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 aggregation (DLA) algorithm which takes interpore surface tension and capillary forces into account. The inv~~g fluid is non-viscous. Cooperative effects are impo~nt when the ratio between capillary forces and tension forces q is rr 1. In that case we introduce a simple rule that considers the wetting displacement (invading fluid wets more ) and the non wetting case ( displaced fluid wets more ). We find qualitative agreement with the experiments of Stokes et. al. ( Phys.Rev. Lett. 57, 1718 (1986)). Furthermore, we study the tree trunk thickness of the patterns generated as a function of the control parameter r 0~ C;‘, ( C,= the capillary number) and study the geometry of the interface. We compare the results with the experiments.