Propagating reaction-diffusion fronts

Florvath D and Showalter K 1995 Instabilities in propagating reaction-diffusion fronts of the iodate-arsenous acid reaction J. Chem. Rhys. 102 2471-8... 

Gray, P., Showalter, K., and Scott, S. K. (1987). Propagating reaction-diffusion fronts with cubic autocatalysis the effects of reversibility. J. Chim. Phys., 84, 1329-33. 

Saul, A. and Showalter, K. (1985). Propagating reaction-diffusion fronts. In Oscillations and traveling waves in chemical systems, (ed. R. J. Field and M. Burger), ch. 11, pp. 419-39. Wiley, New York. 

Scott S K and Showalter K 1992 Simple and complex propagating reaction-diffusion fronts J. Phys. Chem. 96 8702-11... 

We have restricted our discussion in this section to bistability in well-stirred, homogeneous systems. Multiple steady states may also occur in unstirred systems, where domains of the system in one steady state coexist with domains in the other steady state. In addition to the obvious application to nondhemical systems, chemical systems (in fact the iodate-arsenite system considered here) sometimes exhibit domains that are connected by propagating reaction-diffusion fronts. We will return to this system in our discussion of chemical waves, which will include a description of these fronts. 

Chemical Waves Propagating Reaction-Diffusion Fronts... 

Masere, J. Vasquez, D. A. Edwards, B. F. Wilder, J. W, Showalter, K. 1994. Nonaxisymmetric and Axisymmetric Convection in Propagating Reaction-Diffusion Fronts, . 7. Phys. Chem. 98, 6505-6508. 

Propagating reaction-diffusion fronts were first studied around the turn of the century as models for wave behavior in biological systems [1, 2]. However, as recently as 10 years ago they fell into the category of exotic phenomena , as only a few experimental examples were known and their mechanisms were poorly understood. Today, many autocatalytic reactions are known to support propagating fronts [3], and more complex wave behavior is of widespread interest for modeling excitable media in biological systems [4]. The theoretical treatment of reaction-diffusion fronts, while first addressed over a half-century ago [5-7] has also advanced in recent years. Many features are now well understood and, in addition, new theoretical challenges are apparent. 

Based on similar arguments as for the autocatalytic case the width of a filament of the C = 1 state flanked by sharp fronts can be obtained from the balance between the strain A and the propagation speed of the bistable reaction-diffusion front wp ss v/X. By using the expression (4.27), v = (1 — 2a) kD/2, we find for the stable filament solution... 

F utc 16 Evolution of reaction— diffusion fronts. Reaction is initiated locally by addition of a small amount of die autocatalyst (shown as the small rectangle at the origin). The time intervals between the four outermost curves are equal, and the constant propagation distances show that a constant velocity is exhibited. (Reprinted from Ref. 43 with permission of die American Chemical Society.)... 

The details of the oscillatory behavior depend sensitively on the external control parameters, that is, the selected temperature and partial pressures. Figure 7.8 represents a typical series of oscillations (FEM) when the Pt-tip with (1 0 0)-orientation is exposed at 365 K to a gas mixture of P 02) = 5 X lO mbar and P CO) = 8 x 10 mbar. The oscillation ampUtude ranges from the Oads layer (low current) to the COads layer (high cmrent) with a periodicity of 120 sec. A difference of work functions between Oads and COads of 0.4 eV is connected with a change in the electron current. For T = 478 K, for instance, the reaction/diffusion fronts propagate with a speed of 5000 A s [85]. Rates within this order of magnitude ( 3 p.m s ) have been found previously on Pt(l 1 0) surfaces at 485 K in PEEM experiments [86]. Qualitatively similar results were also found on Pt(l 0 0) [87]. 

Then remove the partition. Fig. 5.2b reaction and diffusion will occur and during some transient time a reaction diffusion front may form in an interphase region. Fig. 5.2c, and travel into the less stable state. At external constraints corresponding to equistablity the velocity of propagation of the reaction-diffusion front is zero. 

Here, lowercase x and y denote concentrations of species X and Y, and Dy are diffusivities for species X and Y, 2 is a Cartesian spatial coordinate, and the symbols f x,y) and f x,y) are shorthand for the fluxes due to chemical reactions which increase and decrease X respectively, and ty(x, y) and tY(x,y) are shorthand for the fluxes due to chemical reactions which increase and decrease Y respectively. In order to observe the propagation of a reaction diffusion front and determine the relative stability in an inhomogeneous system, we fix the rate coefficients k and concentrations of A and B such that there are three stationary states - two stable and one unstable -in the homogeneous system. We arrange initially the left half of the system (-00,0) to be in one stable stationary state (xsi,ysi) and the right half of the system (0,00) to be in the other stable stationary state (0 53,2/53)... 

Even in systems which are of more than one dimension, such as a tube, one can envision the propagation of a planar front with the properties described in the preceding sections. Such waves may be solutions to the governing reaction-diffusion or reaction-conduction equations, but if they are to be realized and observed in practice they must also be stable to the inevitable small fluctuations in local concentration and temperature. There is a long history of stability analysis for nonisothermal flame propagation [30-32], although the absence of exact analytical solutions to even the 1-D flame front equation makes these rather difficult. The same questions about the stability of isothermal reaction-diffusion fronts seem not to have been addressed until only recently [12]. 

Nettesheim S, von Oertzen A, Rotermund FI FI and ErtI G 1993 Reaction diffusion patterns in the catalytic CO-oxidation on Pt(110) front propagation and spiral waves J. Chem. Rhys. 98 9977-85... 

This reaction can oscillate in a well-mixed system. In a quiescent system, diffusion-limited spatial patterns can develop, but these violate the assumption of perfect mixing that is made in this chapter. A well-known chemical oscillator that also develops complex spatial patterns is the Belousov-Zhabotinsky or BZ reaction. Flame fronts and detonations are other batch reactions that violate the assumption of perfect mixing. Their analysis requires treatment of mass or thermal diffusion or the propagation of shock waves. Such reactions are briefly touched upon in Chapter 11 but, by and large, are beyond the scope of this book. 

For the catalytic oxidation of malonic acid by bromate (the Belousov-Zhabotinskii reaction), fimdamental studies on the interplay of flow and reaction were made. By means of capillary-flow investigations, spatio-temporal concentration patterns were monitored which stem from the interaction of a specific complex reaction and transport of reaction species by molecular diffusion [68]. One prominent class of these patterns is propagating reaction fronts. By external electrical stimulus, electromigration of ionic species can be investigated. 

M. Cencini, C. Lopez, and D. Vergni. Reaction-diffusion systems front propagation and spatial structures. In A. Vulpiani and R. Livi, editors, The Kolmogorov Legacy in Physics. Springer-Verlag, 2003a. 

M. Paoletti and T. Solomon. Experimental studies of front propagation and mode-locking in an advection-reaction-diffusion system. Europhys. Lett., 69 819, 2005a. 

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