An Integro-differential Model of Cadmium Yellow Photodegradation

TL;DR

This paper introduces a mathematical model for cadmium yellow pigment degradation in paintings, combining chemical reactions and environmental influences, with a new numerical method for accurate simulation and sensitivity analysis.

Contribution

It presents a novel integro-differential model for cadmium yellow photodegradation and a positivity-preserving numerical scheme for reliable simulations.

Findings

The model accurately captures degradation mechanisms.

The numerical method ensures stable and reliable simulations.

Sensitivity analysis identifies key factors affecting degradation.

Abstract

Many paintings from the 19th century have exhibited signs of fading and discoloration, often linked to cadmium yellow, a pigment widely used by artists during that time. In this work, we develop a mathematical model of the cadmium sulfide photocatalytic reaction responsible for these damages. By employing non-local integral operators, we capture the interplay between chemical processes and environmental factors, offering a detailed representation of the degradation mechanisms. Furthermore, we present a second order positivity-preserving numerical method designed to accurately simulate the phenomenon and ensure reliable predictions across different scenarios, along with a comprehensive sensitivity analysis of the model.