Raindrop-formed ‘sandballs’ that erode hillsides tenfold

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On a late summer morning in Switzerland in 2021, Hugo Ulloa, a geophysicist at the University of Pennsylvania, was on a hike with colleague Bertil Trottet when they noticed something strange about how the rain droplets were hitting the dry ground along the hillside.

“When they landed, they splattered,” Ulloa says. The smaller rain droplets then started to roll and change shape, forming structures resembling snowballs rather than simply dissipating or sliding. They called the unusual structures “sandballs.”

These sandballs got the researchers thinking: “What conditions allow them to roll, and how do they aggregate soil and change shape? And has anyone else studied this behavior?”

Upon further investigation, Ulloa and Trottet were surprised to find that much of the literature on how droplets interact with granular landscapes focused on horizontal not sloping surfaces. That lack of literature, they knew, also limited the information used in erosion models.  

This prompted a four-year-long, multi-lab study. They found that the process of these raindrops hitting a dry sloping landscape and forming sandballs greatly amplified the amount of soil a single drop could move by, in some instances, as much as 10 times. The work, now published in the Proceedings of the National Academy of the Sciences, provides fundamental insights into how rain-related erosion happens, helping to improve models of landscape change, soil loss, and agriculture.

“Current geological and agricultural models primarily estimate erosion based on the initial impact and splash of raindrops,” says co-first author Daisuke Noto, a former postdoctoral researcher in Ulloa’s GEFLOW Lab at Penn’s School of Arts & Sciences. But, by ignoring what happens after the initial splash,  they revealed that sandballs are a powerful and previously overlooked erosion mechanism that can move as much as two orders of magnitude more mass than splash erosion alone.

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Partnering with Penn geophysicist Douglas Jerolmack, Noto devised a 1.2-meter-long chute filled with silicate sand, tilted to exactly 30 degrees, just shy of the angle where the sand would naturally avalanche. When they tested raindrops made from mixtures of water and a viscosity-control substance (glycerol), they found that rebounding droplets pick up grains along the way down the chute, allowing the droplets to form two kinds of sandballs: peanut-shaped aggregates with liquid cores and donut-shaped, or toroidal, aggregates, centered with a little air sac that behaves like a solid, a never-before-seen phenomena.

They discovered that the formation of a sandball follows a sequential physical cascade. The raindrop must first survive the impact and then forces decide if it is “to roll or not to roll.” If it rolls, the competition between the fluid’s viscosity and the centrifugal force of the spin determines the shape it forms.

When the fluid is viscous, grains are trapped on the surface, creating the peanut, a shape, Ulloa says, that is observed in everything from spinning drops in space stations and asteroids to the center of the galaxy.

“This is the characteristic of fluids; they have self-similar properties across scales,” Ulloa says. “In the case of peanuts, it is not surprising that you could observe this at the millimeter scale or observe something similar at the asteroid scale. But the donut, this is something different.”

When the viscosity drops, the grains penetrate the center. As the ball spins, the centrifugal force pushes the wet sand outward, nucleating a hole in the center and packing the grains so tightly that the donut achieves a “jammed state,” making it rigid and wheel-like.

“Finding the donut really blew our minds,” says Ulloa. He adds that, although researchers have observed similar, less stable structures in the lab, there has been an ongoing debate in the field over whether it’s possible for nature to generate them.

Ulloa says that this process could prove useful in many industrial, pharmaceutical, and food-production processes that require the aggregation of granular materials. He cites how making donut-shaped sugar-coated gummies or even solid-shelled structures that may have a water-repelling exterior and liquid interior for drug delivery could be simplified by letting gravity roll a droplet down a hill, offering a low-energy alternative to the high-energy mixers currently used.

The team is now aiming to pursue two complementary lines of inquiry.

Ulloa says the team wants to be able to better mimic the natural world, testing, for example, how raindrops behave when they strike complex soils like clay.

“Second, we will take a closer look at the sandballs themselves,” he says, explaining that the researchers  are interested in determining the exact parameters that allow a drop to survive impact.

“These experiments are a reminder to always be humble in the face of nature,” Jerolmack says. “The most fundamental process of erosion is a raindrop striking soil; yet I have never seen sandballs before.”

By pinning down the physics of these soft, mixed materials, the team hopes to sharpen scientists’ understanding of how raindrops impact dry Earth’s surfaces and to inform engineered systems that use liquids to bind granular matter, from soil stabilization to manufacturing processes where droplets act as a kind of glue.

Hugo N. Ulloa is an assistant professor in the Department of Earth & Environmental Science in the School of Arts & Sciences at the University of Pennsylvania.

Daisuke Noto was a postdoctoral researcher in Ulloa’s Geophysical and Environmental Flows Laboratory at Penn Arts & Sciences. He is currently an assistant professor of engineering at Hokkaido University.

Douglas Jerolmack is a professor in the Department of Earth and Environmental Science in the School of Arts & Sciences and in the Department of Mechanical Engineering and Applied Mechanics in the School of Engineering and Applied Science at the University of Pennsylvania.

Bertil Trottet is a graduate researcher at École Polytechnique Fédérale de Lausanne. He was a visiting researcher at Penn during this research.

This work was supported by start-up funding at the University of Pennsylvania.