摘要：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.
