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Urbano SJV, González DL, Téllez G. Steady state of a two-species annihilation process with separated reactants. Phys Rev E 2023; 108:024118. [PMID: 37723765 DOI: 10.1103/physreve.108.024118] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/04/2023] [Accepted: 07/23/2023] [Indexed: 09/20/2023]
Abstract
We describe the steady state of the annihilation process of a one-dimensional system of two initially separated reactants A and B. The parameters that define the dynamical behavior of the system are the diffusion constant, the reaction rate, and the deposition rate. Depending on the ratio between those parameters, the system exhibits a crossover between a diffusion-limited (DL) regime and a reaction-limited (RL) regime. We found that a key quantity to describe the reaction process in the system is the probability p(x_{A},x_{B}) to find the rightmost A (RMA) particle and the leftmost B (LMB) particle at the positions x_{A} and x_{B}, respectively. The statistical behavior of the system in both regimes is described using the density of particles, the gap length distribution x_{B}-x_{A}, the marginal probabilities p_{A}(x_{A}) and p_{B}(x_{B}), and the reaction kernel. For both regimes, this kernel can be approximated by using p(x_{A},x_{B}). We found an excellent agreement between the numerical and analytical results for all calculated quantities despite the reaction process being quite different in both regimes. In the DL regime, the reaction kernel can be approximated by the probability to find the RMA and LMB particles in adjacent sites. In the RL regime, the kernel depends on the marginal probabilities p_{A}(x_{A}) and p_{B}(x_{B}).
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Affiliation(s)
| | - Diego Luis González
- Departamento de Física, Universidad del Valle, A.A. 25360, Cali 760042, Colombia
| | - Gabriel Téllez
- Departamento de Física, Universidad de los Andes, Bogotá 111711, Colombia
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2
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Ostvar S, Wood BD. A non-scale-invariant form for coarse-grained diffusion-reaction equations. J Chem Phys 2016. [DOI: 10.1063/1.4962421] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Sassan Ostvar
- School of Chemical, Biological and Environmental Engineering, Oregon State University, Corvallis, Oregon 97331, USA
| | - Brian D. Wood
- School of Chemical, Biological and Environmental Engineering, Oregon State University, Corvallis, Oregon 97331, USA
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3
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The Effects of Mixing, Reaction Rates, and Stoichiometry on Yield for Mixing Sensitive Reactions—Part I: Model Development. INTERNATIONAL JOURNAL OF CHEMICAL ENGINEERING 2012. [DOI: 10.1155/2012/750162] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
There are two classes of mixing sensitive reactions: competitive-consecutive and competitive-parallel. The yield of desired product from these coupled reactions depends on how fast the reactants are brought together. Recent experimental results have suggested that the mixing effect may depend strongly on the stoichiometry of the reactions. To investigate this, a 1D, dimensionless, reaction-diffusion model at the micromixing scale was developed. Assuming constant mass concentration and mass diffusivities, systems of PDE's were derived on a mass fraction basis for both types of reactions. Two dimensionless reaction rate ratios and a single general Damköhler number emerged from the analysis. The resulting dimensionless equations were used to investigate the effects of mixing, reaction rate ratio, and reaction stoichiometry. As expected, decreasing either the striation thickness or the dimensionless rate ratio maximizes yield, the reaction stoichiometry has a considerable effect on yield, and all three variables interact strongly.
