Geometric effects on surface roughness in electrodeposition

Our aim is to understand the early stages of roughness growth in electrodeposition. We present a study of the branching of steady planar electrode surfaces to steady non-planar electrode surfaces as the voltage imposed at a cathode is decreased through its critical value. We aim to discover the type of branching and to learn whether or not the new branches can be detected by measuring the current. The cross-sectional shape of the electrode makes a difference. Circular electrodes lead to transcritical branching; ordinarily, rectangular electrodes lead to a pitchfork, sometimes forward and sometimes backward.