Modeling Growth Pattern Formation In A Vertically Oriented Thin-Layer Cell Electrodeposition.

Abstract

Electrodeposition in a thin cell (ECD) in a vertical position, with the cathode above
the anode, yields a growth pattern formation whose signature is a dense branched morphology.
However, detailed analysis of front evolution reveals a complex competition between neighboring
branches leading to a locally fluctuating growth. Here we study the nature of this quasi
equilibrium growth through a new macroscopic model and its numerical simulation. The model,
based on first principles, uses the Nernst-Planck equations for ion transport, the Poisson equation
for the electrostatic potential, the Navier-Stokes equations for the fluid flow and a new
growth model, based on a Dielectrical Aggregation Model (DBM), for deposit growth. Numerical
simulations in realistic 3D cells using serial and parallel computing are presented; in the
latter use is made of domain decomposition techniques with a strongly implicit iterative method
implemented in a Beowulf cluster under MPI and Linux. This allows the utilization of very fine
grids with a more realistic physical parametrization and results in a robust scalable algorithm
attaining almost linear speedup. Theory and simulations suggest the detachment of the leading
branch from its neighbors, an enlargement of its tip in the form of a mushroom, and the presence
of vortex rings and vortex tubes wrapping the dendrite tip, in qualitative agreement with
experimental observations.