Hele-Shaw Invasion: Laplacian Growth & Trapped Pockets

A Hele-Shaw cell — two glass plates a hair's width apart — is the textbook 2D setting for viscous fingering, and this simulator treats it as one: rather than reusing the 3D pore network's flat "distance from inlet" stand-in for viscous stabilization, it solves the real Laplace pressure equation over the defending fluid by numerical relaxation every frame, then invades the frontier site the solved field and the Saffman-Taylor stability sign (1−M)/(1+M) say should grow next. A second, independent computation — a live connectivity flood-fill from the outlet — finds every pocket of defending fluid the advancing front has sealed off, the trapped, bypassed saturation that real 2D coreflood and micromodel experiments live with far more than an idealized 3D lattice does. Sweep capillary number and viscosity ratio to move between chaotic capillary fingering, runaway fractal viscous fingering and broad stable displacement, and watch the trapped-pocket fraction grow alongside the fingers that create them.