## Fractal fingers and zero surface tension

Ah always thought a fingering instability was what happened after a misunderstanding on a first date.

But apparently it’s also a hydrodynamic phenomenon, when one fluid displaces another.

This kinda displacement is a complex process; so complex that in most cases it is mathematically intractable. Ya just gotta try it and see.

However, one of the few mathematically tractable examples is the 2-dimensional case of a less viscous fluid displacing a more viscous neighbor with zero surface tension.

The math predicts that fractal-like fingers of the less viscous fluid should penetrate the more viscous one.

And that’s exactly what happens. And here’s the proof, the picture above taken by Sid Nagel and colleagues at the University of Chicago. The grey area is tiny glass beads that have been sandwiched in a thin layer between two flat plates. The black area is air injected into the plates.

The glass beads behave like a liquid but because there are no forces between them, the surface tension is zero. And the air indeed displaces its more viscous neighbor forming a fractal pattern, just as the math predicts.

A neat experiment. Next up, those awkward Prom moments.

Ref: arxiv.org/abs/0712.2019: Toward the Zero Surface Tension Limit: The Granular Fingering Instability