dorsal/arxiv
View SchemaAsymptotics of Reaction-Diffusion Fronts with One Static and One Diffusing Reactant
| Authors | Martin Z. Bazant, Howard A. Stone |
|---|---|
| Categories | |
| ArXiv ID | physics/9904008 |
| URL | https://arxiv.org/abs/physics/9904008 |
| DOI | 10.1016/S0167-2789(00)00140-8 |
| Journal | Physica D 2552, 1 (2000) |
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(\rho_A,\rho_B) = k\rho_A^m\rho_B^n. A uniformly valid asymptotic approximation is constructed from matched self-similar solutions in a reaction front (of width w \sim t^\alpha where R \sim t^\beta enters 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 \alpha = (m-1)/2(m+1) and \beta = 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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"abstract": "The long-time behavior of a reaction-diffusion front between one static (e.g.\nporous solid) reactant A and one initially separated diffusing reactant B is\nanalyzed for the mean-field reaction-rate density R(\\rho_A,\\rho_B) =\nk\\rho_A^m\\rho_B^n. A uniformly valid asymptotic approximation is constructed\nfrom matched self-similar solutions in a reaction front (of width w \\sim\nt^\\alpha where R \\sim t^\\beta enters the dominant balance) and a diffusion\nlayer (of width W \\sim t^{1/2} where R is negligible). The limiting solution\nexists if and only if m, n \\geq 1, in which case the scaling exponents are\nuniquely given by \\alpha = (m-1)/2(m+1) and \\beta = m/(m+1). In the diffusion\nlayer, the common ad hoc approximation of neglecting reactions is given\nmathematical justification, and the exact transient decay of the reaction rate\nis derived. The physical effects of higher-order kinetics (m, n \u003e 1), such as\nthe broadening of the reaction front and the slowing of transients, are also\ndiscussed.",
"arxiv_id": "physics/9904008",
"authors": [
"Martin Z. Bazant",
"Howard A. Stone"
],
"categories": [
"physics.chem-ph",
"cond-mat",
"math.AP"
],
"doi": "10.1016/S0167-2789(00)00140-8",
"journal_ref": "Physica D 2552, 1 (2000)",
"title": "Asymptotics of Reaction-Diffusion Fronts with One Static and One Diffusing Reactant",
"url": "https://arxiv.org/abs/physics/9904008"
},
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