Laplacian growth instability: a less viscous fluid displaces a more viscous one, forming fractal fingers
0.08
1.50
0.15
Interface points: 0
Max radius: 0
Time: 0.0
Saffman-Taylor instability (1958): when a low-viscosity fluid (e.g., air) pushes into a high-viscosity fluid (e.g., oil) in a Hele-Shaw cell (two parallel plates), the interface is governed by Laplace's equation ∇²P = 0. The flat interface is unstable — perturbations grow because the pressure gradient is larger at finger tips (tip-splitting). Surface tension σ provides a stabilizing cutoff at small scales, selecting a finger width ~ σ/(viscosity × velocity). This is identical to diffusion-limited aggregation (DLA) in the zero-noise limit.