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4
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The Effects of Mixing, Reaction Rates, and Stoichiometry on Yield for Mixing Sensitive Reactions—Part II: Design Protocols. INTERNATIONAL JOURNAL OF CHEMICAL ENGINEERING 2012. [DOI: 10.1155/2012/654321] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
Competitive-consecutive and competitive-parallel reactions are both mixing sensitive reactions where the yield of desired product depends on how fast the reactants are brought together. Recent experimental results have suggested that the magnitude of the mixing effect may depend strongly on the stoichiometry of the reactions. To investigate this, a 1D, dimensionless, reaction-diffusion model was developed at the micromixing scale, yielding a single general Damköhler number. Dimensionless reaction rate ratios were derived for both reaction schemes. A detailed investigation of the effects of initial mixing condition (striation thickness), dimensionless reaction rate ratio, and reaction stoichiometry on the yield of desired product showed that the stoichiometry has a considerable effect on yield. All three variables were found to interact strongly. Model results for 12 stoichiometries are used to determine the mixing scale and relative rate ratio needed to achieve a specified yield for each reaction scheme. The results show that all three variables need to be considered when specifying reactors for mixing sensitive reactions.
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5
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Abi Mansour A, Al Ghoul M. Scaling and crossover dynamics in the hyperbolic reaction-diffusion equations of initially separated components. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:026107. [PMID: 21929064 DOI: 10.1103/physreve.84.026107] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/16/2011] [Revised: 04/17/2011] [Indexed: 05/31/2023]
Abstract
In this paper we investigate the dynamics of front propagation in the family of reactions (nA + mB (k)→ C) with initially segregated reactants in one dimension using hyperbolic reaction-diffusion equations with the mean-field approximation for the reaction rate. This leads to different dynamics than those predicted by their parabolic counterpart. Using perturbation techniques, we focus on the initial and intermediate temporal behavior of the center and width of the front and derive the different time scaling exponents. While the solution of the parabolic system yields a short time scaling as t(1/2) for the front center, width, and global reaction rate, the hyperbolic system exhibits linear scaling for those quantities. Moreover, those scaling laws are shown to be independent of the stoichiometric coefficients n and m. The perturbation results are compared with the full numerical solutions of the hyperbolic equations. The crossover time at which the hyperbolic regime crosses over to the parabolic regime is also studied. Conditions for static and moving fronts are also derived and numerically validated.
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Affiliation(s)
- Andrew Abi Mansour
- Program in Computational Science, American University of Beirut, Beirut, Lebanon
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6
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Affiliation(s)
- Haim Taitelbaum
- a Department of Physics , Bar-Ilan University , Ramat-Gan , 52900 , Israel
| | - Zbigniew Koza
- a Department of Physics , Bar-Ilan University , Ramat-Gan , 52900 , Israel
- b Institute of Theoretical Physics, University of Wroclaw , 50204 , Wroclaw , Poland
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7
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Al-Ghoul M, Ghaddar T, Moukalled T. Pulse-Front Propagation and Interaction During the Growth of CdS Nanoparticles in a Gel. J Phys Chem B 2009; 113:11594-603. [DOI: 10.1021/jp9022647] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Mazen Al-Ghoul
- Department of Chemistry, and Center for Advanced Mathematical Sciences, American University of Beirut, Beirut, Lebanon
| | - Tarek Ghaddar
- Department of Chemistry, and Center for Advanced Mathematical Sciences, American University of Beirut, Beirut, Lebanon
| | - Tharwat Moukalled
- Department of Chemistry, and Center for Advanced Mathematical Sciences, American University of Beirut, Beirut, Lebanon
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8
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Makki R, Al-Ghoul M, Sultan R. Propagating Fronts in Thin Tubes: Concentration, Electric, and pH Effects in a Two-Dimensional Precipitation Pulse System. J Phys Chem A 2009; 113:6049-57. [DOI: 10.1021/jp8087226] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Rabih Makki
- Department of Chemistry and Center for Advanced Mathematical Sciences, American University of Beirut, P.O. Box 11-0236, 1107 2020 Riad El Solh, Beirut, Lebanon
| | - Mazen Al-Ghoul
- Department of Chemistry and Center for Advanced Mathematical Sciences, American University of Beirut, P.O. Box 11-0236, 1107 2020 Riad El Solh, Beirut, Lebanon
| | - Rabih Sultan
- Department of Chemistry and Center for Advanced Mathematical Sciences, American University of Beirut, P.O. Box 11-0236, 1107 2020 Riad El Solh, Beirut, Lebanon
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9
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Polanowski P, Koza Z. Reaction-diffusion fronts in systems with concentration-dependent diffusivities. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:036103. [PMID: 17025704 DOI: 10.1103/physreve.74.036103] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/23/2006] [Indexed: 05/12/2023]
Abstract
We examine properties of a reaction front that forms in irreversible reaction-diffusion systems with concentration-dependent diffusivities. We study two different models of such systems and find that in the limit of a vanishingly small diffusivity of the reaction product, the reaction front dynamics enters a separate universality class, with the front width asymptotically tending to a constant value, and the reaction rate at the reaction front center diminishing with time t as t(-1/2). This behavior can be also observed in systems with nonvanishing (but small) diffusivity of the reaction product at intermediate times.
