DIFFUSION-LIMITED AGGREGATION WITH SURFACE-TENSION - SCALING OF VISCOUS FINGERING

Viscous fingers have been generated on square lattices of L×L sites using the diffusion-limited aggregation model plus a simple rule that we propose to take into account surface tension. The wi dths of the generated viscous fingers, as well as mass (m) of the dislodged fluid, depend properly on the capillary number (Ca): They fulfill the hydrodynamic scaling relations Ca-1/2f(Ca1/2L) and m=Ca-1g(Ca1/2L). In addition, mCa-[(d-D)/2]LD in the physically interesting regime (a is the lattice constant, d=2, and D1.6 in our simulations). © 1990 The American Physical Society.