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 matchedasymptotics
is used to show that the reaction-diffusion system leads to two distinct classes of sharpinterface
models. These correspond to different scalings of a small parameter 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.