Oscillation chemical waves

Epstein I R and Pojnian J A 1998 An Introduction to Nonlinear Chemical Dynamics Oscillations, Waves, Patterns and Chaos (Oxford Oxford University Press)... 

A typical chemical system is the oxidative decarboxylation of malonic acid catalyzed by cerium ions and bromine, the so-called Zhabotinsky reaction this reaction in a given domain leads to the evolution of sustained oscillations and chemical waves. Furthermore, these states have been observed in a number of enzyme systems. The simplest case is the reaction catalyzed by the enzyme peroxidase. The reaction kinetics display either steady states, bistability, or oscillations. A more complex system is the ubiquitous process of glycolysis catalyzed by a sequence of coordinated enzyme reactions. In a given domain the process readily exhibits continuous oscillations of chemical concentrations and fluxes, which can be recorded by spectroscopic and electrometric techniques. The source of the periodicity is the enzyme phosphofructokinase, which catalyzes the phosphorylation of fructose-6-phosphate by ATP, resulting in the formation of fructose-1,6 biphosphate and ADP. The overall activity of the octameric enzyme is described by an allosteric model with fructose-6-phosphate, ATP, and AMP as controlling ligands. 

Fig. 19. 2-D MR image of an oscillating chemical reaction occurring within a bed of diameter 15 mm packed with 1-mm-diameter glass beads. In-plane resolution was 195 pm x 195 pm, and the image slice thickness was 1 mm. A single image was acquired in 1 s. Chemical waves are imaged as a result of the...

Winfree, A. T. (1985). Organizing centers for chemical waves in two and three dimensions. In Oscillations and traveling waves in chemical systems, (ed. R. J. Field and M. Burger), ch. 12, pp. 441-71. Wiley, New York. 

I. R. Epstein and J. A. Pojman, An Introduction to Nonlinear Chemical Dynamics Oscillations, Waves, Patterns, and Chaos (New York Oxford University Press, 1998) I. R. Epstein, K. Kustin, P. De Kepper, and M. Orban, Scientific American, March 1983, p. 112 and H. Degn, Oscillating Chemical Reactions in Homogeneous Phase, J. Chem. Ed. 1972,49. 302. 

These models consider the mechanisms of formation of oscillations a mechanism involving the phase transition of planes Pt(100) (hex) (lxl) and a mechanism with the formation of surface oxides Pd(l 10). The models demonstrate the oscillations of the rate of C02 formation and the concentrations of adsorbed reactants. These oscillations are accompanied by various wave processes on the lattice that models single crystalline surfaces. The effects of the size of the model lattice and the intensity of COads diffusion on the synchronization and the form of oscillations and surface waves are studied. It was shown that it is possible to obtain a wide spectrum of chemical waves (cellular and turbulent structures and spiral and ellipsoid waves) using the lattice models developed [283], Also, the influence of the internal parameters on the shapes of surface concentration waves obtained in simulations under the limited surface diffusion intensity conditions has been studied [284], The hysteresis in oscillatory behavior has been found under step-by-step variation of oxygen partial pressure. Two different oscillatory regimes could exist at one and the same parameters of the reaction. The parameters of oscillations (amplitude, period, and the... 

Epstein IR, Pojman JA (1998) An introduction to nonlinear chemical dynamics. Oscillations, waves, patterns, and chaos. Oxford University Press, New York... 

Example 4.8 Chemical reactions and reacting flows The extension of the theory of linear nonequilibrium thermodynamics to nonlinear systems can describe systems far from equilibrium, such as open chemical reactions. Some chemical reactions may include multiple stationary states, periodic and nonperiodic oscillations, chemical waves, and spatial patterns. The determination of entropy of stationary states in a continuously stirred tank reactor may provide insight into the thermodynamics of open nonlinear systems and the optimum operating conditions of multiphase combustion. These conditions may be achieved by minimizing entropy production and the lost available work, which may lead to the maximum net energy output per unit mass of the flow at the reactor exit. 

Oscillating Heterogeneous Catalytic Reactions and Chemical Waves on the Catalyst Surface... 

With many catalysts capable of initiating the rate oscillations in the reac tions they catalyze, the phenomenon of the so called moving chemical waves—the ordered motion of fronts of the surface fragments covered by various adsorbate molecules—is observed (Figure 4.23). The spatially... 

Figure 4.26 Motion of isothermal chemical waves at the oscillation mode of the CO oxidation over the top of a platinum needle. The pattern with the atomic resolution is made by field-ion microscopy (FIM), and the photo frames are acquired in the successive several-second intervals [10]. (Courtesy of V. V. Gorodetsky)...

The spacing between bands of color in a chemical wave from an oscillating reaction is measured to be 1.2 cm, and a new wave appears every 42 s. Calculate the speed of propagation of the chemical waves. 

The Belousov-Zhabotinskii (BZ) reaction has been selected as an example illustrating diverse dynamical states observable in chemical systems. The BZ reagent is very convenient both for experimental and theoretical investigations, since the BZ reaction has many dynamical states of interest, which will be described below. In the BZ reaction one may observe the steady state, the time periodic state (concentration oscillations), the spatially periodic state, the stationary state (dissipative structures), the time and spatially periodic state (propagating chemical waves) and turbulent states (chaotic oscillations, stochastic spatial structures, stochastic chemical waves). 

Chemical sensors have been reported that are based on quartz micro balances or surface acoustic wave oscillators coated with the trimethylsilyl ethers of and 6 " and that are claimed to detect various solvent vapors in ppm amounts. ... 

Kapral R and Wu X-G Internal noise, oscillations, chaos and chemical waves Chemical Waves and Patterns eds R Kapral and K Showalter (Dordrecht Kluwer) ch 18, pp 609-34... 

The Belousov-Zhabotinsky reaction provides an interesting possibility to observe spatial oscillations and chemical wave propagation. If a little less acid and a little more bromide are used in the preparation of the reaction mixture, it is then a stable solution with a red color. After introducing a small fluctuation in the system, blue rings propagate, or even more complex behavior is observed. 

Basin of attraction, see Attraction basin Bell-shaped dependence, of Ca release on Ca, 358,359,379,499 Belousov-Zhabotinsky reaction chaos, 12,283,511 chemical waves, 169,513 excitability, 102,213 oscillations, 1,508 temporal and spatiotemporal organization, 7,169 Bifurcation... 

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