Dropping the Ball: Air pressure helps objects sink into sand

Here’s good news if you happen to drop something while you’re strolling across a sandy section of Mars: You should be able to find what you dropped more easily than if you had dropped it into desert sands on Earth. And that’s not just because of Mars’ weaker gravity. Two teams of physicists have shown that a denser atmosphere, such as Earth’s, makes a falling metal ball penetrate much deeper into grainy terrain.

SPLASH! Video frames tens of milliseconds apart show sand grains under air at one-fifth of atmospheric pressure engulfing a metal ball. The column of sand in the final image would be much higher if the impact occurred under normal air pressure. G. Caballero/Univ. of Twente

“It’s very counterintuitive,” says Detlef Lohse of the University of Twente in Enschede, the Netherlands. “You would expect that, once air is there, there would be more friction,” slowing down a ball’s descent into the sandy bed. Instead, the air’s presence makes the sand act more like a liquid than a solid, Lohse says.

Sand is an example of what physicists call a granular material. Neither fish nor fowl, granular materials display features reminiscent of both solids and fluids. For example, gravel can flow smoothly but then abruptly jam.

In their experiment, Lohse and his colleagues looked at how deeply a marble-size steel ball sank when dropped into loose, dry sand. Falling from a height of 15 centimeters in atmospheric pressure, the ball penetrated as much as 13 cm into the sand. But when the team lowered the air pressure to one-fortieth of an atmosphere, the penetration depth shrank to just 4 cm.

The team also estimated how much the ball’s impact changed the volume of sand in the bed. In the presence of air at atmospheric pressure, the volume of sand stayed roughly constant. But in an experiment under vacuum, the volume decreased, indicating that the sand had compacted.

In an independent experiment, Heinrich Jaeger of the University of Chicago and his colleagues used X rays to image the interior of a sand bed as a steel ball fell in. They, too, found a dramatic difference in how deeply the ball penetrated, depending on air pressure. In a test done under vacuum, the sand surrounding the ball appeared darker, indicating that it had been compacted. No such darkening occurred when the ball fell into sand in the presence of air. Both studies are due to appear in Physical Review Letters.

Lohse says that as the ball pushes into the sand, the air provides a layer of lubrication that allows sand particles to flow around the ball. That reduces drag, allowing the ball to sink. Jaeger agrees, adding that the air’s presence makes it less likely for sand grains to rub against each other and slow down the ball by dissipating energy. He says that his group’s experiments show that in the presence of air, the entire sand bed acts like a liquid.

The new findings may shed light on the formation of lunar and planetary craters by meteorite impacts, the researchers say. The research could also improve models of the behavior of granular materials.

“Careful experiments like these are the only way to go,” says Daniel Goldman of the Georgia Institute of Technology in Atlanta.

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