PATTERN-FORMATION IN SCREENED ELECTROSTATIC FIELDS - GROWTH IN A CHANNEL AND IN 2 DIMENSIONS

It is shown that screening greatly diversifies the type of patterns that can grow in an electro-static field. Screening introduces a new length scale and a nontrivial dependence on the boundary conditions. Growing patterns can either have a fractal character (diffusion-limited-aggregation-like) at scales shorter than the screening length, be similar to the Eden model, or even be dense. A transition from dense to multibranched growth occurs at a point which depends on the potentials at the boundaries, the distance between them, and the screening length. Simulations are carried out in one dimension (growth in a channel) and in two dimensions (with different shapes for the outer electrode). The transition from dense to filamentary growth is also investigated by means of an analytical study of the instability, within a similar scheme to the one proposed by Mullins and Sekerka. The results are qualitatively similar for growth in one and two dimensions. Finally, it is shown that, before the transition (dense growth), the aggregate reproduces the shape of the outer electrode.