Harnessing instabilities in physical and chemical systems, Paul Steen has created an electrical switch made of water and filled with enormous potential.

By Kenny Berkowitz ’81

Paul Steen’s teenage daughters think it’s funny their father earns his living playing with soap bubbles. But after studying the reconfiguration of thin films by surface tension for the last dozen years, Steen has many questions still unanswered, and that unpredictability is at the mathematical heart of his two latest projects: an electrical switch made of water and a method for spin-casting metal in thin, continuous sheets.

“Soap bubbles are simple but very effective,” says Steen, a professor in the School of Chemical and Biomolecular Engineering, sitting in his office at Olin Hall. “The individual soap bubble is relatively well understood, but when you combine a group of them with different geometrical constraints, and when you let them work together or fight one another, you see them elucidating this wonderful set of instabilities. It’s very dramatic, because there’s a balance of forces, and then some disturbance comes to throw everything out of whack, and all of a sudden you’ve got … a catastrophe.”

What kind of man spends his life searching for instability? “It’s a field that draws people who are analytically minded, who want to do quantitative, predictive science,” says Professor Tim Healey, chair of the Department of Theoretical and Applied Mechanics, where Steen is a member of the graduate field faculty. “First and foremost, Paul is a scholar. He’s the quintessential mathematically driven scientist. He’s not using an Edison approach, where you try 185,000 different things until you get something to work. With Paul, the science always comes first. That’s what drives him.”

Playing with a palm-sized prototype of the switch, Steen leans forward, speaking softly, enthusiastically about his work: the thrill in trying to understand these catastrophes, the beauty in the nexus of math and physics, the creativity in designing tools to harness this instability. He talks about the power of surface tension, using a bead of spit between thumb and index finger as an example, and multiplying that effect hundreds of thousands of times.

In the electro-osmotic droplet switch (EODS), Steen uses electricity to create and release an adhesive bond between a droplet of water and a flat plate. With the current flowing in one direction, low voltage moves the water’s positively charged ions through capillaries in a porous glass disk, forming a micrometer-sized droplet that quickly attaches itself to a flat surface; flowing in the other, the droplet detaches itself just as easily, breaking the bond as it returns through the glass pores.

It’s a project that was originally inspired by the palm beetle, which can cling to a leaf with a strength equal to a hundred times its body weight — imagine Steen supporting six or seven cars with that bead of spit — and by Cornell entomologist Tom Eisner, who first brought him the idea, based on Eisner’s work with Professor Dan Aneshansley in the Department of Biological and Environmental Engineering. “This after-dinner talk at the Statler and the image of the beetle clinging and releasing itself stuck in my mind for the next few years,” says Steen. “And the more I rolled it around, while I was riding my bike or jogging or walking, the more I thought I should take a closer look at how we could put it to practical use.”

By fall 2003, when he sat down with long-term collaborator Peter Ehrhard at the Institute for Nuclear and Energy Technologies (IKET) in Karlsruhe, Germany, it was still on his mind, and soon became the focus of Steen’s sabbatical at IKET. “We were discussing what we might do together,” says Steen. “I had this idea of designing a landscape for capillary systems, but I had no way of triggering the system from one state to another. Peter suggested electro-osmosis, which is another idea that’s been around for a while, but never used this way. So it wasn’t a matter of technical prowess; it was a product of bringing together two things that had never been combined before. I spent the next two months running all these calculations with pencil and paper. And instead of being off by orders of magnitude, everything worked out — which doesn’t usually happen.”

Built by Mike Vogel, a post-doctoral associate in chemical and biomolecular engineering, that first device cost under $100 with basic equipment that can be found in any chemistry stockroom. It’s surprisingly simple: a robust, easily fabricated switch that has no solid moving parts, turns on and off in under a second, runs on less than five volts, and can be used either by itself or in larger arrays. Engineered down to the hundred-nanometer scale, which seems a stretch but within reach, an array of switches could enable Steen to walk across the ceiling of his office, focus the lens of a cell phone camera, or act as a microscopic, energy-efficient lab-on-a-chip. The implications are enormous — it’s no surprise that the Defense Advanced Research Projects Agency (DARPA) is underwriting the fabrication of the first complex array of droplet switches — and though Steen grows uncomfortable with its comparison to the transistor, the full range of applications is still unimaginable.

