Published online 28 January 2008 | Nature | doi:10.1038/news.2008.531

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Gas fingers in glass beads confirm fluid-theory prediction.

Snowflake: injected gas makes a fractal-shaped intrusion in a plate of glass beads. Courtesy of the researchers

Researchers have confirmed a previously unobserved property of fluids by watching the fractal expansion of a pocket of gas into a thin layer of glass beads.

The experiment adds detail to the understanding of a phenomenon called ‘viscous fingering’, which has been studied for more than 50 years. When two fluids with different viscosities are mixed together, the more freely flowing fluid expands in finger-shaped intrusions into the other fluid. This has been observed in many different systems, including between fine grains such as sand1.

One prediction of models of viscous fingering is that, in fluids with no surface tension, the interface of the fluids should be riddled with points. Although there has been some effort to look for this in fluids2, no one has yet been successful; adding surfactant can help to reduce surface tension in liquids, but not eliminate it. The remaining surface tension — the interaction between fluid molecules — and thermal motion tends to smooth out any rough edges.

Fractal patterns

To investigate a situation with surface tension as near zero as possible, Xiang Cheng of the University of Chicago set up an experiment with small glass spheres less than half a millimetre in diameter, like course, uniform sand. Granular systems like this involve very little surface tension, because there is little attraction between grains — Cheng and his colleagues estimate the surface tension in their glass bead system to be roughly a million times less than in water or ethyl alcohol. Cheng sandwiched the beads between two transparent circular plates and pushed nitrogen gas into the mass of beads through a small hole in the centre of one of the plates.

At high pressures, the nitrogen quickly blew all the beads to the edges of the plates. But if the gas was pushed in very slowly, with just enough pressure to shuffle grains along, it expanded in finger-shaped intrusions into the mass of beads; the dimensions of these intrusions match those seen in fluids. But, unlike the behaviour of fluids, the boundaries between the gas and the beads were studded with points. The resulting 'snowflake' shape has fractal qualities — small parts of the shape look very similar to the shape as a whole.

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“People knew in theory that when the surface tension goes to zero, you would see this behaviour,” says Cheng. “This is the first time we can see that shape in a real experiment.” The results are published this week in Nature Physics3.

Although the mass of beads behaved like a fluid in some ways, it also showed some properties that seem unique to a granular system. The faster a finger formed, the bigger it got, for example. In fluids, the opposite is true – a finger that is moving fast is much thinner.