Front Tracking in Thin-Layer Electrodeposition

Abstract

We present an experimental and theoretical study of front interaction during the growth of patterns in thin-layer electrochemical deposition. Simultaneous schlieren and particle image velocimetry techniques are used to follow front development of concentration fields and convection rolls in gravitoconvection prevailing flows. A theoretical model describing full front nonlinear interaction taking into account diffusive, migratory and convective motion of ions in a viscous fluid subject to an electric field is presented. The equations are written in terms of a set of dimensionless numbers showing the significance of the gravity Grashof number in a gravitoconvection prevailing regime. Our experiments reveal that concentration and gravity driven convection fronts which develop near the electrodes coincide and that the two evolve together. Prior to the appearance of rough growth, cathodic and anodic concentration and convective fronts are parallel to the electrodes. After branching develops, the cathodic fronts become slaved to the deposit front, all three growing linearly in time. Our model predicts that, in the parallel flow regime, the convective and concentration fronts coincide, both scaling first as t ^4/5 and then slowing down to t ^1/2 , as it is observed in our experiments. After branching develops, this behavior applies only to the anodic front.