Modelling electrochemistry in metallurgical processes

Mathematical modeling is an important tool for the development of materials and processes for making them. Modeling electrochemical processes for smelting or plating metals presents several particularly difficult challenges. Boundary conditions are nonlinear and time dependent, often because phenomena at multiple length scales are inextricably linked. For example, the Angstrom-scale double layer gives rise to nonlinear voltage-current behavior which is a boundary condition for macroscopic models. And development of micrometer-scale dendrites dramatically changes both the product form and the apparent resistance at the interface; chemical additives can suppress dendrites and produce super conformal filling of very rough surfaces. This paper gives an overview of modeling approaches at all length scales from Angstroms to meters, including both mean field and atomistic approaches.