COME breakfast time, most of us like to drink our coffee. Sidney Nagel prefers to spill his. It all started one morning when Nagel was struck by the dried coffee stain on his kitchen counter. Why, he mused, did all the dark stuff end up at the rim of the stain? Why wasn鈥檛 it evenly spread over the whole area after the liquid had evaporated? The more he thought about it, the more puzzled he was. And being a physicist, he couldn鈥檛 let it drop.
Nagel began to realise that the same pattern occurs with other stains鈥攖he one left behind when salty water evaporates, for instance, or the ring left when a drop of paint dries. And when he arrived at his laboratory in the University of Chicago鈥檚 Materials Center, he found that everyone else was as perplexed as he was. 鈥淲e asked around, and no one seemed to know why,鈥� he says.
Dribbling drops
Advertisement
There was only one thing for it. Nagel and his colleague Tom Witten began simple experiments and calculations. Soon half a dozen researchers had caught the fever, and were dribbling drops onto every surface in sight. 鈥淚t became an obsession,鈥� says Nagel.
First the experimenters checked to see if the phenomenon really was universal. They tried different solvents such as water, oil and alcohol, in which they dissolved or suspended a variety of substances ranging from salt to polystyrene colloids. They deposited their drops on surfaces made of metal, plastic and glass.
Sure enough, they saw the same thing every time: when the liquid had evaporated, the particles left behind clustered round the rim of the drop, leaving nothing in the middle. It didn鈥檛 even matter whether the drop was dried right-side up or upside down.
Next, an undergraduate student, Olgica Bakajin, tried covering different parts of the drop, to prevent evaporation there. If she left a hole over the middle of the drop and covered the edges, there was no ring at all鈥攋ust a smudge under the hole. But if she left part of the edge uncovered, a segment of the ring formed there. Intrigued, the team realised that evaporation at the edge must be the key.
Meanwhile, peering at the evaporating liquid through a microscope, Nagel and his students Bakajin and Robert Deegan saw something even more peculiar. Rather than drifting aimlessly in the expected Brownian motion, all the particles in the liquid seemed to be moving purposefully towards the edges of the drop. 鈥淚t looks like a New York City street at rush hour鈥攖hey鈥檙e all trying to get some place,鈥� says Nagel. Something was driving the particles to the edges, where they were deposited as the liquid evaporated, leaving the rings.
As the researchers progressed through a painstaking series of experiments and calculations it dawned on them that something was pinning the edges of the patch of liquid in place, preventing them from moving inwards as the liquid evaporated. With the edges forced to stay put, more liquid has to flow towards them to replace what is lost by evaporation. And as the liquid flows outwards, it takes particles with it, neatly explaining why the particles pile up around the edges.
But what is doing the pinning? It turns out to be due to the slight roughness in all but the most perfect surfaces. Any liquid has a specific angle that it likes to form with the surface it is resting on. The angle is a delicate balance between the surface tension in the liquid trying to pull it into a ball, and the adhesive forces sticking the liquid to the surface it is on.
Random bounces
If the surface is completely flat and smooth, the edges of an evaporating drop have to move inwards to maintain the required angle. But real surfaces are never that smooth. If the surface is even the tiniest bit rough, when the edge loses some liquid it only has to draw back slightly before it encounters a bit of the roughness that gives it the right angle again. This way, it moves inwards so slowly that it is effectively pinned in place. As solvent evaporates at the edge, depositing particles, the surface becomes even rougher, helping to pin the edge even more firmly.
But there were still some more details to be worked out. One question was whether the pinning itself was enough. Another of Nagel鈥檚 colleagues, Todd Dupont, realised that evaporation occurs more rapidly at the edges of a drop of solution than in the middle, and wondered if this could be an important factor. Working with Greg Huber, he calculated this effect. If a molecule of water tries to escape from the middle of a coffee drop, it is still surrounded by liquid. So unless its random bounces take it way up into the air, the chances are it will land back down on the drop again. At the edges, it鈥檚 a different story: a molecule can leap off and land on the empty surface next to the drop, leaving the drop for good. So was this extra evaporation at the edges helping to drive the formation of the rings?
Escape from the edge
To test this, Nagel and Deegan made an island in a large pool of liquid and placed a smaller drop inside, with its edge only a fraction of a millimetre from the larger pool of liquid. Now the edges had lost their advantage over the centre. For every molecule of liquid that escaped from the edge of the smaller drop and landed on the bigger one, one from the bigger drop would also land on the smaller. Sure enough, the ring left by the inner drop became broader and more diffuse. But it was still there, showing that the extra edge evaporation was not critical: the pinning is the key factor.
Armed with all this information, the team has come up with a quantitative model, published in this week鈥檚 Nature, which predicts exactly how the rings develop and how thick they eventually become. They have discovered all sorts of subtleties.
For instance, says Nagel, you can sculpt the thickness of the rings depending on whether the edge of the spill curves inwards or outwards鈥攊f it is concave or convex. If the edge is convex, there is more empty surface for the liquid to evaporate on to, so you get faster evaporation at the edge and a thicker ring. When the drop has concave edges, there is more chance that an escaping molecule will land on liquid than on empty surface, so evaporation takes place more slowly and the ring is thinner. The resulting shapes can be beautiful. 鈥淚 can鈥檛 pass a drop on the street any more without stopping to bend down and look at it,鈥� says Nagel.
When it comes to practical uses for these findings, Nagel is not making any great claims. They probably won鈥檛 help you combat the effect when it鈥檚 a nuisance, he says鈥攚hen paint is deposited unevenly, for instance. But at least it may be more entertaining if you understand what鈥檚 going on: 鈥淚 find watching paint dry very exciting these days.鈥�
But there are some applications where the rings could come into their own. Using the process to paint fine gold wires is one. Given a drop with the right concentration and shape, evaporation should do the rest, providing a whole new way of producing micro-electronic devices.
Nagel admits this is speculative, but he and his colleagues are busy investigating further. Meanwhile, he says, drinking coffee has taken on a whole new meaning. And the best part is that he no longer feels the need to clean up after himself. 鈥淭he rings are so beautiful I just leave them. There are times when I鈥檝e made a particularly splendid mess and have left it there for a week.鈥�
