Viscous Fingering Lab simulates the Saffman-Taylor instability — the branching pattern that forms when a less viscous fluid (like air) is injected into a more viscous fluid (like oil) confined between two closely spaced plates (a Hele-Shaw cell). The interface between the two fluids becomes unstable and develops finger-like protrusions that repeatedly split at their tips.
The shader models this instability using the Mullins-Sekerka dispersion relation, which describes how different wavelength perturbations grow at different rates — short wavelengths are stabilized by surface tension while long wavelengths are driven by the pressure gradient. The competition produces a characteristic branching scale. The tip-splitting cascade creates ever-finer branches as fingers advance and bifurcate.
The advancing interface is highlighted with emission glow. Interactive controls adjust viscosity ratio, injection rate, surface tension, and the resulting branching morphology from broad fingers to fine dendritic structures.