Saffman-Taylor Viscous Fingering

Instability when μ₁ > μ₂: growth rate σ = (k/μ̄)·(μ₁−μ₂)/(μ₁+μ₂)·U − T·k³/(μ₁+μ₂)
15
1.0
0.8
3
Low-viscosity fluid (oil) displaces high-viscosity fluid (water) in a Hele-Shaw cell. The Saffman-Taylor instability causes fingers to grow; surface tension selects wavelength λ* ∝ √(T/U·Δμ).