An ordinary differential equation model for the EIS generating process could be fruitful even if it fell short of predicting the results of actual processes with accuracy, at least in early, simplistic attempts.
An ODE model could explain phenomena that are generally accepted. For example, no one doubts that the rate of electrolysis falls off with the distance separating the electrodes. Does it fall off inversely as the distance itself? Or, as the square of the distance? The latter is the more likely answer (a priori) because it preserves the symmetry of displacement in the ODE. As another example, no one doubts that the electolysis process accelerates if allowed to proceed without current control or limitation. Yet the process will eventually limit itself by saturating, producing oxides or floating sol. So a sigmoid (S-shaped) signal for concentration vs. time would be expected for the ODE model. Such a sigmoid has an inflection point. What can it tell us? Maybe a lot. The process of electrolysis bears a strong resemblance to the charge carrier transport phenomena in semiconductor devices, it we view these processes abstractly, based on their ODEs. Charge carrier mobility is an important and fairly easily measured parameter. But a purely empirical approach to electrolysis might have a tough time finding a way to measure ion mobility. It takes at least a simple ODE model to explain how to find mobility. And finding charge mobilitycould have very practical, clinical implications. It may be tantamount to measuring charge sizes. Thus, a Poor-Man's ultramicroscopy substitute, perhaps. Best regards, Matthew
