Asymptotics of reaction-diffusion fronts with one static and one diffusingreactant

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 (m)(A)rho (n)(B). A uniformly valid asymptotic approximation is con structed from matched self-similar solutions in a "reaction front" (of widt h w similar to t(alpha), where R similar to t(beta) enters the dominant bal ance) and a "diffusion layer" (of width W similar to t(1/2), where R is neg ligible). The limiting solution exists if and only if m, n greater than or equal to 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 commo n ad hoc approximation of neglecting reactions is given mathematical justif ication, and the exact transient decay of the reaction rate is derived. The physical effects of higher-order kinetics (m, n > 1), such as the broadeni ng of the reaction front and the slowing of transients, are also discussed. (C) 2000 Elsevier Science B.V. All rights reserved.