Crossover Time Behavior in a+b⃗c And a+2b⃗c Reaction-Diffusion Front Systems in a Capillary

1998 ◽  
Vol 543 ◽  
Author(s):  
Sung Hyun Park ◽  
Andrew Yen ◽  
Zhong-You Shi ◽  
Raoul Kopelman
Keyword(s):  
Reaction Rate ◽  
Early Time ◽  
Reaction Diffusion ◽  
Time Behavior ◽  
Explicit Dependence ◽  
Diffusion Front ◽  
Front Width ◽  
Time Regime ◽  
Global Reaction ◽  
Mechanism Of The Reaction

AbstractThe crossover time from the early-time regime to the asymptotic regime for the A+B⃗+C reaction-diffusion system with initially separated reactants has been derived analytically by matching the rate expressions for the two regimes. The crossover time expression thus obtained shows an explicit dependence on the rate constant (k) and the initial reactant concentrations (ao, bo). For the A+2B⃗C system we performed computer simulations using two different methods. Crossover behaviors for the global reaction rate and reaction front width have been observed for both methods. The crossover time depends on the mechanism of the reaction.

Effect of non-uniform passive advection on A+B->C radial reaction-diffusion fronts 

2021 ◽  
Author(s):  
Alessandro Comolli ◽  
Anne De Wit ◽  
Fabian Brau
Keyword(s):  
Molecular Diffusion ◽  
Early Time ◽  
Reaction Diffusion ◽  
Transport Processes ◽  
Calcium Carbonate Precipitation ◽  
Atmospheric Reactions ◽  
Passive Advection ◽  
Reaction Fronts ◽  
Time Regime ◽  
Long Time

<p>The interplay between chemical and transport processes can give rise to complex reaction fronts dynamics, whose understanding is crucial in a wide variety of environmental, hydrological and biological processes, among others. An important class of reactions is A+B->C processes, where A and B are two initially segregated miscible reactants that produce C upon contact. Depending on the nature of the reactants and on the transport processes that they undergo, this class of reaction describes a broad set of phenomena, including combustion, atmospheric reactions, calcium carbonate precipitation and more. Due to the complexity of the coupled chemical-hydrodynamic systems, theoretical studies generally deal with the particular case of reactants undergoing passive advection and molecular diffusion. A restricted number of different geometries have been studied, including uniform rectilinear [1], 2D radial [2] and 3D spherical [3] fronts. By symmetry considerations, these systems are effectively 1D.</p><p>Here, we consider a 3D axis-symmetric confined system in which a reactant A is injected radially into a sea of B and both species are transported by diffusion and passive non-uniform advection. The advective field <em>v<sub>r</sub>(r,z)</em> describes a radial Poiseuille flow. We find that the front dynamics is defined by three distinct temporal regimes, which we characterize analytically and numerically. These are i) an early-time regime where the amount of mixing is small and the dynamics is transport-dominated, ii) a strongly non-linear transient regime and iii) a long-time regime that exhibits Taylor-like dispersion, for which the system dynamics is similar to the 2D radial case.</p><p>                                  <img src="https://contentmanager.copernicus.org/fileStorageProxy.php?f=gnp.ff5ab530bdff57321640161/sdaolpUECMynit/12UGE&app=m&a=0&c=360a1556c809484116c55812c8c06624&ct=x&pn=gnp.elif&d=1" alt="" width="299" height="299">                                                     <img src="https://contentmanager.copernicus.org/fileStorageProxy.php?f=gnp.671a6980bdff51231640161/sdaolpUECMynit/12UGE&app=m&a=0&c=c5a857c3fab835057e3af84001a91d15&ct=x&pn=gnp.elif&d=1" alt="" width="302" height="302"></p><p>                                                   Fig. 1: Concentration profile of the product C in the transient (left) and asymptotic (right) regimes.</p><p> </p><p>References:</p><p>[1] L. Gálfi, Z. Rácz, Phys. Rev. A 38, 3151 (1988);</p><p>[2] F. Brau, G. Schuszter, A. De Wit, Phys. Rev. Lett. 118, 134101 (2017);</p><p>[3] A. Comolli, A. De Wit, F. Brau, Phys. Rev. E, 100 (5), 052213 (2019).</p>

Study of an A+2B--->C Reaction-Diffusion System with Initially Separated Components

1994 ◽  
Vol 366 ◽  
Author(s):  
Andrew Yen ◽  
Raoul Kopelman
Keyword(s):  
Reaction Front ◽  
Reaction Rate ◽  
Reaction Diffusion ◽  
Biological Processes ◽  
Local Production ◽  
Kinetic Behavior ◽  
Acetate Trihydrate ◽  
Physical Chemical ◽  
Global Reaction ◽  
Front Dynamics

