Data-Informed Mathematical Characterization of Absorption Properties in Artificial and Natural Porous Materials

TL;DR

This paper combines laboratory experiments and mathematical modeling to characterize water absorption in porous materials, aiding cultural heritage preservation.

Contribution

It introduces a novel fitting and simulation framework to accurately determine absorption properties from experimental data.

Findings

Effective noise reduction in measurements

Validated PDE model for imbibition process

Reliable characterization of diverse porous materials

Abstract

In this work, we characterize the water absorption properties of selected porous materials through a combined approach that integrates laboratory experiments and mathematical modeling. Specifically, experimental data from imbibition tests on marble, travertine, wackestone and mortar mock-ups are used to inform and validate the mathematical and simulation frameworks. First, a monotonicity-preserving fitting procedure is developed to preprocess the measurements, aiming to reduce noise and mitigate instrumental errors. The imbibition process is then simulated through a partial differential equation model, with parameters calibrated against rough and smoothed data. The proposed procedure appears particularly effective to characterize absorption properties of different materials and it represents a reliable tool for the study and preservation of cultural heritage.