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

Abstract

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 τ the width of the carbonated region is proportional to √ τ , while the width of the reaction front is proportional to τ p−1 2(p+1) for carbonation-reaction rates with a power law structurewhere 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 CO 2 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 We offer an alternative to the (asymptotic) √ τ expression of the carbonation-front position obtained in Papadakis et al. (AIChE J. 35:1639(AIChE J. 35: , 1989).

Interface conditions for fast-reaction fronts in wet porous mineral materials: the case of concrete carbonation

“…Similar dimensional arguments suggest that the speed of the reaction strip is directly proportional to 1/ . Motivated by the results reported in [38][39][40], we expect that algebraic connections between and the partial reaction orders p and q (see (23)) can be obtained for models of types 1-3 at least for large times. A singular perturbation study may recover the sharp interface setting via shrinking the reaction strip as goes to zero.…”

Cost-effective design of reinforced concrete with use of self-terminated carbonation model

“…The most common model used by most of the researchers (e.g. mentioned before [6][7][8][9][10][11][12][13][14][15][16][17]) as a basic model that determines the depth of carbonation, x after the time of exposure, t can be expressed in the form:…”

Modelling of concrete carbonation; is it a process unlimited in time and restricted in space?

“…the amount of material flowing through a unit cross section per unit time mol/m 2 s, D -is the diffusion coefficient m 2 /s, ϕ -is the concentration of the diffusing substance mol/m 3 , x -is the way of diffusion, m. Fick's first law allows to describe the diffusion process under a constant, unchanging in time, density of the diffusion flux [12,13].…”

“…This model is used by most researchers, for example, Bars et al [15], Burkan et al [16], Hossain et al [17], Ishida and Maekawa [18,19], Loo et al [20], Masuda [21]. These Ming Liang et al [22], Monteiro et al [23], Muntean [13], Steffens et al [24] as a basic model that determines the depth of carbonation x after the time of exposure t in the concentration of CO 2 equal to ϕ ext :…”