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 th at can grow in an electro-static field. Screening introduces a new len gth scale and a nontrivial dependence on the boundary conditions. Grow ing patterns can either have a fractal character (diffusion-limited-ag gregation-like) at scales shorter than the screening length, be simila r to the Eden model, or even be dense. A transition from dense to mult ibranched growth occurs at a point which depends on the potentials at the boundaries, the distance between them, and the screening length. S imulations 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 m eans of an analytical study of the instability, within a similar schem e to the one proposed by Mullins and Sekerka. The results are qualitat ively similar for growth in one and two dimensions. Finally, it is sho wn that, before the transition (dense growth), the aggregate reproduce s the shape of the outer electrode.