The long time behavior of initially separated A+B->0 reaction-diffusion systems with arbitrary diffusion constants

Abstract

We examine the long time behaviour of A+B->0 reaction diffusion systems with initially segregated species A and B. All of our analysis is carried out for arbitrary (positive) values of the diffusion constants $D_A$, $D_B$, and initial concentrations $a_0$ and $b_0$ of A's and B's. We divide the domain of the partial differential equations describing the problem into several regions in which they can be reduced to simpler, solvable equations, and we merge the solutions. Thus we derive general formulae for the concentration profiles outside the reaction zone, the location of the reaction zone center, and the total reaction rate. An asymptotic condition for the reaction front to be stationary is also derived. The properties of the reaction layer are studied in the mean-field approximation, and we show that not only the scaling exponents, but also the scaling functions are independent of $D_A$, $D_B$, $a_0$ and $b_0$.

A single LaTeX file, 13 pages, no extra figures or macros, to appear in J. Stat. Phys. (1996)

References in corpus (6)

• Renormalization Group Study of the A+B->0 Diffusion-Limited Reaction
• Scaling of Reaction Zones in the A+B->0 Diffusion-Limited Reaction
• FLUCTUATION EFFECTS AND MULTISCALING OF THE REACTION-DIFFUSION FRONT FOR A+B->0
• Dynamic Multiscaling of the Reaction-Diffusion Front for mA+nB ->0
• Diffusion-Limited Annihilation with Initially Separated Reactants
• Refined Simulations of the Reaction Front for Diffusion-Limited Two-Species Annihilation in One Dimension

Cited by in corpus (16)

• Reaction Front in an A+B -> C Reaction-Subdiffusion Process
• Derivation of the Matalon-Packter law for Liesegang patterns
• Formation of Liesegang patterns: A spinodal decomposition scenario
• Asymptotics of Reaction-Diffusion Fronts with One Static and One Diffusing Reactant
• The asymptotic behaviour of the initially separated A + B(static) -> 0 reaction-diffusion systems
• Formation of Liesegang patterns: Simulations using a kinetic Ising model
• Localization-delocalization transition of a reaction-diffusion front near a semipermeable wall
• Diffusion-controlled annihilation $A+B\to 0$ with initially separated reactants: The death of an $A$ particle island in the $B$ particle sea
• Concentration Profiles and Reaction Fronts in A + B -> C Type Processes: Effect of Background Ions
• Comparison of models and lattice-gas simulations for Liesegang patterns
• Diffusion-controlled death of $A$-particle and $B$-particle islands at propagation of the sharp annihilation front $A+B\to 0$
• Diffusion-controlled annihilation $A+B\to 0$: The growth of an $A$ particle island from a localized $A$-source in the $B$ particle sea
• Asymptotic expansion for reversible A + B <-> C reaction-diffusion process
• Diffusion-controlled formation and collapse of a d-dimensional A-particle island in the B-particle sea
• Reaction-Diffusion Processes with Nonlinear Diffusion
• Diffusion-controlled coalescence, fragmentation and collapse of $d$-dimensional $A$-particle islands in the $B$-particle sea