A free-boundary problem for concrete carbonation: Front nucleation and rigorous justification of the $\sqrt{{t}}$-law of propagation
Toyohiko Aiki, Adrian Muntean · Interfaces and Free Boundaries Mathematical Analysis Computation and Applications · 2013
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 \sqrt{t} asymptotic behavior. Previously we obtained the upper bound s(t)\leq C'\sqrt{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)\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 nucleation of the moving carbonation front – a scenario that until now was open from the mathematical analysis point of view.