Hydrodynamic instability and the structural phase transition in diffusion-limited aggregation with drift

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Abstract
The Saffman-Taylor instability is extended to diffusive systems with an imposed drift. Under uniform motion of the interface with velocity V, the modified Saffman-Taylor instability is found to occur in the growth process. When the strength of the attractive drift becomes larger than a critical value, the flat interface is stabilized. The structural phase transition from dense aggregation, through diffusion-limited aggregation, to the needle pattern, which occurs when the direction of the drift changes, gives evidence for the presence of a hydrodynamic instability. The morphology diagram is obtained to describe distinct patterns in the diffusion-limited aggregation with drift. The similarity to viscous fingering under a gravitational field is discussed.