A paper whose writing Principal Adam Powell led for the May 2007 issue of JOM summarizes electrochemistry modeling techniques over all lengthscales; that paper reference is:
The goal of macroscopic modeling is to predict the distribution of current
density at the electrodes for various process design parameters. This enables
the engineer to control the uniformity of metal plating, to determine whether
some regions will plate with a rough instead of smooth surface, and to
calculate the distribution of heat generation in some processes. Such modeling
is also crucial for the design of cathodic protection systems for corrosion
prevention.The image on the right shows the output of a boundary element simulation of molten salt magnesium electrowinning using solid oxide membranes (SOM). The three blue test tube-shaped electrodes are the anodes, which are encased in a yttria-stabilized zirconia SOM, which permits oxygen ions to pass through but blocks electrons. The uniform blue color indicates that the current density through the SOM is uniform, resulting in uniform heat generation. This is very important to maintaining the integrity of the fragile ceramic membranes. The other tubes are stainless steel cathodes where magnesium gas is produced. The intensely localized red color indicates high cathodic current, and thus the location where most of the magnesium vapor is produced.
Boundary element modeling using the open source Julian package is a robust method for macroscopic electrochemistry modeling. The SOM processes for producing magnesium, titanium and tantalum, and for deoxidizing copper, are described in the following paper:
Electroplating is an inherently unstable process, in that it tends to form a
rough deposit made up of tiny metal dendrites. It is possible to avoid this by
either using very low current (which is slow), or periodically reversing the
current, or adding chemical additives to the plating bath. In some
circumstances, such as the production of powder metal, this can be beneficial:
one can control the shape and rate of growth of metal powder particles. In
other circumstances, one can tune the current over time to engineer the shape
of dendrites in a rough deposit.In these cases, a microscopic model is helpful for predicting and understanding how such deposited structures will form. Phase field is a method for calculating the formation of dendritic structures, which was first used to simulate spinodal decomposition and dendritic solidification. My research group at MIT first used it to simulate electrochemical deposition processes such as electroplating and liquid metal reduction from a molten salt or slag.
Useful results of such calculations include: