Viscous Fingers and Diffusion-Limited Aggregates near Percolation

Viscous fingers (VF) and diffusion-limited aggregates (DLA) are shown to exhibit different features when they grow on dilute percolating networks. On the infinite incipient cluster at the site-percolation threshold pc on the square lattice, both fractal dimensionalities are DVFDDLA1.3, but the mass amplitudes obey AVFADLA1.3. The effective DVFᵉᶠᶠ seems to increase for wider pores, while DDLAᵉᶠᶠ remains 1.3. For p>pc, the crossover to homogeneous behavior is very slow, and 1.3<DDLAᵉᶠᶠ<DVFᵉᶠᶠ<1.7.