Structure and variability of spinning reaction waves in three-dimensional excitable media

Ivleva, T. P.; Мержанов, А. Г.

doi:10.1103/physreve.64.036218

Cited by 35 publications

(20 citation statements)

References 11 publications

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“…38 Finally, we note that the obtained rotating, as well as axially-''frozen,'' patterns were found to emerge in two-variable bistable systems that exhibit ideal fronts in a 1D case, if the ratio of the diffusivities of the inhibitor to the activator exceeds certain critical values. This is contrary to the rotating and nonrotating oscillating patterns in the case of oscillatory kinetics which can emerge 37,38 with Pe C ) Pe T , as well as the contrary to spinning mode of gasless combustion (self-propagating high-temperature synthesis), 39,40 which was revealed for a completely nondiffusive inhibitor under kinetic and thermodynamic conditions corresponding to unstable 1D front propagation. 41 …”

Section: Discussioncontrasting

confidence: 52%

Transversal thermal patterns in packed‐bed reactors with simple kinetics: Bifurcation criterion and simulations

Nekhamkina

Sheintuch

2011

AIChE Journal

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We derive a new criterion for transversal instability of planar fronts based on the bifurcation condition dV f /dK| K¼0 ¼ 0, where V f and K are the front velocity and its curvature, respectively. This refines our previously obtained condition, which was formulated as a ¼ (DT ad Pe T )/(DT m Pe C ) [ 1 to a [ 1 þ |d|, where DT ad and DT m are the adiabatic and maximal temperature rise, respectively, Pe C and Pe T are the axial mass and the heat Pe numbers, respectively, and d is a small parameter. The criterion is based on approximate relations for DT m and V f , which account for the local curvature of a propagating front in a packed bed reactor with a first-order activated kinetics. The obtained relations are verified by linear stability analysis of planar fronts. Simulations of a simplified 2D model in the form of a thin cylindrical shell are in good agreement with the critical parameters predicted by dispersion relations. Three types of patterns were detected in simulations: ''frozen'' multiwave patterns, spinning waves, and complex rotating-oscillating patterns. We map bifurcation diagrams showing domains of different modes using the shell radius as the bifurcation parameter. The possible translation of the 2D cylindrical shell model results to the 3D case is discussed. V V C 2010 American Institute of Chemical Engineers AIChE J, 57: 735-748, 2011 Keywords: reactor analysis, simulation, process, fronts, bifurcations, transversal patterns IntroductionHeterogeneous catalysts are extensively used in the chemical and petrochemical industry and for pollution abatement purposes. It is usually assumed that the temperature and concentrations of the reactants at any transversal cross section of an adiabatic packed-bed reactor are uniform. However, various industrial and laboratory experimental observations revealed formation of nonuniform temperature in the reactor cross section. Such patterns may pose severe safety hazards by altering the wall strength and inducing cracks. Ignoring such patterns in design and simulations may lead to erroneous results. Understanding which kinetics may lead to spatiotemporal pattern formation is essential for the development of design and control strategies that circumvent them.Symmetry-breaking leading to either spatial and/or spatiotemporal pattern formation has been observed in many biological, physiological, chemical, and electro-chemical systems [1][2][3][4][5][6][7][8] governed by the interaction of diffusion and reaction processes. Majority of the studies of pattern formation in chemically reacting systems are of homogeneous systems. Pattern formation in heterogeneous catalytic and electrochemical systems, like wires, pellets, and packed bed reactors has been known for 20 years. Recent reviews of the and Krischer. 12 The current knowledge and understanding about the formation of transversal temperature patterns has been reviewed by Viswanathan et al. 13The obtained results are kinetics-dependent 14 and in the present study we focus on kinetics that admits multiple steady sta...

