Invasion Percolation with Trapping

Drainage front morphology, capillary pressure thresholds, and trapped clusters
Invade lowest P_c neighbor  |  P_c ~ 1/r (capillary pressure)  |  Trapping: isolated defending clusters

Controls

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Invaded cells
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Trapped cells
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Saturation
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Front size
Invading fluid
Trapped clusters
Defending fluid
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.