Unfolding-based corrector estimates for a reaction-diffusion system predicting concrete corrosion

TL;DR

This paper develops corrector estimates for a reaction-diffusion model of concrete corrosion in sewer pipes using periodic unfolding, providing a rigorous framework for multiscale analysis of perforated domains.

Contribution

It introduces a novel application of periodic unfolding to derive corrector estimates for a complex, coupled reaction-diffusion system in perforated domains, advancing multiscale modeling techniques.

Findings

Derived corrector estimates for the upscaled model

Established solvability of the pore-scale reaction-diffusion system

Provided a convergence rate for the homogenization process

Abstract

We use the periodic unfolding technique to derive corrector estimates for a reaction-diffusion system describing concrete corrosion penetration in the sewer pipes. The system, defined in a periodically-perforated domain, is semi-linear, partially dissipative, and coupled via a non-linear ordinary differential equation posed on the solid-water interface at the pore level. After discussing the solvability of the pore scale model, we apply the periodic unfolding techniques (adapted to treat the presence of perforations) not only to get upscaled model equations, but also to prepare a proper framework for getting a convergence rate (corrector estimates) of the averaging procedure.