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 invading fluid is non-viscous. Cooperative effects are important when the ratio between capillary forces and tension forces q is 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 ∞ Ca−1, (Ca = the capillary number) and study the geometry of the interface. We compare the results with the experiments.