An effective nonlinear boundary condition for a corroding surface. Identification of the damage based on electrostatic data.

We give a formal derivation of an effective nonlinear boundary condition associated with an electrostatic voltage potential on a corroding metal surface. Subsequently we use this boundary condition to analyze the determination of corrosion damage based on measurements of the boundary voltage potential and the associated current flux. 1 Introduction A central objective of this paper is to derive an effective nonlinear boundary condition for an electrostatic voltage potential on a rough metal surface covered by a thin layer of a corrosive fluid. Our motivation is the desire to develop nondestructive evaluation techniques that are capable of determining corrosion damage from boundary voltage and current data. The derivation of the effective boundary condition is based on a multiscale asymptotic expansion and the use of a potential model for the electrostatic problem in the fluid as well as in the metal component. The normal current is assumed to be continuous across the fluid-metal inter..