An Integro-differential Model of Cadmium Yellow Photodegradation

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.