Viscous fingering: a less viscous fluid displaces a more viscous one — unstable interface grows fractal fingers
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Hele-Shaw / DLA model: The pressure satisfies Laplace's equation ∇²P=0 outside the growing region. The interface velocity is proportional to the pressure gradient (Darcy's law): v_n = -K·∂P/∂n. This creates the Saffman-Taylor instability — longer fingers grow faster (Laplacian screening), shorter fingers are suppressed. The result is fractal branching patterns identical to dielectric breakdown, coral growth, and mineral dendrites. Surface tension stabilizes at small scales; without it growth is ill-posed.