COOPERATIVE EFFECTS DUE TO INTERPORE SURFACE-TENSION IN UNSTABLE DISPLACEMENT IN POROUS-MEDIA

We model fluid-fluid displacement in d=2 by a diffusion limited aggreg ation (DLA) algorithm which takes interpore surface tension and capill ary forces into account. The invading fluid is non-viscous. Cooperativ e effects are important when the ratio between capillary forces and te nsion forces q is congruent to 1. In that case we introduce a simple r ule that considers the wetting displacement (invading fluid wets more) and the non wetting case ( displaced fluid wets more). We find qualit ative agreement with the experiments of Stokes et. al. ( Phys. Rev. Le tt. 57, 1718 (1986)). Furthermore, we study the tree trunk thickness o f the patterns generated as a function of the control parameter r prop ortional to C-a(-1), (C-a = the capillary number) and study the geomet ry of the interface. We compare the results with the experiments.