Sustained chemical waves in an annular gel reactor: a chemical pinwheel

Noszticzius, Zoltán; Horsthemke, Werner; McCormick, W. D.; Swinney, Harry L.; Tam, Wing Yim

doi:10.1038/329619a0

Cited by 216 publications

(93 citation statements)

References 18 publications

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“…Waves can be created in the central region, however, by perturbation with UV light. Pacemakers and sustained rotating waves (pinwheels [5,6]) can form spontaneously in the rim of the membrane, where the residence time is long because the plexiglas plates that support the membrane prevent the direct feed of reagent to that region. Pinwheels can be seen in the rim in figs.…”

Section: Resultsmentioning

confidence: 99%

“…One type has an imposed chemical gradient, as in the two-dimensional ring-shaped reactor of Noszticzius et al [5] and Kreisberg et al [6], and in the effectively one-dimensional Couette reactor developed in Austin [7] and Bordeaux [8]. A second type of reactor has a uniform diffusive feed orthogonal to the line or plane in which a pattern forms.…”

Section: Introductionmentioning

confidence: 99%

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Spatial patterns in a uniformly fed membrane reactor

Kshirsagar

Noszticzius

McCormick

et al. 1991

Physica D: Nonlinear Phenomena

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A novel reactor, consisting of a thin membrane with each side exposed to fluid from a well-stirred flow reservoir, has been developed for the study of sustained chemical spatial patterns. This reactor bears some similarity to another continuously fed unstirred reactor with a uniform feed, the disk-shaped reactor developed by Tam et al. [J. Chem. Phys. 88 (1988) 3395], but the present reactor differs in two important aspects: (1) The effective residence time, which is determined by the thickness of the gel, can be very short (of the order of seconds). (2) The feed is from two reservoirs rather than one; this opens up new regions of chemical composition for study. Examples are presented of patterns obtained for the Belousov-Zhabotinsky reaction in the membrane reactor.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Spatial patterns in a uniformly fed membrane reactor

Kshirsagar

Noszticzius

McCormick

et al. 1991

Physica D: Nonlinear Phenomena

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“…This has been achieved by the use of gel filled reactors (which prevents advective motion) coupled to well-stirred reactant reservoirs at the boundaries. Early experiments with gel reactors were performed by Noszticzius et al [12] and Tam et al [13] who reported results for the BZ reaction while later studies by Bagyan et al [14] and Lavrova et al [15] considered glycolytic reactions.…”

Section: Introductionmentioning

confidence: 99%

“…In the case with delay the smooth ODE Hopf bifurcation curves do intersect so the composite curves shown in Figure 6 are not smooth, unlike those in figure 5 for the no delay case. The stability formula (12) does not generalise to our system with delay and a precise estimate of the Hopf bifurcation region is not available. However for smaller values of the diffusion coefficient and the stoichiometric factor, k 2 and f 4 (which corresponds to chemically realistic values), the intermediate region of mixed stability is small and hence precise estimates of the region in which Hopf bifurcations occur, are available.…”

Section: Hopf Bifurcation Regions and Limit Cycles For The 1-d Geometrymentioning

confidence: 99%

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Non-smooth feedback control for Belousov–Zhabotinskii reaction–diffusion equations: semi-analytical solutions

2016

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The Belousov-Zhabotinskii reaction is considered in one and two-dimensional reaction-diffusion cells. Feedback control is examined where the feedback mechanism involves varying the concentrations in the boundary reservoir, in response to the concentrations in the centre of the cell. Semi-analytical solutions are developed, via the Galerkin method, which assumes a spatial structure for the solution, and is used to approximate the governing delay partial differential equations by a system of delay ordinary differential equations. The form of feedback control considered, whilst physically realistic, is non-smooth as it has discontinuous derivatives. A stability analysis of the sets of smooth delay ordinary differential equations, which make up the full non-smooth system, allows a band of Hopf bifurcation parameter space to be obtained. It is found that Hopf bifurcations for the full non-smooth system fall within this band of parameter space. In the case of feedback with no delay a precise semi-analytical estimate for the stability of the full nonsmooth system can be obtained, which corresponds well with numerical estimates. Examples of limit cycles and the transient evolution of solutions are also considered in detail. Abstract The Belousov-Zhabotinskii reaction is considered in one and two-dimensional reactiondiffusion cells. Feedback control is examined where the feedback mechanism involves varying the concentrations in the boundary reservoir, in response to the concentrations in the centre of the cell. Semi-analytical solutions are developed, via the Galerkin method, which assumes a spatial structure for the solution, and is used to approximate the governing delay partial differential equations by a system of delay ordinary differential equations. The form of feedback control considered, whilst physically realistic, is non-smooth as it has discontinuous derivatives. A stability analysis of the sets of smooth delay ordinary differential equations, which make up the full non-smooth system, allows a band of Hopf bifurcation parameter space to be obtained. It is found that Hopf bifurcations for the full non-smooth system fall within this band of parameter space. In the case of feedback with no delay a precise semi-analytical estimate for the stability of the full non-smooth system can be obtained, which corresponds well with numerical estimates. Examples of limit cycles and the transient evolution of solutions are also considered in detail.

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Spatial Patterns and Spatiotemporal Dynamics in Chemical Systems

Wit

1999

Advances in Chemical Physics

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Sustained chemical waves in an annular gel reactor: a chemical pinwheel

Cited by 216 publications

References 18 publications

Spatial patterns in a uniformly fed membrane reactor

Spatial patterns in a uniformly fed membrane reactor

Non-smooth feedback control for Belousov–Zhabotinskii reaction–diffusion equations: semi-analytical solutions

Spatial Patterns and Spatiotemporal Dynamics in Chemical Systems

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