Finding Beauty and Truth in Mundane Occurrences
Sidney Nagel, pictured in his office at the University of Chicago, concerns himself with coffee stains, traffic jams and “all the ways in which nature works, not just the ones that sound esoteric and deep.”
Kristen Norman for Quanta Magazine
Introduction
A stain drying on the counter. A raindrop splashing onto the sidewalk. A pile of gravel settling. Historically, such phenomena have rarely caught the attention of physicists, as they seem mundane and devoid of fundamental significance. At the same time, these everyday happenings are also deceptively hard to understand. Out of balance and disordered, they sit outside the comfort zone of the typical physicist.
But Sidney Nagel of the University of Chicago is not typical. In the 1970s, he began his career by studying the structure of glass — a traditional topic in condensed matter physics. Then he branched out into quirkier, softer forms of matter that the physics community had largely overlooked.
Nagel and his collaborators have developed theories of “jamming” that help explain the flow (or lack of flow) of both sand and traffic. They’ve also stumbled upon new phenomena in droplets and splashes.
“My deep and abiding feeling is that if you look at anything closely enough, there will be new riches to be found,” Nagel said.
Unorthodox though it is, his work has been highly impactful and widely celebrated: Nagel won the 1999 Oliver E. Buckley Prize, one of the most coveted awards in condensed matter physics, and the 2023 Medal for Exceptional Achievement in Research of the American Physical Society.
He also takes great pains to capture aesthetically pleasing visuals in the course of his research. Images from his experiments have graced museum walls, an achievement that seems to make Nagel at least as proud as his discoveries do. “When people see this image on the wall, I hope that it makes them feel more enriched,” he said. “It matters that it takes a full human being” — someone capable of appreciating both art and science — “to look at it. There isn’t just one aspect involved.”
Quanta caught up with Nagel during a meeting of the American Physical Society in Anaheim in March. We sat on a stone bench under the California sun and talked of coffee stains, surprising splashes, and the role of aesthetics in his scientific practice. The interview has been condensed and edited for clarity.
Your most cited paper was about the ring-shaped stains left by drops of coffee on a countertop. What got you curious about those?
I’m not the neatest person. And I need my coffee every morning. So one day I was sitting there waiting for the caffeine to hit, and I noticed that my counter was covered in coffee stains from the day before. I started wondering, “Why do they look so bizarre?”
Nagel once cracked the puzzle of why drops of coffee (and other liquids) leave dark rings behind when they dry.
Sidney Nagel
What looked weird about them?
Imagine a drop of liquid. It’s tall in the center and comes down at the edges. So there would be more coffee in the middle of the drop. Then when it dries, the stain should be darker in the center with nothing at the edge. But the stains on my counter were the opposite. Everything, all the coffee, was at the outer edge of the rings. We asked a bunch of people why that would be, and everyone gave a different answer.
How did you figure out what was going on?
If you want to understand the cause of something, you should be able to make it go away. But this ring phenomenon was very robust. It works almost everywhere — for example, you see it in the salt stains on the floor from what you track in on your boots in winter. The salt collects at the perimeters of the drops and pools that melted from the slush dripping from your boots. As the drops evaporate, they leave behind white rings of crystallized salt.
Eventually one of my students stopped the edge stain from forming by covering the outer rim of the drop with a glass slide, leaving just the center exposed. That was the key to thinking about the problem.
So why does the coffee all end up at the edge?
We’d been assuming that the overall shape of the drop stays the same as it evaporates, that it just uniformly shrinks in size — a theory that goes back to the work of Thomas Young in the early 1800s. But that’s not what it does. The drop gets pinned to the surface and then evaporates from all over, and especially from the edge. Anything that evaporates from the edge has to be replenished by a flow from the inside. That pulls the coffee to the outside, leaving a stain that’s predominantly at the edges.
In his office at the University of Chicago, Nagel keeps an assortment of toys and demos, such as a device for studying the way mustard seeds cascade (top right).
Nagel keeps an assortment of toys and demos in his office, such as a device for studying the way mustard seeds cascade (top center).
Kristen Norman for Quanta Magazine
What else have you discovered about liquids?
We started wondering what happens when a drop hits a surface and splashes into a bunch of smaller droplets. So first we started recording these beautiful movies of the splashes.
But what causes the splash? Can I control the way it breaks up? We had the idea to try this in a vacuum. Without any air to slow the drop down, we figured we’d get a bigger, more violent splash.
What happened?
