Abstract
We model fluid-fluid displacement in d=2 by a diffusion-limited-aggregation (DLA) algorithm which takes random capillary forces into account. Interpore surface tension is neglected. The invading fluid is nonviscous. We find a crossover length . On length scales much smaller (larger) than , invasion percolation (DLA) patterns are obtained. We argue by scaling, and check by simulations, that ∼(Δp̃/Ca), Δp̃ stands for a measure of spatial variations of the capillary pressure, Ca is the capillary number, and is the interface fractal dimension on small length scales (we find =1.3).
- Received 24 June 1991
DOI:https://doi.org/10.1103/PhysRevLett.67.2958
©1991 American Physical Society