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Affiliation(s)
- Piotr Polanowski
- Department of Molecular Physics, Technical University of Łódź, Zeromskiego 116, 90-924 Łódź, Poland
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10
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Hecht I, Taitelbaum H. Perturbation analysis for competing reactions with initially separated components. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:012101. [PMID: 16907140 DOI: 10.1103/physreve.74.012101] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/23/2005] [Revised: 01/23/2006] [Indexed: 05/11/2023]
Abstract
We study a competitive reaction-diffusion system with initially separated components. In this system, two similar species on one side of the system compete to react with the species on the other side. The competition is due to significant differences in the microscopic reaction constants and the initial densities of the two competing species. In the short-time limit, each of the competitive reactions is considered as perturbation with respect to the diffusion, the latter is essential for the effective mixing of the reactants. We identify the small parameters required for the perturbation analysis of the competitive scheme. The resulting perturbative expressions provide the rich spatiotemporal reaction front patterns, which were experimentally observed for Cr3+ + Xylenol Orange (XO) --> products, where the aggregated and nonaggregated forms of Cr3+ in aqueous solution compete to react with the XO.
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Affiliation(s)
- Inbal Hecht
- Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel
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11
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Hecht I, Moran Y, Taitelbaum H. Reaction-diffusion front width anomalies in disordered media. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:051109. [PMID: 16802920 DOI: 10.1103/physreve.73.051109] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/24/2005] [Revised: 02/03/2006] [Indexed: 05/10/2023]
Abstract
We study the front characteristics of the A + B --> C reaction-diffusion system with initially separated reactants in disordered media, exemplified by two-dimensional (2D) percolation. We investigate the front characteristics as a function of the disorder degree in this system, in particular close to criticality. We show that the front width exponent is larger than the mean-field (MF) exponent of 1/6, and at criticality it approaches 1/4, which is the one-dimensional (1D) exponent. We show that previous predictions in the literature for the 2D percolation cluster at criticality are wrong. The results are discussed in the context of other systems with attenuated transport where the front width exponent is smaller than the MF exponent. We also study the short-time behavior of the front width exponent, and discuss the validity of the scaling relations between the relevant exponents.
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Affiliation(s)
- Inbal Hecht
- Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel
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12
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Szalai ES, Kukura J, Arratia PE, Muzzio FJ. Effect of hydrodynamics on reactive mixing in laminar flows. AIChE J 2006. [DOI: 10.1002/aic.690490115] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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13
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Yuste SB, Acedo L, Lindenberg K. Reaction front in an A+B-->C reaction-subdiffusion process. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 69:036126. [PMID: 15089380 DOI: 10.1103/physreve.69.036126] [Citation(s) in RCA: 39] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/19/2003] [Indexed: 05/24/2023]
Abstract
We study the reaction front for the process A+B-->C in which the reagents move subdiffusively. Our theoretical description is based on a fractional reaction-subdiffusion equation in which both the motion and the reaction terms are affected by the subdiffusive character of the process. We design numerical simulations to check our theoretical results, describing the simulations in some detail because the rules necessarily differ in important respects from those used in diffusive processes. Comparisons between theory and simulations are on the whole favorable, with the most difficult quantities to capture being those that involve very small numbers of particles. In particular, we analyze the total number of product particles, the width of the depletion zone, the production profile of product and its width, as well as the reactant concentrations at the center of the reaction zone, all as a function of time. We also analyze the shape of the product profile as a function of time, in particular, its unusual behavior at the center of the reaction zone.
