Pattern formation in nonlinear diffusion-limited aggregation

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Abstract
The effect of concentration-dependent diffusivity on diffusion-limited aggregation (DLA) is investigated by a computational method. The growth process is governed by a nonlinear diffusion equation with a concentration-dependent diffusivity. The aggregate grows proportionally to the mass flux on the surface of the aggregate. The development of distinct morphologies is found in nonlinear diffusive pattern-forming systems. When the dependence of diffusivity on the concentration increases, the aggregate crosses over from the DLA fractal to dense aggregation. The crossover phenomenon also occurs with an increase of the concentration difference between the aggregate and the outer boundary. A new dimensionless parameter is found to govern the crossover phenomenon. The morphology diagram is described in terms of the coefficient of the nonlinear part of the diffusivity and the concentration difference between the boundaries. Similarity with pattern formation in electrochemical deposition is discussed.