This research project is concerned with modeling the flow and transport in electrochemical systems with significant shape change effects. Typical examples are electrochemical deposition and etching processes. While the diffusion dominated limit will be studied, the main focus is on systems with significant convective transport effects. The research utilizes a Galerkin finite element method coupled with an adaptive mesh technique implemented on a Class VI computer to solve the appropriate continuum models. The development of such techniques coupled with numerical experiments will allow the technical community to gain new insights into the fundamentals of such processes, as well as provide for the possibility of predicting "operating windows" and forecasting scale-up problems in the commercialization of such processes.