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Affiliation(s)
- S B Yuste
- Departamento de Física, Universidad de Extremadura, E-06071 Badajoz, Spain
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14
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Monson E, Kopelman R. Nonclassical kinetics of an elementary A+B-->C reaction-diffusion system showing effects of a speckled initial reactant distribution and eventual self-segregation: experiments. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 69:021103. [PMID: 14995423 DOI: 10.1103/physreve.69.021103] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/21/2003] [Indexed: 05/24/2023]
Abstract
We demonstrate here the implementation of an experimental system suitable for the study of the diffusion limited A+B-->0, nonclassical reaction behavior. Using a combination of a fluorescent calcium indicator and a calcium ion which is initially "caged," a pulse of near-UV light initiates the reaction which is followed as product formation vs time. Sensitive dependence on the initial reactant distribution is observed through patterns in the uncaging UV light profile. In one case, the reaction progress passes through two nonclassical time regimes, one due to roughness originating from laser speckles, followed by one consistent with the three-dimensional Zeldovich rate of (1/rho(A)-1/rho(A0)) approximately t(3/4), with features matching Monte Carlo simulations on this initial distribution. This behavior is contrasted with reactions initiated by a homogeneous source which induces random initial reactant distributions, though both systems seem to approach the asymptotic limit of self-segregation of reactants.
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Affiliation(s)
- Eric Monson
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
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15
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Sinder M, Pelleg J, Sokolovsky V, Meerovich V. Competing reactions with initially separated components in the asymptotic time region. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 68:022101. [PMID: 14525025 DOI: 10.1103/physreve.68.022101] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/13/2003] [Indexed: 05/24/2023]
Abstract
Two competing irreversible reactions with initially separated components and with essentially different reaction constants are theoretically studied in the asymptotic time region. The description of the two simultaneous reactions is reduced to the consideration of two reactions separated in space. It is shown that the reaction rate profile can have two maxima and their ratio is independent of time. The location and relative value of the maxima are functions of the reaction constants and initial concentrations.
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Affiliation(s)
- Misha Sinder
- Department of Materials Engineering, Ben Gurion University of the Negev, Beer-Sheva 84105, Israel
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16
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Shipilevsky BM. Diffusion-controlled annihilation A+B-->0 with initially separated reactants: the death of an A particle island in the B particle sea. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 67:060101. [PMID: 16241185 DOI: 10.1103/physreve.67.060101] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/21/2003] [Indexed: 05/04/2023]
Abstract
We consider the diffusion-controlled annihilation dynamics A+B-->0 with equal species diffusivities in the system where an island of particles A is surrounded by the uniform sea of particles B. We show that once the initial number of particles in the island is large enough, then at any system's dimensionality d the death of the majority of particles occurs in the universal scaling regime within which approximately 4/5 of the particles die at the island expansion stage and the remaining approximately 1/5 at the stage of its subsequent contraction. In the quasistatic approximation, the scaling of the reaction zone has been obtained for the cases of mean-field (d>or=d(c)) and fluctuation (d<d(c)) dynamics of the front.
