Simulation study of reaction fronts

Jiang, Zifan; Ebner, C.

doi:10.1103/physreva.42.7483

Cited by 132 publications

(102 citation statements)

References 6 publications

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“…The largest domain involved a computational grid of 1024 Â 64 points for L x ¼ 1024 and L z ¼ 20, and a typical time step dt ¼ 0:1ðdzÞ 2 $ 9:8 Â 10 À3 . For zero Rayleigh numbers, we also recovered the RD results previously obtained (see Galfi and R acz, 1988;Jiang and Ebner, 1990;Koza, 1996). We now recall the main characteristics of this RD system in the absence of flow.…”

Section: ð14þsupporting

confidence: 67%

“…The large time analytical scalings characterizing A þ B-C fronts, as well as the asymptotic condition for a stationary front have been verified numerically by simulations of microscopic stochastic two-dimensional (2D) models for both equal and unequal diffusion coefficients, see Jiang and Ebner (1990), Larralde et al (1992) and Cornell (1995). Several experimental works in gels have validated these RD scalings using A þ B-C types of reaction, see Koo et al (1990), Taitelbaum et al (1992) and Yen et al (1996), like for instance the complexation reaction of Cu 2 þ with a substrate studied by Koo and Kopelman (1991) in an agarose gel.…”

Section: Introductionmentioning

confidence: 99%

“…For an infinite domain and in the asymptotic limit of large times, exact scaling laws characterizing the RD dynamics without convection were derived in the work of Galfi and Racz (1988) and in subsequent other theoretical studies including Jiang and Ebner (1990), Cornell et al (1995), Koza (1996) and Sinder and Pelleg (2000). They found that the position x f and the width w of the reaction front (defined as the position along x where the production rate is maximum and as the square root of the second moment of the production rate distribution, respectively) scale with time as x f $ t 1=2 and w $ t 1=6 .…”

Section: Introductionmentioning

confidence: 99%

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Influence of buoyancy-driven convection on the dynamics of A+B→C reaction fronts in horizontal solution layers

Rongy

Trevelyan

Wit

2010

Chemical Engineering Science

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a b s t r a c tThe dynamics of initially vertical A þ B-C reaction fronts propagating in covered horizontal solution layers can be influenced by buoyancy-driven convection. Experiments have provided evidence that a much faster propagation of the front occurs in solutions than that predicted by reaction-diffusion (RD) theories, thereby suggesting the influence of convective effects arising if A, B, and C have different densities. Here we analyze numerically and theoretically the dynamics resulting from the coupling of a simple A þ B-C chemical reaction with diffusion and convection induced by density differences across the reaction front. The important parameters of the related reaction-diffusion-convection (RDC) model are the three dimensionless Rayleigh numbers, quantifying the contribution of each species concentration to the density of the solution, the layer thickness, and the initial reactant concentration ratio. The presence of buoyancy-driven convection at the front induces a propagation of this front even in the case of equal diffusion coefficients and equal initial reactant concentrations for which RD theories predict a non-moving front. In the case of equal initial concentrations, even in the presence of convection, the classification of the various possible dynamics and the prediction of the direction of front propagation can be obtained from simple criteria on the Rayleigh numbers. In the case of different initial reactant concentrations for which, in the absence of convection, the RD front propagates towards the side of the less concentrated reactant, the introduction of buoyancy convection not only invalidates the long time RD scalings but can lead to a double reversal in the direction of propagation of the reaction front for intermediate times. The influence of the different parameters on the RDC dynamics is presented.

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Section: ð14þsupporting

confidence: 67%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Influence of buoyancy-driven convection on the dynamics of A+B→C reaction fronts in horizontal solution layers

Rongy

Trevelyan

Wit

2010

Chemical Engineering Science

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“…The diffusion-reaction system with two initially separated diffusing particles of spices A and B reacting according to the formula m ′ A + n ′ B → P (inert) has been intensively studied during past years [1,2,3,4,5,6,7,8,9,10,11,12,13]. As the diffusion-reaction equations describing the system are nonlinear, it is difficult to solve them and their general solutions remain unknown (except of very special cases).…”

Section: Introductionmentioning

confidence: 99%

“…Thus, to simplify the calculations one usually uses various approximations, such as the quasistationary approximation [1,2,3], the scaling method [1,4,5,6,7], or the perturbation one [9,10]. Using these methods, there were derived characteristic functions of the system which include: the time evolution of the reaction front x f (t), the width of the reaction zone W R (t) or the width of the depletion zone W Dep (t) [1,2,4,5,6] which all appear to be the power functions of time f (t) = Kt γ . The results were confirmed by numerical calculations and simulations [3,5,6].…”

Section: Introductionmentioning

confidence: 99%

Time Evolution Of The Reaction Front In A Subdiffusive System

Kosztołowicz

Lewandowska²

2007

AIP Conference Proceedings

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Using the quasistatic approximation we show that in a subdiffusion-reaction system with arbitrary non-zero values of subdiffusion coefficients, the reaction front x f (t) evolves in time according to the formula x f (t) = Kt α/2 , with α being the subdiffusion parameter and K which is controlled by the subdiffusion coefficients. The parameter K is determined by the equation derived in this paper. To check correctness of our analysis, we compare analytical functions derived in this paper with the results obtained numerically for the subdiffusion-reaction equations.

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Influence of fractal kinetics on molecular recognition

Savageau

1993

J of Molecular Recognition

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Molecular recognition is a central issue for nearly every biological mechanism. The analysis of molecular recognition to date has been conducted within the framework of classical chemical kinetics, in which the kinetic orders of a reaction have positive integer values. However, recent theoretical and experimental advances have shown that the assumptions inherent in this classical framework are invalid under a variety of conditions in which the reaction environment may be considered nonideal. A good example is provided by reactions that are spatially constrained and diffusion limited. Bimolecular reactions confined within two-dimensional membranes, one-dimensional channels or fractal surfaces in general exhibit kinetic orders that are noninteger. An appropriate framework for the study of these nonideal phenomena is provided by the Power-Law formalism, which includes as special cases the Mass-Action formalism of chemical kinetics and the Michaelis-Menten formalism of enzyme kinetics. The Power-Law formalism is an appropriate representation not only for fractal kinetics per se, but also for other nonideal kinetic phenomena, provided the range of variation in concentration is not too large. After defining some elementary concepts of molecular recognition, and showing how these are manifested in classical kinetic terms, this paper contrasts the implications of classical and fractal kinetics in a few simple cases. The principal distinction lies in the ability of fractal kinetics to nonlinearly transform, rather than proportionally transmit, the input S/N ratio. As a consequence, fractal kinetics create a threshold for the input signal below which no recognition occurs and above which amplified recognition takes place.(ABSTRACT TRUNCATED AT 250 WORDS)

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Simulation study of reaction fronts

Cited by 132 publications

References 6 publications

Influence of buoyancy-driven convection on the dynamics of A+B→C reaction fronts in horizontal solution layers

Influence of buoyancy-driven convection on the dynamics of A+B→C reaction fronts in horizontal solution layers

Time Evolution Of The Reaction Front In A Subdiffusive System

Influence of fractal kinetics on molecular recognition

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