On the interplay between fast reaction and slow diffusion in the concrete carbonation process: a matched-asymptotics approach

A matched-asymptotics approach is proposed to show the occurrence of two distinct characteristic length scales in the carbonation process. The separation of these scales arises due to the strong competition between reaction and diffusion effects. We show that for sufficiently large times t the width of the carbonated region is proportional to , while the width of the reaction front is proportional to for carbonation-reaction rates with a power law structure like k[CO2] p [Ca(OH)2] q , where k>0 and p,q>1 and identify the proportionality coefficient asymptotically. We emphasize the occurrence of a water barrier in the reaction zone which may hinder the penetration of CO2 by locally filling with water air parts of the pores. This non-linear effect may be one of the causes why a purely linear extrapolation of accelerated carbonation test results to natural carbonation settings is (even theoretically) not reasonable. Finally, we compare our asymptotic penetration law against measured penetration depths from Bune (Zum Karbonatisierungsbedingten Verlust der Dauerhaftigkeit von Außenbauteilen aus Stahlbeton, 1994). The novelty consists in the fact that the factor multiplying is now identified asymptotically by solving a non-linear system of ordinary differential equations, and hence, fitting arguments are not necessary to estimate its size. We offer an alternative to the (asymptotic) expression of the carbonation-front position obtained in Papadakis et al.