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17
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Sinder M, Pelleg J. Two reaction zones in a competing reactions system with initially separated components. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 65:060101. [PMID: 12188690 DOI: 10.1103/physreve.65.060101] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/27/2001] [Revised: 03/25/2002] [Indexed: 05/23/2023]
Abstract
The long-time properties of a system with initially separated components and two competing reactions, reversible A1+B<-->C1 and irreversible A2+B-->C2, are studied. It is assumed that the backward constant g(1) of the reversible reaction A1+B<-->C1 is small. The dynamics of the system is described by means of a crossover from an "irreversible" regime (for times t<<g(-1)(1)) to a "reversible" regime (for times t>>g(-1)(1)). It is shown that in contrast to the "irreversible" regime, where both reactions occur in one reaction zone, the "reversible" regime is characterized by two distinctive reaction zones. These are the A1+B<-->C1 reversible reaction zone and the A2+C1-->A1+C2 irreversible reaction zone. Numerical computations of the mean-field kinetic equations confirm these asymptotic results.
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Affiliation(s)
- Misha Sinder
- Department of Materials Engineering, Ben Gurion University of the Negev, P.O. Box 653, Beer-Sheva 84105, Israel
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18
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Sinder M. Theory for competing reactions with initially separated components. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 65:037104. [PMID: 11909315 DOI: 10.1103/physreve.65.037104] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/09/2001] [Indexed: 05/23/2023]
Abstract
The asymptotic long-time properties of a system with initially separated components and two competing irreversible reactions A1+B-->C1 and A2+B-->C2 are studied. It is shown that the system is characterized by a single reaction zone, with width growing like t(1/6), in which both reactions occur. Numerical computations of the mean-field kinetic equations confirm these asymptotic results.
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Affiliation(s)
- Misha Sinder
- Department of Materials Engineering, Ben Gurion University of the Negev, Beer-Sheva 84105, Israel
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19
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Park SH, Parus S, Kopelman R, Taitelbaum H. Gel-free experiments of reaction-diffusion front kinetics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 64:055102. [PMID: 11735998 DOI: 10.1103/physreve.64.055102] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/23/2001] [Indexed: 05/23/2023]
Abstract
We present a gel-free experimental system to study the kinetics of the reaction front in the A+B-->C reaction-diffusion system with initially-separated reactants. The experimental setup consists of a CCD camera monitoring the kinetics of the front formed in the reaction-diffusion process Cu(2+) + tetra [disodium ethyl bis(5-tetrazolylazo) acetate trihydrate] -->1:1 complex, in aqueous, gel-free solution, taking place inside a 150 microm gap between two flat microscope slides. The experimental results agree with the theoretical predictions for the time dependence of the front's width, height, and location, as well as the global reaction rate.
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Affiliation(s)
- S H Park
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
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20
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Cox SM, Finn MD. Behavior of the reaction front between initially segregated species in a two-stage reaction. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 63:051102. [PMID: 11414882 DOI: 10.1103/physreve.63.051102] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/05/2000] [Indexed: 05/23/2023]
Abstract
The large-time asymptotic behavior of a two-stage reaction (A+B-->R, B+R-->S) with initially segregated reactants is described. The concentration of the reactants is found to be significantly less than the initial concentrations in a depletion zone of width proportional to t(1/2), where t is time; the reaction takes place in a thinner zone of width proportional to t(1/6). Similarity solutions for the chemical concentration profiles in the reaction zone are calculated, and are compared with numerical simulations of the full partial differential reaction-diffusion equations. The large-time asymptotic scalings reported here are the same as in the absence of the secondary reaction, but we find that the location of the reaction zone is significantly shifted due to the secondary reaction. The reaction zone may behave in an exotic fashion at large time, moving first one way, then reversing its direction.
