Diffusion-limited aggregation and viscous fingering in a wedge: Evidence for a critical angle

We show that both analytic and numerical evidence points to the existence of a critical angle of η≈60°–70° in viscous fingers and diffusion-limited aggregates growing in a wedge. The significance of this angle is that it is the typical angular spread of a major finger. For wedges with an angle larger than 2η, two fingers can coexist. Thus a finger with this angular spread is a kind of building block for viscous fingering patterns and diffusion-limited aggregation clusters in radial geometry.