Stable, quasi-stable and unstable physicochemical hydrodynamic flows in thin-layer cell electrodeposition

Electrodeposition in thin cells of different orientations relative to gravity leads to dendrite growth with a uniform front of the growing tips or to a hierarchy of branch sizes, competing with stable, quasi-stable or unstable physicochemical hydrodynamic flows. Here we report experimental measurements of electrodeposition in cells in the vertical position and we introduce a theoretical model predicting many features of these experiments. When the cathode is above the anode, our model predicts that the flow remains globally stable as long as there is no dendrite growth; when dendrites are present, zones of lowered concentration adjacent to a downwards growing finger appears, inducing a gravity driven convective vortex roll wrapped to the finger, leading to a quasi stable flow. In a vertical cell with the anode above the cathode, our model predicts the existence of an unstable flow in the form of vortex tubes or plumes detaching from each electrode, expanding toward one another and mixing. For both cases, in the presence of dendrites, the existence of an electrically driven vortex ring at the dendrite tip is predicted; it allows fluid to penetrate the dendrite tip and to be ejected from its side.