A macroscopic model for growth pattern formation of ramified copper electrodeposits

This is a first attempt to construct a macroscopic model for the description of growth pattern formation in copper electrodeposits. The theoretical model is formulated as a Stefan-like problem consisting in the Nernst-Planck equations for the concentration of the solute, coupled to an equation for the electric potential and the Navier-Stokes equations for the solvent, with a moving boundary. A discrete version of these equations in a DBM scheme with a random moving boundary constitutes the computational model. Preliminary numerical results show that, with a proper variation of the relevant control parameters, the model proposed is able to describe from fractal to dense branch morphology and, in particular, the interplay of the electroconvective, migration and diffusive motion of the ions near the growing tips.