Mathematical modelling of the oxidation of nickel titanium alloys

A one-dimensional bulk reaction model for the oxidation of nickel titanium is formulated, with preferential oxidation of titanium being included. The modelling is directed at the better understanding of the dominant mechanisms involved in the oxidation process and their significance for the biocompatibility of the alloy. Two different regimes for the relative diffusivities of oxygen and the metals are investigated. By assuming fast bulk reactions, different asymptotic structures emerge in different parameter regimes and the resulting models take the form of moving boundary problems. Different profiles of nickel concentration are obtained: in particular a nickel-rich layer (observed in practice) is present below the oxide/metal interface for the case when oxygen and the metals diffuse at comparable rates.