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.
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.
