Chemical wave propagation

The previous chapters have discussed the behaviour of non-linear chemical systems in the two most familiar experimental contexts the well-stirred closed vessel and the well-stirred continuous-flow reactor. Now we turn to a number of other situations. First we introduce the plug-flow reactor, which has strong analogies with the classic closed vessel and which will also lead on to our investigation of chemical wave propagation in chapter 11. Then we relax the stirring condition. This allows diffusive processes to become important and to interact with the chemistry. In this chapter, we examine one form of the reaction-diffusion cell, whose behaviour can be readily understood by comparison with the responses observed in the CSTR. 

Coupling between surface diffusion and reaction. If this mode is dominating [such as with the CO oxidation on Pt(100)], chemical waves propagating across the surface will give rise to spatiotemporal pattern formation. 

Figure 4.23 Schematic of the phenomenon of the isothermal "chemical" wave propagation. The profiles exhibit the concentrations of catalytic intermediates in the successive moments of time tt < T2 < T3.

Fin. 10.1.2 Displace mem-irr.vH.v-ti me plots of chemical waves. l,efl schematic illustration of the coiistructioii by slacking ID projcction.s. Right chemical waves propagating down wards in the sample tube. The vertical coordinate is the lield of view with a range of 70 mm, the horizontal coordinate is time (2S6 s). The velocity i of the waves is about 2.7 0.2 mm/inin. Adapted from [T7.a2 with permission from Flsevier Science. 

L. Kuhnert, L. Pohlman and H.-J. Krug, Chemical wave propagation with a chemically induced hydrodynamical instability , Physica, D29, 416 (1988). 

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. 

A common example is the Belousov - Zhabotinsky reaction [24], Beautiful patterns of chemical wave propagation can be created in a chemical reaction - diffusion system with a spatiotemporal feedback. The wave behavior can be controlled by feedback-regulated excitability gradients that guide propagation in the specified directions [25, 26]. 

Chemical Waves Propagating Reaction-Diffusion Fronts... 

Fgure 4 shows the rectangular piece of the gel (ca. 1mm x 1mm x 20mm) which was immersed in the aqueous solution containing the three reactants of the BZ reaction. The chemical waves propagate in the gel at a constant speed in the... 

Logic gates based on chemical wave propagation in geometrically constrained excitable media have been investigated in a Belousor-Zhabatbuskit membrane system [58]. 

Mass spectrometry has been implemented as an on-line detection tool to monitor the transmission of chemical signals due to natural processes such as diffusion and convection as well as a bienzymatic autocatalytic process [6]. Using a mass spectrometer as the detector, it was found that an enzyme-accelerated chemical wave propagates faster than a chemical wave propelled by other processes. The two enzymes involved in the process (pyruvate... 

Figure 13.5 Spatiotemporal effects of a bioautocatalytic chemical wave revealed by time-resolved mass spectrometry, (a) Investigation of a chemical wave due to "passive" transduction and a bienzymatic amplification system. (A) Experimental setup incorporating a horizontal drift cell and mass spectrometer. (B) Schematic representation of chemical wave propagation in the drift cell due to the passive and the enzyme-accelerated transduction. (b) Transduction of labeled and unlabeled ATP along the drift cell. Concentration of the C. g-ATP trigger 0 M (A) and 5 x 10 M (B). Exponential smoothing with a time constant of 4.1 s has been applied, and followed by normalization (scaling to the maximal value). The dashed line denotes the time lapse between half-maxima of the normalized curves (0.5 level) corresponding to the passive and accelerated chemical transduction 93 and 740 s in the case of the 10 and 5 x 10 iW trigger solutions, respectively [6], Adapted from Ting, H., Urban, P.L (2014) Spatiotemporal Effects of a Bioautocatalytic Chemical Wave revealed by Time-resolved Mass Spectrometry. RSCAdv. 4 2103-2108 with permission from the Royal Society of Chemistry...

Control of Chemical Wave Propagation in Self-Oscillating Cel Array... 

Tateyama, S., Shibuta, Y., and Yoshida, R. (2008) Direction control of chemical wave propagation in self-oscillating... 

Layers are specific systems with one dimension being much shorter than two others. In our case the wavelength is a principal space scale. Here we consider layers in which the thickness is less than the wavelength, while two other dimensions are much larger. Zhabotinsky et al. [51] and Winston et al. [52] have recently reported interaction of chemical waves propagating in two sublayers separated by a poorly excitable sublayer. 

We begin this chapter with a discussion of the automaton and present the details of the model construction in Section 2. A number of different systems has been studied using this method in order to investigate fluctuation effects on chemical wave propagation and domain growth in bistable chemical systems [6], excitable media and Turing pattern formation [3,4,7], surface catalytic oxidation processes [8], as well as oscillations and chaos [9]. Our discussions will be confined to the Willamowski-Rossler [10] reaction which displays chemical oscillations and chaos as well as a variety of spatiotemporal patterns. This reaction scheme is sufficiently rich to illustrate many of the internal noise effects we wish to present the references quoted above can be consulted for additional examples. Section 3 applies the general considerations of Section 2 to the Willamowski-Rossler reaction. Sections 4 and 5 describe a variety of aspects of the effects of fluctuations on pattern formation and reaction processes. Section 6 contains the conclusions of the study. 

If chemical wave propagation is studied in the vicinity of chaos one has the possibility that internal noise can lead to perturbations of the dynamics that cause the system to behave as if it were in nearby period-doubled or even chaotic regions. Such local fluctuations can then give rise to new wave patterns that are not observed in deterministic systems. These effects are the spatial analogs of the noisy bifurcation shifts seen in systems described by ODEs or maps [23, 24]. 

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