Effect of growing interface on the diffusion-limited aggregation: Crossover from the diffusion-limited-aggregation fractal

A generalization of the diffusion-limited-aggregation model is introduced to take into account the effect of the velocity of the moving interface. The growth process is governed by the diffusion field with a convection induced by the growing interface. In the limit of a slow-moving interface, the convection is approximated to be proportional to the local mass flow with changing sign. The convective diffusion field is simulated by the biased-random walker. The development of the distinct morphologies is found with varying strength of the growing interface. The velocity of the moving interface is governed by the dimensionless parameter χ=(${\rho }_g$/${\rho }_a$)ΔC, where ${\rho }_a$ is the density of the aggregate, ${\rho }_g$ the density of the diffusing particles in the diffusion field, and ΔC the concentration difference between the aggregate and the outer boundary. With the increase of χ, the aggregate crosses over to the dense aggregation with the flat interface. The moving interface acts as a stabilizing force on the interface. In the case of a negative χ, the aggregate crosses over to the needle crystal. The growing interface acts as a destabilizing force. The similarities with the pattern formation in the electrochemical deposition and solidification are discussed.