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Spilled Coffee: Mathematical Model For Sloshing Beverage Addresses Cup Design, Walking Speed

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Scientists face many obstacles on the path to greater knowledge. But new research suggests how to avoid one of the more common pitfalls: spilled coffee.

"I cannot say for sure if coffee spilling has been detrimental to scientific research to any significant extent," says study author Rouslan Krechetnikov, a mechanical engineer at the University of California, Santa Barbara. "But it can certainly be disruptive for a train of thought."

Krechetnikov and his graduate student Hans Mayer decided to investigate coffee spilling at a fluid dynamics conference last year when they watched overburdened participants trying to carry their drinks to and fro. They quickly realized that the physics wasn't simple. Aside from the mechanics of human walking, which depends on a person's age, health, and gender, there is the highly involved science of liquid sloshing, which depends on a complex interplay of accelerations, torques, and forces.

Back at the lab, Krechetnikov and Mayer set up an experiment: They asked a person to walk at different speeds along a straight path with a filled coffee mug in hand. The volunteer did this in one of two ways-either focusing on the coffee mug, or looking straight ahead. A camera recorded the person's motion and the mug's trajectory, while a tiny sensor on the mug recorded the instant of spillage.

A fluid's back-and-forth movement has a certain natural frequency, and this is determined by the size of its container. In their paper published last week in Physical Review E, Krechetnikov and Mayer show that everyday mug sizes produce natural frequencies that just happen to match those of a person's leg movements during walking. This means that walking alone, without any other interference, is tuned to drive coffee to oscillate in a mug. But the researchers also found that even small irregularities in a person's walking are important: These amplify the wilder oscillations, or sloshing, which bumps up the chance of a spillage.

"This is a very cool study," says Lei Ren, a specialist in the biomechanics of walking at the University of Manchester in the United Kingdom. "It reveals the sophisticated interplay between human body dynamics and the fluid mechanics of spilling coffee."

So how does one avoid a spill? Krechetnikov and Mayer's answers may not come as a big surprise. Starting your walk slower—that is, accelerating less—will help. So will leaving a decent gap between the top of the coffee and the mug's rim; this should be at least one-eighth of the mug's diameter-for a normal mug, about a centimeter should do it. But the researchers' "take home" advice is to look at what you're doing—so long as your mug isn't filled too high, a watched mug almost guarantees a clean run.

Most people will have worked out these tips for themselves, says Matthew Turner, a mathematician who specializes in liquid sloshing at the University of Surrey in Guildford, U.K. But he says the researchers' mathematical model will enable scientists to investigate different cup designs without actually making them. Engineers already know of slosh-control techniques: Tanker trucks contain inner ridges, or baffles, to damp the gasoline's motion, for instance, because too much sloshing could make a truck overturn.

But Turner believes mug makers are unlikely to take these ideas on board. "I expect it is more cost-effective for manufacturers to just provide a lid for our coffee mugs, which some already do," he says. "But this study could provide us with a fill line inside our mug below which we should keep our coffee, to minimize the chance of spillage."

However, physicist Andrzej Herczynski at Boston College thinks Krechetnikov and Mayer's study didn't go far enough. "I was personally a bit disappointed that the study is limited to cylindrical mugs … leaving out the very common curved or conical cups, such as those used for cappuccinos and lattes in Italy," he says. "Still, the paper seems at minimum destined for the Ig Nobel Prize."

ScienceNOW, the daily online news service of the journal Science

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The Physics of Spilled Coffee