Data-Informed Mathematical Characterization of Absorption Properties in Artificial and Natural Porous Materials
For cultural heritage conservation, this provides a reliable tool to characterize absorption in porous materials, though it is an incremental application of existing methods.
The study characterizes water absorption in porous materials (marble, travertine, wackestone, mortar) using experiments and mathematical modeling, developing a noise-reducing fitting procedure and PDE simulation. The method effectively distinguishes material properties and aids cultural heritage preservation.
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.