Asymptotics of reactiondiffusion fronts with one static and one diffusing reactant
Abstract
The longtime behavior of a reactiondiffusion front between one static (e.g. porous solid) reactant A and one initially separated diffusing reactant B is analyzed for the meanfield reactionrate density R( ρ_{A}, ρ_{B})= kρ_{A}^{m}ρ_{B}^{n}. A uniformly valid asymptotic approximation is constructed from matched selfsimilar solutions in a “reaction front” (of width w∼ t^{α}, where R∼ t^{β} enters the dominant balance) and a “diffusion layer” (of width W∼ t^{1/2}, where R is negligible). The limiting solution exists if and only if m, n≥1, in which case the scaling exponents are uniquely given by α=( m1)/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 higherorder kinetics ( m, n>1), such as the broadening of the reaction front and the slowing of transients, are also discussed.
 Publication:

Physica D Nonlinear Phenomena
 Pub Date:
 December 2000
 DOI:
 10.1016/S01672789(00)001408
 arXiv:
 arXiv:physics/9904008
 Bibcode:
 2000PhyD..147...95B
 Keywords:

 Physics  Chemical Physics;
 Condensed Matter;
 Mathematics  Analysis of PDEs
 EPrint:
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