Asymptotics of Reaction-Diffusion Fronts with One Static and One Diffusing Reactant

Abstract

The long-time behavior of a reaction-diffusion front between one static (e.g. porous solid) reactant A and one initially separated diffusing reactant B is analyzed for the mean-field reaction-rate density R(ρ_A,ρ_B) = kρ_A^mρ_B^n. A uniformly valid asymptotic approximation is constructed from matched self-similar solutions in a reaction front (of width w \sim t^αwhere R \sim t^βenters the dominant balance) and a diffusion layer (of width W \sim t^{1/2} where R is negligible). The limiting solution exists if and only if m, n \geq 1, in which case the scaling exponents are uniquely given by α= (m-1)/2(m+1) and β= m/(m+1). In the diffusion layer, the common ad hoc approximation of neglecting reactions is given mathematical justification, and the exact transient decay of the reaction rate is derived. The physical effects of higher-order kinetics (m, n > 1), such as the broadening of the reaction front and the slowing of transients, are also discussed.

final version, new title & combustion references

References in corpus (6)

• Scaling of Reaction Zones in the A+B->0 Diffusion-Limited Reaction
• The long time behavior of initially separated A+B->0 reaction-diffusion systems with arbitrary diffusion constants
• FLUCTUATION EFFECTS AND MULTISCALING OF THE REACTION-DIFFUSION FRONT FOR A+B->0
• Dynamic Multiscaling of the Reaction-Diffusion Front for mA+nB ->0
• The asymptotic behaviour of the initially separated A + B(static) -> 0 reaction-diffusion systems
• Asymptotics of solutions in nA+nB->C reaction Diffusion systems

Cited by in corpus (4)

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• Deionization Shocks in Crossflow
• Asymptotic expansion for reversible A + B <-> C reaction-diffusion process
• Non-Fickian macroscopic model of axial diffusion of granular materials in a long cylindrical tumbler