Abstract
A generalized three-dimensional model for ion transport in electrodeposition is introduced. Ion transport is mainly governed by diffusion, migration, and convection. When convection prevails, in particular, in the limiting case of gravity-driven convection, the model predicts concentration shells and convection rolls and their interaction mode with a deposit tip: shell and roll bend and surround the tip forming a three-dimensional envelope tube squeezed at the deposit tip. In the limiting case of electrically driven convection, a vortex ring and an electric spherical drop crowning the deposit tip are predicted. When gravity and electric convection are both relevant, the interaction of ramified deposits, vortex tubes and rings, and electric spherical drops, leading to complex helicoidal flow, is predicted. Many of these predictions are experimentally observed, suggesting that ion transport underlying dendrite growth is remarkably well captured by our model.
Highlights
In a thin-layer electrochemical depositionECDexperiment, the electrolytic cell consists of two glass plates sandwiching two parallel electrodes and a metal salt electrolyte
In particular, in the limiting case of gravity-driven convection, the model predicts concentration shells and convection rolls and their interaction mode with a deposit tip: shell and roll bend and surround the tip forming a three-dimensional envelope tube squeezed at the deposit tip
When dendrites grow through an electrochemical thinlayer cell, they encounter complex 3D ion transport phenomena
Summary
In a thin-layer electrochemical depositionECDexperiment, the electrolytic cell consists of two glass plates sandwiching two parallel electrodes and a metal salt electrolyte. Issues of ECD are pertinent in the cases of bipolar electrodeposition22,23͔ in the field of macrowiring, in which an applied electric field can be exploited to create directional growth of copper deposits between copper particles that are not connected to an external circuit, and in microwiring, in the assembly of a new class of microwires by dielectrophoresis from suspension of metallic nanoparticles24͔ In both techniques a complex flow near the tips of the growing wire was observed. The ion concentration is decreased as metal ions are reduced and deposited out and anions drift away These concentration variations lead to density variations, and to the development of gravity-driven convection rolls at the electrodes12͔. This is illustrated, showing schlieren images of the cathodic and anodic concentration rollsbright pixelsnear the cathode and anodedark pixels, respectively, and in Fig. 4 ͑reproduced from Ref.
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