  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.