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Section: Discussioncontrasting

confidence: 52%

Transversal thermal patterns in packed‐bed reactors with simple kinetics: Bifurcation criterion and simulations

Nekhamkina

Sheintuch

2011

AIChE Journal

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“…With a further increase in Λ, the velocities of the combustion waves increase for all values of R 1 (curves [4][5][6]. It is of interest that the curves for Λ = 0.004 and 10 almost coincide for R 1 < 24.…”

Section: Resultsmentioning

confidence: 97%

“…3b, however, that the front near the rod stays behind the front on the specimen surface if the line with η = 0.9 is considered as the front, while the outer part of the front moves ahead of the inner part of the front if the line with η = 0.2 is used. In both cases, the front near the rod has the form of a cone directed by its narrow side toward the products in the first case [6] and toward the original reagents in the second case. The structure described in [12] could not be obtained.…”

Section: Resultsmentioning

confidence: 99%

“…Threedimensional unsteady modes were first obtained in experiments with filtration combustion [10] and later with "gasless" combustion [3,4]. The results of numerical studies of three-dimensional unsteady modes of combustion of a solid cylindrical specimen can be found in [5][6][7][8].…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…Numerous interesting effects were observed in studying simple models of the medium where the kinetics is characterized by the simplest first-order reaction and heat transfer is characterized by one value of thermal diffusivity. In addition to steady-state combustion waves propagating with a constant velocity, the effects observed were front autooscillations [2], spinning waves [3][4][5][6], and chaotic flame propagation [7,8]. Solid-state combustion in thermally and chemically heterogeneous systems involves new effects that would be of interest to study.…”

Section: Introductionmentioning

confidence: 99%

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Modeling of solid-state combustion in thermally and chemically heterogeneous media

Ivleva

Мержанов

2007

Combust Explos Shock Waves

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A thermally and chemically heterogeneous medium is modeled by a set of cylinders pressed from a mixture of solid reagents with coaxially aligned cylindrical rods made from an inert material. The change in velocity of combustion waves propagating over one cylinder is studied by numerical methods under the assumption that there is no heat release from the cylinder surface. The mean velocity of the combustion front in the specimen is shown first to decrease and then to increase with increasing thermal conductivity of the inert rod. Spinning waves are obtained in the range of low velocities of the combustion front. The laws of variations of the maximum temperature in the combustion front are determined. It is shown that the inert rod may serve as a heat sink from the hot charge mixture, may be manifested as dilution by an inert component, enhance heat recuperation, and increase the combustion-wave velocity. Introduction of the inert rod may either destabilize combustion-wave propagation in the region of a stable plane front or stabilize the combustion wave in the range of parameters where the plane front is unstable.

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An Adaptor Domain‐Mediated Autocatalytic Interfacial Kinase Reaction

Liao

Mrksich

2009

Chemistry A European J

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This paper describes a model system for studying the autocatalytic phosphorylation of an immobilized substrate by a kinase enzyme. This work uses self-assembled monolayers (SAMs) of alkanethiolates on gold to present the peptide substrate on a planar surface. Treatment of the monolayer with Abl kinase results in phosphorylation of the substrate. The phosphorylated peptide then serves as a ligand for the SH2 adaptor domain of the kinase and thereby directs the kinase activity to nearby peptide substrates. This directed reaction is intramolecular and proceeds with a faster rate than does the initial, intermolecular reaction, making this an autocatalytic process. The kinetic non-linearity gives rise to properties that have no counterpart in the corresponding homogeneous phase reaction: in one example, the rate for phosphorylation of a mixture of two peptides is faster than the sum of the rates for phosphorylation of each peptide when presented alone. This work highlights the use of an adaptor domain in modulating the activity of a kinase enzyme for an immobilized substrate and offers a new approach for studying biochemical reactions in spatially inhomogeneous settings.

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Structure and variability of spinning reaction waves in three-dimensional excitable media

Abstract: A mathematical simulation for a reaction wave that propagates in a cylindrical sample is performed. The propagation modes that have not yet been observed experimentally are predicted. The areas of existence for these modes have been determined.

Cited by 35 publications

References 11 publications

Transversal thermal patterns in packed‐bed reactors with simple kinetics: Bifurcation criterion and simulations

Transversal thermal patterns in packed‐bed reactors with simple kinetics: Bifurcation criterion and simulations

Modeling of solid-state combustion in thermally and chemically heterogeneous media

An Adaptor Domain‐Mediated Autocatalytic Interfacial Kinase Reaction

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