## How raindrops fall

July 20, 2009 By Fiona Tomkinson This article courtesy of Nature News.

Exploding drops produce miniature showers.

A single drop of water can produce a shower of droplets that has all the hallmarks of rainfall, an elegant model by researchers in France suggests. Scientists had previously thought that the pattern of rainfall seen at ground level was created by drops of rain colliding as they fell.

Fluid dynamicist Emmanuel Villermaux of Aix-Marseille University and graduate student Benjamin Bossa filmed small drops of water dripping from a tap to see what happened to the drops as they fell.

The air resistance on an accelerating drop increases until it exceeds the cohesive forces that keep it together — and the drop bursts into a shower of droplets (see video).

But to see that, Villermaux says, "the experiment would need a height of typically 10 metres — that is high for a standard lab". So he and Bossa used jets of air blowing upwards to increase the air resistance drops experienced as they fell. This meant that the drops fragmented within a shorter distance.

Researchers knew that in still air, a drop initially flattens into a pancake, then deforms into an upturned bowl-shape before bursting into droplets.

Villermaux and Bossa used these shape changes together with their observations to connect the bursting of a single drop to the distribution of raindrop sizes in showers. Their model, published in Nature Physics, shows that the explosion of a drop into droplets is enough to explain the distribution1.

## Lessons from history

Villermaux's work on rain was inspired by Wilson Bentley2, a farmer from Vermont. More than 100 years ago, Bentley took plates covered with a layer of flour, and left these out in the rain for a brief period. He measured the damp patches of flour and, from this, documented the number and sizes of raindrops.

"He had no fast camera as we have, but he was clever," says Villermaux. "He was the first to notice that within a given rain, the question is not: what is the size of a raindrop? The question is: why is there a distribution?"

The distribution is closely connected to the intensity of the rainfall. Measurements taken more than 60 years ago by Stewart Marshall and Walter Palmer3 of McGill University in Montreal, Canada, indicated that drop sizes are more broadly distributed in heavy storms than in fine mists. Villermaux and Bossa reproduced the Marshall–Palmer distribution in their study to answer Bentley's question.

The answer was simpler than scientists had thought: the mechanism behind the size distribution of droplets could be accounted for just by considering the dynamics of single drops falling through air. The time it takes for a drop to fall from beneath a cloud and spray into droplets is typically shorter than the time it would take for two individual drops to collide within a cloud.

Fluid-dynamics expert Jens Eggers of the University of Bristol, UK, says, "I was expecting things to get complicated, with lots of empirical relationships thrown together. Instead, based on a few physical ideas, the authors manage to explain a beautiful empirical relationship: the mean drop size is related to the intensity of the rain in a simple and universal way."

"This work certainly is refreshing," agrees Yangang Liu of Brookhaven National Laboratory in Upton, New York. "However, much remains to be explored. For example, a major portion of surface rainfall — hence surface-observed raindrop size distributions — arises from melting of snowflakes." How, he asks, can Villermaux and Bossa's theory be reconciled with this type of rainfall?

## References

1. Villermaux, E. & Bossa, B. Nature Phys. doi:10.1038/NPHYS1340 (2009).
2. Bentley, W. Mon. Weath. Rev. 10, 450-456 (1904).
3. Marshall, J. S. & Palmer, W. M. J. Meteorol. 5, 165-166 (1948).

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