Single and two-scale sharp-interface models for concrete carbonation : asymptotics and numerical approximation

We investigate the fast-reaction asymptotics for a one-dimensional reaction-diffusion system describing the penetration of the carbonation reaction in concrete. The technique of matched-asymptotics is used to show that the reaction-diffusion system leads to two distinct classes of sharp-interface models. These correspond to different scalings of a small parameter $\epsilon$ representing the fast-reaction and defined here as the ratio between the characteristic scale of diffusion for the fastest species and the characteristic scale of the carbonation reaction. We explore three conceptually different diffusion regimes in terms of the behavior of the effective diffusivities for the driving chemical species. The limiting models include one-phase and two-phase generalized Stefan moving-boundary problems as well as a nonstandard two-scale (micro-macro) moving-boundary problem---the main result of the paper. Numerical results, supporting the asymptotics, illustrate the behavior of the concentration profiles for relevant parameter regimes.