Viscous Fingering — Hele-Shaw / Saffman-Taylor

Saffman-Taylor instability (1958): when a less-viscous fluid pushes a more-viscous one in a Hele-Shaw cell, the flat interface is unstable. Perturbation growth rate σ_k = Vk(1−A) − Tk³b²/12μ where A=(μ₂−μ₁)/(μ₂+μ₁). Fastest-growing mode: k* = √(V(1−A)/(Tb²/4μ)). Beyond linear stage: dendritic/fractal branching. Connection to DLA, electrodeposition, oil recovery, tumor growth.