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 Nemst-Planck equations for the concentration of the solute, coupled to an equation for the dectric 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 f%actal to dense branch mo~holo~ and, in particular, the interplay of the electroconvective, migration and diffusive motion of the ions near the growing tips.