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Affiliation(s)
- S M Cox
- School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
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21
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Sinder M, Pelleg J. Asymptotic properties of a reversible A+B<-->C (static) reaction-diffusion process with initially separated reactants. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 2000; 62:3340-8. [PMID: 11088833 DOI: 10.1103/physreve.62.3340] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/10/2000] [Indexed: 04/15/2023]
Abstract
The asymptotic properties of the reaction front formed in a reversible reaction-diffusion process A+B<-->C (static) with initially separated reactants are investigated. The case of arbitrary nonzero values of the diffusion constants D(A) and D(B) and initial concentrations a(0) and b(0) of the reactants A and B is considered. The system is studied in the limit of t-->infinity and g-->0, where t and g are the time and the backward reaction rate constant, respectively. The dynamics of the reaction front is described as a crossover between the "irreversible" regime at times t<<g(-1) and the "reversible" regime at times t>>g(-1). The general properties of the crossover are studied with the help of an extended scaling approach formulated in this work. On the basis of the mean-field equations the analytical solutions in the reversible regime t>>g(-1) inside the reaction zone are discussed. It is shown that in the immobile reaction zone the reaction rate profile has two distinct maxima. This profile differs drastically from the usual single-maximum reaction rate profile inherent in the mobile reaction zone. The two-hump reaction zone profile is the result of the influence of C on the reaction rate in the reversible regime. Numerical computation of the mean-field kinetics equations supports the results of the asymptotic consideration.
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Affiliation(s)
- M Sinder
- Department of Materials Engineering, Ben Gurion University of the Negev, Beer Sheva 84105, Israel
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22
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Sinder M, Pelleg J. Properties of the crossover from nonclassical to classical chemical kinetics in a reversible A+B<-->C reaction diffusion process. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1999; 60:R6259-62. [PMID: 11970609 DOI: 10.1103/physreve.60.r6259] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/03/1999] [Indexed: 04/18/2023]
Abstract
We study the properties of the reaction front formed in a reversible reaction diffusion process A+B<-->C, with initially separated reactants. The case of the mobile C component is considered. In accordance with Chopard et al. [Phys. Rev. E 47, R40 (1993)] the dynamics of the front is described as a crossover between the "irreversible" regime at short times and the "reversible" regime at long times. A refined definition for the rate of C production is suggested, taking into account both the forward and the backward reaction rates. By this definition within the framework of the mean-field equations it is shown that the reversible regime is characterized by scaling of the local rate of C production as R(local) approximately t(-1) and by scaling of the global rate of C production as R(global) approximately t(-1/2). It is also established that in the considered special case of equal diffusion coefficients and equal initial concentrations, the macroscopic properties of the reaction front, such as the global rate of the C production R(global) and the concentration profiles of the components outside the front reaction, are unchanged through this crossover.
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Affiliation(s)
- M Sinder
- Department of Materials Engineering, Ben-Gurion University of the Negev, Beer Sheva 84105, Israel
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23
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Léger C, Argoul F, Bazant MZ. Front Dynamics during Diffusion-Limited Corrosion of Ramified Electrodeposits. J Phys Chem B 1999. [DOI: 10.1021/jp990486+] [Citation(s) in RCA: 40] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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24
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Crouch SR, Cullen TF, Scheeline A, Kirkor ES. Kinetic Determinations and Some Kinetic Aspects of Analytical Chemistry. Anal Chem 1998. [DOI: 10.1021/a1980005s] [Citation(s) in RCA: 67] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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25
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Yen A, Lin AL, Koo YEL, Vilensky B, Taitelbaum H, Kopelman R. Spatiotemporal Patterns and Nonclassical Kinetics of Competing Elementary Reactions: Chromium Complex Formation with Xylenol Orange in a Capillary. J Phys Chem A 1997. [DOI: 10.1021/jp962994e] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Andrew Yen
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109-1055, and Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel
| | - Anna L. Lin
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109-1055, and Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel
| | - Yong-Eun Lee Koo
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109-1055, and Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel
| | - Baruch Vilensky
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109-1055, and Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel
| | - Haim Taitelbaum
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109-1055, and Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel
| | - Raoul Kopelman
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109-1055, and Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel
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Taitelbaum H, Yen A, Kopelman R, Havlin S, Weiss GH. Effects of bias on the kinetics of A+B-->C with initially separated reactants. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 54:5942-5947. [PMID: 9965810 DOI: 10.1103/physreve.54.5942] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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