Laplacian Growth at Reaction Surface

Abstract

Laplacian growth at reaction surface is considered to study the effect of surface reaction on the diffusion-limited aggregation (DLA). A two-parameter renormalisation-group method is developed to investigate the crossover phenomenon between the reaction-limited aggregation and the diffusion-limited aggregation. The global flow diagram in the two-parameter space is obtained. it is found that there are two nontrivial fixed points, the Eden point and the DLA point. The Eden point presents the reaction-limited aggregation. The DLA point corresponding to the DLA fractal is stable in all directions, while the Eden point is a saddle point. When the reaction rate is small, the aggregate crosses over from the dense structure on small length scales to the DLA fractal on large length scales. When the order m of reaction is not equal to one, the concentration of diffusing particles has an important effect upon the crossover.