Fragmentation Transition for Invasion Percolation in Hydraulic Gradients

Abstract

Air injected into a two-dimensional porous medium displaced a flowing defending fluid. At low flow rates the invading air formed chains of fractal clusters similar to those observed in gradient percolation. The defending fluid was excluded from the invading region and moved around the invading clusters. Above a critical flow rate the invaded region fragmented into a plumelike structure that permitted the defending fluid to flow through the invaded region. Invasion percolation simulations, modified to include fragmentation and pressure gradients due to flow, describe the observations well.