Uncovering the analytical Saffman-Taylor finger in unstable viscous fingering and diffusion-limited aggregation

Very unstable viscous fingers moving in a linear channel are investigated as well as diffusion-limited aggregates grown in a strip between two reflecting walls. In both cases a large number of independent runs are performed and the cell occupancy distribution is measured. It is shown that the zone of large occupancy has the width and shape of the Saffman-Taylor finger {λ}=0.5. Similarly, in sector-shaped cells, the width of the large occupancy region is the limit width of the stable fingers. In the case of a 90^∘{} cell, its shape is that of a predicted analytical solution.