其他摘要：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.
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