Invade lowest P_c neighbor | P_c ~ 1/r (capillary pressure) | Trapping: isolated defending clusters
Invasion percolation (Wilkinson & Willemsen 1983): Model for slow drainage in porous media. The invading fluid (wetting phase) advances by always entering the neighboring pore with lowest capillary threshold P_c. No global optimization — purely local rule generates fractal invasion front.
Trapping: When the defending fluid (non-wetting) is surrounded by invaders with no path to the outlet (bottom), it becomes trapped. Trapping makes the invasion front more compact (fractal dimension d_f ≈ 1.82 → 1.46 in 2D), increasing residual saturation.
Applications: Oil reservoir simulation (CO₂ sequestration), groundwater contamination, lung airway reopening (cascade dynamics), microfluidics. The invasion front is statistically equivalent to the hull of critical percolation clusters.