JournalsifbVol. 15, No. 2pp. 167–180

A free-boundary problem for concrete carbonation: Front nucleation and rigorous justification of the t\sqrt{{t}}-law of propagation

  • Toyohiko Aiki

    Japan's Women's University, Tokyo, Japan
  • Adrian Muntean

    Eindhoven University of Technology, Netherlands
A free-boundary problem for concrete carbonation: Front nucleation and rigorous justification of the $\sqrt{{t}}$-law of propagation cover
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Abstract

We study a one-dimensional free-boundary problem describing the penetration of carbonation fronts (free reaction-triggered interfaces) in concrete. Using suitable integral estimates for the free boundary and involved concentrations, we reach a twofold aim:

(1) We fill a fundamental gap by justifying rigorously the experimentally guessed t\sqrt{t} asymptotic behavior. Previously we obtained the upper bound s(t)Cts(t)\leq C'\sqrt{t} for some constant CC'; now we show the optimality of the rate by proving the right nontrivial lower estimate, i.e. there exists C>0C''>0 such that s(t)Cts(t)\geq C''\sqrt{t}.

(2) We obtain weak solutions to the free-boundary problem for the case when the measure of the initial domain vanishes. In this way, we allow for the {\em nucleation of the moving carbonation front} – a scenario that until now was open from the mathematical analysis point of view.

Cite this article

Toyohiko Aiki, Adrian Muntean, A free-boundary problem for concrete carbonation: Front nucleation and rigorous justification of the t\sqrt{{t}}-law of propagation. Interfaces Free Bound. 15 (2013), no. 2, pp. 167–180

DOI 10.4171/IFB/299