Surface tension selects finger width λ = 1/2 in Hele-Shaw flow
When a less viscous fluid (air) is injected into a more viscous fluid (oil) in a thin Hele-Shaw cell, the interface is unstable (Saffman-Taylor instability). Surface tension selects a unique steady finger of relative width λ ≈ 1/2. Below the critical B, tip-splitting occurs and fingers compete. The finger shape is given by exact conformal mapping x + iy = z − (1−λ)/π · log((1+e^{πz})/(2)).