A model for lime consolidation of porous solids

TL;DR

This paper introduces a mathematical model for lime water impregnation in porous building materials, capturing chemical reactions and fluid flow to enhance structural integrity, with proven solution existence and supportive numerical results.

Contribution

The paper develops a novel 3D convection-diffusion model coupled with chemical reactions for lime consolidation, and proves the existence of solutions for physically relevant initial data.

Findings

Model aligns qualitatively with experimental observations

Solution existence is mathematically proven

Numerical tests support the model's validity

Abstract

We propose a mathematical model describing the process of filling the pores of a building material with lime water solution with the goal to improve the consistency of the porous solid. Chemical reactions produce calcium carbonate which glues the solid particles together at some distance from the boundary and strengthens the whole structure. The model consists of a 3D convection-diffusion system with a nonlinear boundary condition for the liquid and for calcium hydroxide, coupled with the mass balance equations for the chemical reaction. The main result consists in proving that the system has a solution for each initial data from a physically relevant class. A 1D numerical test shows a qualitative agreement with experimental observations.