Growth model for ramified electrochemical deposition in the presenceof diffusion, migration, and electroconvection

A growth pattern formation model for the macroscopic description of ramified electrochemical deposition is presented. The model describes the diffusive, migration and electroconvective motion of ions and its deposition in thin cells through the evolutionary two-dimensional Nernst-Planck equations for cation and anion concentration, the Poisson equation for the electric field, the Navier-Stokes equations for the laminar fluid flow and a dielectric breakdown model scheme for the random deposition of ions. A new set of dimensionless numbers governing the model regimes is introduced. We present numerical results showing that, for a given set of dimensionless numbers, the electroconvective forces produce vortex-tip interaction yielding a basic growth pattern formation mechanism, i.e., tip splitting and fanning. This mechanism gives a reasonable picture of reality.