The splash disappeared! And we fell on the floor laughing hysterically. When we eventually picked ourselves back up, we started to study this effect seriously. People have studied splashing for 100 years, and nobody had thought to take the air out. It’s a stupid experiment! Air is 1,000 times less dense than water; it really shouldn’t make a big difference.
Why does it?
We certainly didn’t think of this right away, but by process of elimination we zeroed in on the competition between the drop trying to expand outward after it hits the surface and the air trying to hold the drop back. Normally, as the liquid expands outward, some air slips underneath and raises it up a bit. Now the edge of the droplet is floating, so it can go much faster than if it were still stuck to the surface. It shoots outward in a corona, which then breaks up. Without air, the drop stays on the surface and never has the chance to splash. So you can have splashes on Earth. But you can’t have them on the moon. Maybe you can have them on Mars where there is at least a little atmosphere.
You’ve looked at sand too. What’s intriguing about sand?
Let’s do a little experiment. Pour sand into a container. What’s its density? OK, you write down what you think. Now I tap the container a few times. The height goes down and the density goes up, and not by a small amount! Maybe 10% in some cases.
This is not how any “normal” material behaves. I give you a container of water, and you know the density. But if I give you a tube full of some granular material — which includes almost everything you eat in some sense — how do we even describe what I gave you? You don’t know unless I tell you everything I’ve done to the system, that is, how much I’ve shaken it and how much I’ve tapped it.
How should we think about sand, then?
It’s a beautiful example of something that’s disordered and far from thermal equilibrium. Temperature is normally what brings, say, a gas or a liquid into equilibrium by jostling the molecules around. But you’d have to make a room a trillion times hotter before there’d be enough energy for the air to start rearranging the grains of sand. So in that sense, it’s like the sand is incredibly cold. We can let it sit there, and the temperature won’t equilibrate it.
In that way it’s a lot like glass, which is what I started out studying in the ’70s. Glass is also this disordered, out-of-equilibrium material that is somewhat but not entirely frozen in place at room temperature.
While investigating the shape that drops of liquid take as they break free, Nagel captured images with a Hasselblad film camera and a high-speed strobe light. The falling drop interrupted a laser, setting off the strobe.
Sidney Nagel
You’ve studied all sorts of other phenomena, too — the shape of drops as they fall, and materials that deform in useful ways. What kind of physicist do you see yourself as?
Weird.
Look, I don’t know how to really answer that. Clearly, I like things that I consider aesthetically pleasing. That’s very important to me.
We’ve spent an incredible amount of time trying to get the photographs of drops just right — not just the physics but the ineffable beauty of the phenomenon. I’m a human being. I’m not just a physicist. So I want this thing we do to appeal to me on the scientific level and the aesthetic level. There’s also something rewarding about seeing what you’re doing directly rather than having it hidden behind some black box of an apparatus, which is what happens so often in certain fields of physics.
A major drive in physics is to reduce the world to its fundamental rules and parts, but you’ve gone in a different direction. Why?
We’re taught to look for finer and finer explanations that take us to a deeper level. And I have a lot of respect for that side of physics. My wife is a particle physicist. But my belief is that our job is also much richer than that. It matters to me all the ways in which nature works, not just the ones that sound esoteric and deep.
Kristen Norman for Quanta Magazine
In some sense I think of doing what has been called “fundamental” physics as like sticking to “modernist” architecture, where form must follow function — a single endeavor. But exciting structures can emerge from pushing away from that single ideal and exploring, for example, postmodern architecture, where buildings can have aspects that are not strictly bounded by their function. We had closed off physics from looking at such weirder things, but this stuff is part of the world too. It is snobby to proclaim that there is only one acceptable way of choosing problems that are worthy of study.
I sense that you’ve faced some resistance or skepticism in your career.
Yes, here and there. Some pushback came because a few people did not consider certain subjects I studied to be “serious.” Others were upset because I was emphasizing what seemed to them unscientific aspects. We could have captured the same physics without working nearly as hard as we did to perfect the photography, and this made people upset. They said, “You’re a scientist, you’re not supposed to care about things like that.” But it matters to me that you appeal to as many aspects of the human endeavor as you can.
That’s why, for me, the idea of having tenure is such a meaningful thing. Most places wouldn’t have encouraged this stuff, but Chicago has been very good to me. I mean, would you give tenure to someone who’s studying coffee stains?
I might. The paper has been cited more than 7,000 times, including by engineers developing inkjet printers and nanotechnology.
Maybe now, but not back then. People did not like what I was doing, and they told me so. But, you know, I’ve had a lot of fun.
