Silk and soap settle a century-old flap

For more than 120 years, the English physicist Lord Rayleigh has had the last word on why flags flap in the breeze. A keen observer who figured out how the scattering of light makes the sky blue, Rayleigh attributed flag flutter to the interplay between deformations of a flag’s surface and subtle gusting of the wind. Because the tiniest ripples in the flag and puffs of wind end up amplifying each other, even a smooth, or so-called laminar, wind inevitably causes the larger motions of flags, he reasoned.

Caught in a current, a silk thread in a soap film can flap like a flag (above) or remain intriguingly still. Zhang, et al./Nature

Now, an experiment involving a thread buffeted by a flowing film of soapy water suggests that the time-honored view was wrong. Furthermore, the new research may provide fluid-dynamics specialists with a new model for studying questions as disparate as how blood flows in vessels and how insectlike fluttering might best propel aerial microrobots.

Still, the new findings don’t answer the question of why flags flap in the breeze. “That’s a big mystery,” says Greg Huber of the University of Massachusetts–Boston. And it remains a particularly tough one to solve, he notes, because scientists have yet to master problems in which fluids are confined by deformable boundaries like those posed by a flag’s fabric.

The new study by Jun Zhang and his colleagues at New York University and Rockefeller University, also in New York City, appears in the Dec. 14 Nature. The team let a filament of silk extend from the tip of a tube into a flowing soap film suspended between two vertical nylon wires. Continuously replenished, the film cascaded downward under the influence of gravity (SN: 8/19/00, p. 125: Available to subscribers at Answer blows in wind, swirls in soap).

Like a one-dimensional flag in a two-dimensional breeze, the thread waved. But to the experimenters’ surprise, they found that this thin cord could also fully unfurl and hold that pose. This unanticipated position “refutes a common belief that a flag in a laminar wind should be always flapping,” says Zhang.

What’s more, while the waving thread sheds eddies of “wind” from its tip, there are no signs that they contribute to flapping, he says. In the conventional view, eddies—perhaps caused by the flagpole—set off the flutters.

Rayleigh went astray, Zhang suggests, because his theorizing became too abstract. For instance, his imagined flag was only a line with neither mass nor resistance to being bent. Because a thread has both, “we’re a few steps closer to the real situation,” Zhang says.

By taking into account “the elastic reaction of the flag to the flow . . . this beautiful experiment focuses on an important interaction,” comments Michael P. Brenner of the Massachusetts Institute of Technology.

What’s more, the New York findings closely match predictions of the only current theoretical study of flag motion. This work, by Alistair D. Fitt and Martin P. Pope of the University of Southampton in England, will appear in a future issue of the Journal of Engineering Mathematics.

Huber says one application might be modeling how a flexible insect wing moves in the air. This might prove useful for developing miniature military aircraft.

Curious about how a pair of nearby flags might interact, Zhang and his colleagues placed threads about a centimeter apart. By adjusting the lengths and separation of two threads, the researchers could control whether the strings would stick straight down, wave in unison, or undulate completely out of phase, clapping their tips together.

Those two-flag tests simulate a general situation—fluids passing between flexible boundaries, Zhang says. The work therefore could prove relevant to flows through blood vessel walls and lung passages—or even to snoring. After all, “people snore basically because the airflow in and out of soft tissues causes the tissues to deform,” he notes.

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