We've all been there. You're heading in to work or to that meeting or down the hall with you coffee, and it NEVER fails. Splish splash and you're leaving a little trail of coffee dots in the hall so everyone will know where you've been. We put lids on our coffee cups and even those sometimes fail (I swear every fourth one at Starbucks does), causing the little drips to get all over your hand. Even when you shuffle along with your coffee, trying hard not to spill it, the sloshing is imminent, and you can feel it waiting, waiting to spill your precious coffee, the only hope you had of making it through that morning alive.

But what causes coffee to spill like that when you walk? Why can't it just rock gently back and forth? To study this, we need a hero. A hero of FLUID DYNAMICS.

Presenting the Ignobel prize in fluid dynamics.

(Source)

Mayer and Krechetnikov. "Walking with coffee: why does it spill?" Physical review, 2012.

When I met Krechetnikov at the Ignobels and asked about where the study came from, he said he got the idea at a conference. While many ideas have been hatched at conferences during deep discussions or casual chat between scientists, this one was during the coffee break. Specifically Krechetnikov and his graduate student were watching other people at the coffee break, and watching them shuffle around as they tried desperately not to spill their coffee. And they got to wondering why, exactly, coffee behaves that way in a cup when you walk.

Luckily for them, they were both researchers in fluid dynamics.

So they got high speed video, some brave volunteers, and a cup of coffee (well, probably more than one cup of coffee was harmed in the making of this paper). The cup of coffee was equipped with spill sensors and with sensors to detect the movement of the coffee. The participants walked at various paces, either focused on not spilling the coffee, or not focused and just walking.

What the analysis of the videos showed was three competing motions of the coffee in the cup. The side to side sloshing,the forward-back sloshing, and the up and down motion of the walking. This ends up producing the motion of coffee that ends up swirling around in the cup, as well as rising up and down, resulting in spills.

Here you can see the oscillations involved, with the red line at the point of spill.

So how do we build up those oscillations? It depends, not on how FAST we are walking, but how quickly we get to that speed. In other words, on the acceleration. If you start to move more quickly, you will spill quickly, and if you accelerate slowly, you will spill less. In addition, when you focus on NOT spilling, you walk slower. But once you stop accelerating and are walking at a constant pace, you get a natural frequency of excitation and are less likely to spill.

So first your acceleration sets the "initial sloshing amplitude". This gets amplified by the rocking motion of your walk. Noise of moving side to side, moving your arm, etc, adds to the sloshing and generates a swirl in the cup. And of course, there is your pace, and there is the coffee level. A less full cup will still slosh, but will not reach heights high enough to spill.

When it comes to how to control the slosh, the authors suggest coffee cups that have more give in the walls, allowing them to act to absorb sloshes (though that might present shape problems that would make it hard to carry), and hypothesize that concentric rings inside the coffee cup might help break up the oscillations. But when I asked, Krechetnikov admitted that the best way was probably to use a lid, and maybe fill your coffee cup a little less.

*Sci would like to note that she had to stop in the middle of writing this, get up, and make some coffee. Because otherwise it was just WRONG.