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 (RD) system describing the penetration of the carbonation reaction in concrete. The technique of matched-asymptotics is used to show that the RD system leads to two distinct classes of sharp-interface models, that correspond to different scalings in a small parameter e representing the fast-reaction. Here e is the ratio between the characteristic scale of the diffusion of the fastest species and the one of the carbonation reaction. We explore three conceptually different scaling regimes (in terms of e) of the effective diffusivities of the driving chemical species. The limiting models include one-phase and two-phase generalised 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. Keywords: Concrete carbonation; Reaction layer analysis; Matched asymptotics; Fast-reaction asymptotics; two-scale sharp-interface models; numerical approximation of reaction front