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Physicists Dive into Oscillation Frequency of Coffee

Scientists puzzle out when and why coffee spills















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Image: Anthony Bradshaw/Getty Images

At a recent math conference, Rouslan Krechetnikov watched his colleagues gingerly carry cups of coffee. Why, he wondered, did the coffee sometimes spill and sometimes not? A research project was born.

Although the problem of why coffee spills might seem trivial, it actually brings together a variety of fundamental scientific issues. These include fluid mechanics, the stability of fluid surfaces, interactions between fluids and structures, and the complex biology of walking, explains Krechetnikov, a fluid dynamicist at the University of California, Santa Barbara.

In experiments, he and a graduate student monitored high-speed video of the complex motions of coffee-filled cups people carried, investigating the effects of walking speed and variability among those individuals. Using a frame-by-frame analysis, the researchers found that after people reached their desired walking speed, motions of the cup consisted of large, regular oscillations caused by walking, as well as smaller, irregular and more frequent motions caused by fluctuations from stride to stride, and environmental factors such as uneven floors and distractions.

Coffee spilling depends in large part on the natural oscillation frequency of the beverage—that is, the rate at which it prefers to oscillate, much as every pendulum swings at a precise frequency given its length and the gravitational pull it experiences. When the frequency of the large, regular motions that a cuppa joe experiences is comparable to this natural oscillation frequency, a state of resonance develops: the oscillations reinforce one another, much as pushing on a playground swing at the right point makes it go higher and higher, and the chances of coffee sloshing its way over the edge rise. The small, irregular movements a cup sees can also amplify liquid motion and thus spilling. These findings were to be detailed at a November meeting of the American Physical Society in Baltimore.

Once the key relations between coffee motion and human behavior are understood, it might be possible to develop strategies to control spilling, “such as using a flexible container to act as a sloshing absorber,” Krechetnikov says. A series of rings arranged up and down the inner wall of a container might also impede the liquid oscillations. 



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  1. 1. Knackfloh 06:45 AM 11/19/11

    Once again, science takes up the hard problems. Just thinking about the dynamics of sloshing steadies my mind, and with that my cup on its way to me desk. Steady on.

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  2. 2. jehen 12:38 PM 11/21/11

    I have adopted a fool-proof strategy to control spillage even in the presence of significant oscillations incurred on brisk walks of up to 3 miles. My coffee mug has a lid. It has the added benefit of keeping the coffee hot longer.

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  3. 3. BillR 08:36 AM 11/22/11

    I have noticed that when I loosen my shoulder a bit and allow my arm to swing from the shoulder freely, the oscillations are reduced. In effect, I configure my arm to act as a dampener and this allows me to walk faster without spilling the coffee. Of course fools that get in my way back to my desk are likely to get spilled on...

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  4. 4. truittjs 09:38 AM 11/22/11

    I worked with an engineer who had a saucer with 3 cords about 18 inches long connect in three places equal distance around the perimeter. The cords go up to form a loop with which to carry the coffee and saucer. The engineer would place his cup of coffee on the saucer and walk back to his office with cup and saucer swinging merrily like a pendulum but never spilling. If you made a comment he would tell you if you understood fluid dynamics you’d know why it doesn’t spill and proceed to whirl it in a complete circle over his head without losing a drop.

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  5. 5. dbtinc 10:43 AM 11/22/11

    Guess cancer's next on the list ...

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  6. 6. Quinn the Eskimo 02:24 AM 11/25/11

    Ummm. I'm not a physicist. And I don't have any grant money. Nor do I have a Lab. But, in the question of spilling coffee:

    I'd bet some real donuts that tipping the cup too far to one side has a lot to do with it. Certainly, oscillating it in a jostling manner won't be of significant help in keeping the desired brown liquid inside.

    But then, I'm no physicist. Either.



    .

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  7. 7. iWind 01:23 PM 11/25/11

    Would a simpler strategy not be to identify suitable cup dimensions to match the individuals? With resonant frequencies much different from the frequency of their steps.

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  8. 8. stanstumbo 01:40 PM 11/25/11

    To avoid spilling the coffee -- Don't Look At It! This interrupts the feedback loop between your brain and your arm which tends to reinforce the resonant frequency of oscillation.

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  9. 9. jfortier 01:43 PM 11/26/11

    Sorry to burst everyone's bubble, or spill their coffee, but the way to stop coffee from spilling while carrying it back to one's desk is to leave the spoon in the cup.

    the spoon breaks up the oscillations of the coffee in the cup, forms vortexes and prevents the coffee from achieving its resonant frequency of slosh.

    Add to that the added convenience of being able to stir that sugar sludge from the bottom of the cup once one is again seated, and the advantages of leaving the spoon in become overwhelming.

    John Fortier
    Newfane, NY

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  10. 10. Albert Fonda 12:42 PM 12/10/11

    I just looked up “Avoid Spilling” at wikihow.com, and found nothing even as good as BillR’s above suggestion to loosen your shoulder. But, an even better suggestion is the tried-and-true one I then posted there. To wit:
    BEND YOUR WRIST! Merely rotate your carrying hand 45 degrees toward your waist. This horizontally isolates the container from arm and body motion due to walking. (I -- WideAwake Inventor -- did not invent this. I read it in print well before the Internet even started. I do not find it there yet. It is (sadly) overlooked in research at UC Berkeley, reported in Scientific American, Dec 2011, page 22.)

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  11. 11. Albert Fonda 12:45 PM 12/10/11

    Oops. UC Santa Barbara. Many a slip!

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