ABSTRACTThe presence of a reaction front is a characteristic feature of a variety of physical, chemical and biological processes. A chemical reaction exhibits a front (spatially localized region where concentration of product is non zero), provided the diffusing reactants are separated in space. We study the reaction front dynamics of a termolecular A+2B--->C reaction with initially separated components in a capillary. The reaction tetra+2Ni2+--->1:2 complex is used, where ‘tetra’ is disodium ethyl bis(5-tetrazolylazo) acetate trihydrate. We measure and compare with theory the dynamic quantities that characterize the kinetic behavior of the system: the global reaction rate R(t), the location of the reaction center xf(t), the front's width w(t), and the local production rate R(xf,t). The non-classical nature of this dynamical system is confirmed.

Experimental Study of a Reaction-Diffusion System in a Capillary: Complex Behavior of a Seemingly Simple System

1994 ◽  
Vol 366 ◽  
Author(s):  
Anna Lin ◽  
Andrew Yen ◽  
Yong-Eun Koo ◽  
Raoul Kopelman
Keyword(s):  
Reaction Front ◽  
Reaction Rate ◽  
Capillary Tube ◽  
Xylenol Orange ◽  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Product Concentration ◽  
Global Rate ◽  
Global Reaction

ABSTRACTWe study a reaction-diffusion system within the confines of a thin capillary tube. Xylenol orange and Cr 3+ are introduced into a capillary tube from opposite ends and meet in the middle forming a reaction front. Unequal initial concentrations of the reactants causes the center of the reaction front to move in time. Characteristics of the front such as the width of the reaction zone, w, the position of the center of the front, xf, the global reaction rate, R, and the local reaction rate, r(xf,t) are determined by continuously monitoring the product concentration in space vs. time. We observe crossover of the global rate from classical to non-classical behavior and a splitting of the reaction front.

Reaction-diffusion front width anomalies in disordered media

2006 ◽  
Vol 73 (5) ◽  
Author(s):  
Inbal Hecht ◽  
Yochi Moran ◽  
Haim Taitelbaum
Keyword(s):  
Reaction Diffusion ◽  
Disordered Media ◽  
Diffusion Front ◽  
Front Width

Study of A+B-4C and A+2B–C Reaction-Diffusion System with Initially Separated Components

1995 ◽  
Vol 407 ◽  
Author(s):  
Andrew Yen ◽  
Raoul Kopelman
Keyword(s):  
Dynamical System ◽  
Reaction Front ◽  
Reaction Rate ◽  
Reaction Diffusion ◽  
Biological Processes ◽  
Local Production ◽  
Kinetic Behavior ◽  
Physical Chemical ◽  
Global Reaction ◽  
Front Dynamics

ABSTRACTThe presence of a reaction front is a characteristic feature of a variety of physical, chemical and biological processes. The reaction exhibits a front, provided that the diffusing reactants are separated in space. We study the reaction front dynamics of both A+B→C bimolecular and A+2B→C termolecular reactions with initially separated components in a capillary. We measure and compare with theory and simulations the dynamic quantities that characterize the kinetic behavior of the system: the global reaction rate R(t), the location of the reaction center xf(t), the front's width w(t), and the local production rate R(xft). The non-classical nature of this dynamical system is confirmed.

scholarly journals Dynamic multiscaling of the reaction-diffusion front formA+nB→0

1995 ◽  
Vol 52 (4) ◽  
pp. 3500-3505 ◽  
Author(s):  
Stephen Cornell ◽  
Zbigniew Koza ◽  
Michel Droz
Keyword(s):  
Reaction Diffusion ◽  
Diffusion Front

scholarly journals Asymptotic Behavior of Solutions to Reaction-Diffusion Equations with Dynamic Boundary Conditions and Irregular Data

2018 ◽  
Vol 2018 ◽  
pp. 1-13
Author(s):  
Yonghong Duan ◽  
Chunlei Hu ◽  
Xiaojuan Chai
Keyword(s):  
Asymptotic Behavior ◽  
Boundary Conditions ◽  
Reaction Diffusion ◽  
Large Time Behavior ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Asymptotic Behavior Of Solutions ◽  
Time Behavior ◽  
Dynamic Boundary Conditions ◽  
Dynamic Boundary

This paper is concerned with the asymptotic behavior of solutions to reaction-diffusion equations with dynamic boundary conditions as well as L1-initial data and forcing terms. We first prove the existence and uniqueness of an entropy solution by smoothing approximations. Then we consider the large-time behavior of the solution. The existence of a global attractor for the solution semigroup is obtained in L1(Ω¯,dν). This extends the corresponding results in the literatures.

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