具有一个静态反应物和一个扩散反应物的反应扩散波前的渐近性
Asymptotics of Reaction-Diffusion Fronts with One Static and One Diffusing Reactant
摘要：
在平均场反应速率密度R（ρ_A，ρ_B）= kρ_A^mρ_B^n的条件下，分析了一个静态（如多孔固体）反应物A和一个初始分离的扩散反应物B之间的反应扩散前沿的长时间行为.从反应前沿（宽度为w \sim t^α，其中R \sim t^β进入主导平衡）和扩散层（宽度为W \sim t^{1/2}，其中R可忽略）中匹配的自相似解构造一致有效的渐近近似。极限解存在当且仅当m，n \geq 1，在这种情况下标度指数由α=（m-1）/2（m+1）和β= m/（m+1）唯一给出.在扩散层中，给出了忽略反应的一般adhoc近似的数学证明，并导出了反应速率的精确瞬态衰减。高阶动力学（m，n > 1）的物理效应，如反应前沿的加宽和瞬态的减慢，也进行了讨论。
英文摘要：
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.
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