Effect of low-frequency AC forcing on the morphological instability arising in electrodeposition

Electrodeposition in the presence of a DC field is an unstable process leading to morphological patterns on the cathode. The effect of a low-frequency and small amplitude AC forcing superimposed on a base DC field, \(\Delta V\), is investigated by perturbation theory and Floquet analysis. It is shown that we can forecast the stability behavior of the AC problem from the nature of the graph of electrode base speed, U, versus \(\Delta V\). The key finding is this: when this graph is always of negative curvature, the effect of AC forcing is stabilizing, whereas when the curvature changes sign, the effect of AC forcing can be either destabilizing or stabilizing. The difference in the two types of U–\(\Delta V\) curves is characterized by a single dimensionless group that signals the change from diffusion-controlled transport to transport controlled by reaction kinetics at the electrodes. The critical value of this parameter that marks the transition is obtained analytically.