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

TL;DR

This paper develops and analyzes sharp-interface models for concrete carbonation using asymptotic methods, revealing different regimes and including numerical validation of concentration profiles.

Contribution

It introduces a novel asymptotic approach to derive one- and two-scale sharp-interface models for concrete carbonation, including new micro-macro moving-boundary problems.

Findings

Derived three distinct sharp-interface models for carbonation.

Identified regimes where one-phase, two-phase, and micro-macro models apply.

Numerical results support the validity of the asymptotic models.

Abstract

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 \epsilon representing the fast-reaction. Here \epsilon 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 \epsilon) 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.