A free-boundary problem for concrete carbonation: Front nucleation and rigorous justification of the √t-law of propagation

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 root t asymptotic behavior. Previously we obtained the upper bound s(t) <= C'root t for some constant C'; now we show the optimality of the rate by proving the right nontrivial lower estimate, i.e., there exists C '' > 0 such that s(t) >= C '' root 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 nucleation of the moving carbonation front - a scenario that until now was open from the mathematical analysis point of view.