A Free-Boundary Model of Corrosion

Deterioration of copper and bronze artifacts is one of the main concerns for people working in cultural heritage. In particular a significant effort has been devoted to study the corrosion due to environmental conditions, such as temperature, moisture and the concentration of pollutants. We introduce a mathematical model able to describe the corrosion effects on a copper layer, which is subject to deposition of SO ₂. The present model is based on a partial differential equation system with a double free boundary for monitoring and detecting copper corrosion products (mainly brochantite and cuprite).We assume to have a copper sample on which is formed a non protective oxide layer (Cu ₂ O), and, over this layer, a corrosion product (brochantite) grows. We aim to create a new approach to forecasting corrosion behavior without the necessity of an extensive use of laboratory testing using chemical-physical technologies, while taking into account the main chemical reactions. Although the model was kept simple, just describing the main reaction and transport processes involved, the mathematical simulations and the related model calibration are in agreement with the laboratory experiments.