Two-scale model for aggregation and etching

We propose a dual scale drift-diffusion model for interfacial growth and etching processes. The two scales are (i) a depletion layer width ΔW surrounding the aggregate, and (ii) a drift length l. The interplay between these two antithetical scales yields a variety of distinct morphologies reported in electrochemical deposition of metals, in viscous fingering in fluids, and in porous silicon formation. Further, our algorithm interpolates between existing growth models (diffusion limited aggregation, ballistic deposition, and Eden) for limiting values of ΔW and l.