Investigation of travelling waves on catalytic wires

Barelko, V. V.; Kurochka, I.I.; Мержанов, А. Г.; Шкадинский, К. Г.

doi:10.1016/0009-2509(78)85169-0

Cited by 70 publications

(25 citation statements)

References 10 publications

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“…In other words, it is possible to view the integral equation (1.9) as a description of travelling-wave solutions of (1.1) in their phase-space. The relationship between travelling-wave solutions of equations of the type (1.1) and the ordinary differential equation (1.11) has been noted and utilized by previous authors [20][21][22][23][32][33][34][35][36][37][38]61,90,93,96,97,159,162,172,191,192,213,222,246,247,250,254,266,268,270,282], and for a related problem in [153,154,282].…”

Section: C(r)a (R) G(r) Drmentioning

confidence: 99%

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Travelling Waves in Nonlinear Diffusion-Convection Reaction

Gilding¹,

Kersner²

2004

170

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The study of travelling waves or fronts has become an essential part of the mathematical analysis of nonlinear diffusion-convection-reaction processes. Whether or not a nonlinear second-order scalar reaction-convection-diffusion equation admits a travelling-wave solution can be determined by the study of a singular nonlinear integral equation. This article is devoted to demonstrating how this correspondence unifies and generalizes previous results on the occurrence of travelling-wave solutions of such partial differential equations. The detailed comparison with earlier results simultaneously provides a survey of the topic. It covers travelling-wave solutions of generalizations of the Fisher, Newell-Whitehead, Zeldovich, KPP and Nagumo equations, the Burgers and nonlinear Fokker-Planck equations, and extensions of the porous media equation.

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Section: C(r)a (R) G(r) Drmentioning

confidence: 99%

“…A revealing illustration of Theorem 32 is provided by a model studied by Barelko, Kurochka, Merzhanov and Shkadinskii [23]. This model is a simplified description of an exothermic heterogeneous reaction on a catalytic wire, such as the oxidation of ammonium on the surface of a wire of platinum.…”

Section: ) In This Case Is θ(S) = S Ln( /S)mentioning

confidence: 99%

Travelling Waves in Nonlinear Diffusion-Convection Reaction

Gilding¹,

Kersner²

2004

170

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“…Recently, Barelko et al [150][151][152][153][154][155] put forward а new version of this theory. They suggested а branching-chain process mechanism based оп the concepts implying the existence of а two-dimensional gas of adsorbed atoms (adatoms) оп solid surfaces which are in equilibrium with their crystallattice.…”

Section: Phenomenological Model Of Branched·chain Reactions On аmentioning

confidence: 99%

Chapter 2 The Development of Basic Concepts of Chemical Kinetics in Heterogeneous Catalysis

1991

Kinetic Models of Catalytic Reactions

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“…It turned out that the oscillatory behavior changed substantially if the wire loop was cut into two parts, again demonstrating the importance of heat transport in such systems [190]. Systematic studies on wave propagation in electrically heated wires have been reported for various reactions, including oxidation of ammonia and hydrocarbons [182,[192][193][194][195][196][197][198] as well as the endothermic decomposition of CH 3 NH 2 on a Pt wire [199]. Stationary (Turing) patterns as well as moving fronts were observed, the latter being associated with macroscopic rate oscillations.…”

Section: 7 Thermokineticsmentioning

confidence: 99%

“…Local variations of temperature can most conveniently be recorded by infrared thermography [182], and numerous reports on such phenomena associated with catalytic CO oxidation on supported catalysts can be found in the literature [183][184][185][186][187][188]. Among others, these experiments demonstrated the importance of thermal coupling between different catalyst pellets, whose variation affects the degree of synchronization of the rate oscillations [187,188].…”

Section: 7 Thermokineticsmentioning

confidence: 99%

Non‐Linear Dynamics: Oscillatory Kinetics and Spatio‐Temporal Pattern Formation

Ertl

2008

Handbook of Heterogeneous Catalysis

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The rate of a catalytic reaction is governed by the underlying mechanism, i.e. the sequence of elementary reaction steps, and depends on the external control parameters such as the concentrations (= partial pressures) p j of educt and product species and temperature T, if transport processes are excluded in this context. More specifically, usually the adsorbed species are assumed to be randomly distributed over the surface, and their concentrations (= coverages) θ i are described within a mean-field approximation so that the reaction rate (= number of molecules r formed per unit time, dn r /dt t ) is given by dn r dt = f θ i , T ( ) (1) whereby the coverages θ i are in turn determined by a set of differential equations (modeling the individual steps of adsorption, desorption and surface reaction) of the typeProper treatment then requires that additional constraints given by heat and mass balance are taken into consideration.Under flow conditions with the external control parameters being kept fixed, usually the reaction proceeds at steady state with constant rate, i.e., dn r /dt = constant and dθ i /dt = 0. Due to the nonlinear character of the quoted differential equations, this has, however, not necessarily to be the case; the kinetics may -for certain ranges of parameters -become oscillatory or even irregular (chaotic). Such systems are typically far away from equilibrium, and (i) By far the most detailed insights into the underlying mechanisms and the general phenomenology of spatio-temporal self-organization were obtained in studies with well-defined single crystal surfaces by applying the arsenal of modern surface physical methods.(ii) Single crystal studies are usually conducted with bulk samples under low pressure conditions (≤ 10 -4 mbar)where the temperature changes associated with varying reaction rate are negligible. In addition, the mean-free path of gaseous molecules is comparable or even larger than the dimensions of the reaction vessel, which is operated as a continuous flow reactor. Hence, concentration gradients in the gas phase are practically instantaneously (≤ 10 -3 s)transmitted. Analysis of such experiments is thus appreciably simplified.(iii) Experiments with polycrystalline, i.e. "real", catalysts are usually conducted at elevated partial pressures (≥ 1 mbar) under which the heat released by the reaction may lead to noticeable temperature variations. The resulting thermokinetic effects may become dominating, so that even the nonuniformity of the surface chemistry is masked and quite novel phenomena may arise. Ideally, the reaction is conducted in a way, which may be described by a continuously stirred tank reactor (CSTR), i.e., perfect mixing ensures that the concentrations are everywhere identical.However, frequently a concentration profile exists along the reactor, which is hence rather of the plug-flow type. It is thus evident that heat and mass transfer limitations may play important roles with such systems.Generally, an extended system such as a single crystal surface, or even more ...

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Investigation of travelling waves on catalytic wires

Cited by 70 publications

References 10 publications

Travelling Waves in Nonlinear Diffusion-Convection Reaction

Travelling Waves in Nonlinear Diffusion-Convection Reaction

Chapter 2 The Development of Basic Concepts of Chemical Kinetics in Heterogeneous Catalysis

Non‐Linear Dynamics: Oscillatory Kinetics and Spatio‐Temporal Pattern Formation

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