Hele-Shaw cell: less viscous fluid displacing more viscous fluid
Viscosity Ratio η20
Surface Tension γ30
Injection Rate4
Noise Level40
The Saffman-Taylor instability occurs when a less viscous fluid (e.g. air, water) is injected into a more viscous fluid (oil, glycerol) in a Hele-Shaw cell. The interface is unstable: small perturbations grow into finger-like protrusions. Finger width λ* ≈ 1/2 for large viscosity contrast. Surface tension stabilizes short-wavelength modes.