types of bifurcations leading to periodic orbits, a two-dimensional phase portrait of an excitable system, and a perturbation technique to reveral that portrait are also discussed.
Continuous-flow, stirred tank reactor (CSTR) experiments with the oscillatory Belousov-Zhabotinsky (BZ) reaction provide the most important examples of chemical chaos. Experiments performed at low flow rates at the University of Texas in Austin are particularly important because of the large amount of data accumulated and the apparent low dimensionality of the attractor. Although the mechanism of the BZ reaction is largely elucidated, it has not been previously possible to simulate this aperiodicity by using realistic models of the homogeneous dynamics of the BZ system. We present here such a model based on the interaction of two frequency sources within the homogeneous flow system. One frequency is that of the Oregonator core of the model. The other originates in the dynamics of the major bromide ion precursor, bromomalonic acid (BrMA), which is a product of the overall reaction as well as a bifurcation parameter of the Oregonator core. Its concentration remains high but undergoes small-amplitude oscillations. There is a critical value of [BrMA] above which the reduced steady state of the Oregonator core becomes stable, causing [BrMA] to decrease because it is not produced in significant amounts in this state but is still washed out in a first-order manner by the flow. This negative feedback of [BrMA] on itself establishes a second frequency source within the homogeneous BZ dynamics. The interaction of the two frequencies creates the complex dynamics observed. The model, consisting of 11 dynamic variables and 19 reactions, simulates very well for the experimental conditions the observed series of major periodic states, the bifurcations of these states to chaos, and the presence of periodic-chaotic windows. Both the simulated waveforms and their next-maximum maps agree well with the measured ones. Several regions of hysteresis and very long transients also are observed in the simulations.
The sensitivity to stirring shown by the oscillatory Belousov-Zhabotinskii (BZ) reaction when carried out in batch mode has been experimentally examined. Different series of experiments were designed in order to test the influence of both the flow rate of a deaerating agent and the reactant initial concentrations on the observed stirring susceptibility. In addition, distinctive stirring effects associated with the different phases of the oscillatory reaction were analyzed. The experimental results indicate that stirring effects strongly depens on the initial concentrations of the BZ mixture and on the detailed chemical dynamics inherent in each phase of the reaction.
It is experimentally shown that a chemical nonequilibrium bistable system presents metastability and stirring rate sensitivity in full agreement with theoretical predictions of nucleation induced transitions.
The effect of stirring on the transitions between multiple steady states is analyzed in exothermic reactions giving rise to ignition and explosion, as well as in reactions occurring under isothermal conditions. It is found that, to first order, deviations from perfectly effective stirring amount to a renormalization of the value of the heat- or mass-transfer coefficients, whereas higher-order corrections introduce a coupling between stirring and the effects of chemical kinetics.