“It’s one of the most ingenious ideas that I’ve seen in a long time,” says Professor Paulette Clancy, the William C. Hooey Director of the School of Chemical and Biomolecular Engineering. “It is so clever and so thoroughly backed up with theory. That’s what Paul brings to his projects: a deep understanding of the mathematics that underlie a principle and the experimental tour de force of actually showing what can be done.”

It will be the third patent for Steen; in the first, applied for in 2002 and awarded in spring 2006, he designed a system for casting molten metal into thin, solid ribbons in a single step, manipulating the surface tension of the cooling, hardening metal on a rapidly spinning wheel. It’s a dream that dates back over 150 years: feeding molten metal into one end of a machine and retrieving solid, continuous sheets from the other; and though the patents seem dramatically different, to Steen, they’re two sides of the same coin. With the droplet switch, his goal is to harness instability driven by surface tension; in casting metal, he’s trying to suppress instability.

“Paul is using surface treatments of the casting wheel to modify the behavior of the melt puddle. This has the possibility of modifying the instabilities and, equally important, of modifying the microstructure, and thus the final properties, of the finished product,” says Associate Professor Shefford Baker, a faculty member in the Department of Materials Science and Engineering and one of Steen’s collaborators on the spin casting project. “Paul has been looking at the fluid dynamics of this process for a long time. He’s very meticulous, very good at thinking through problems from different angles, and very careful to ensure that the path he’s on is the right one.”

The “beer-belly” instability occurs for a short enough soap-film bridge. Initially, (1) a soap film is stretched between circular plexiglass grips to form a cylindrical-shaped bridge. As the grips are slowly moved closer and closer together, the bridge becomes fatter (2) and fatter (3) until it suddenly snaps through to a shape that is no longer a surface of revolution (4).

Clancy calls it “an incredibly exciting project,” and at a time when the world is once again focused on conserving energy, casting by design could become a huge boon to producers of flat products of aluminum and steel.  For aluminum foil alone, the savings would amount to 300 gigawatt hours of power per year with a reduction of carbon dioxide emissions by 250,000 tons a year in the United States alone. But for Steen, who’s still hard at work refining the process, talking about the applications is far less interesting than thinking about the science behind it, and as both projects move to the next stage, he finds himself spending more time in the search for funds, acting as a reluctant salesman.

“It reminds me of when I was a young boy in rural Pennsylvania, selling strawberries door-to-door,” says Steen. “It’s almost the same thing. You grit your teeth, and even though you really don’t want to do it, you walk up to the door, knock, and start your pitch: ‘I’ve got this great thing I want to sell you….’ I was the last of five children, climbing trees and picking wild berries, and it’s hard to imagine how I ended up here.”

Growing up in Meadville, a small city located between Erie and Pittsburgh, Steen didn’t think much about his career. His father taught math at Allegheny College and his mother taught business at the local high school. As his siblings grew older, they all found work in science, but Paul wavered between English, history, math, and engineering. (“With what I now understand about genetics,” he says, “when I look back at my family, I can guess that I would have gone into science.”) Attending Brown University, Steen graduated in 1975 with two bachelor’s degrees, one in English literature and the other in biomedical engineering, though he suspected he’d have a brighter future as an engineer than as a novelist. Five years later, he completed his Ph.D. in fluid mechanics at Johns Hopkins University, and after a two-year post-doctoral appointment at Stanford University, he joined the faculty at Cornell.

In the years since, he’s risen to full professor in the School of Chemical and Biomolecular Engineering, becoming a member of the graduate field faculty in applied mathematics in 1984 and in theoretical and applied mechanics in 2002. He’s a fellow of the American Physical Society, serves or has served on its executive, program, publications, and prize committees, and as a member of the Science Advisory Council of the Universities Space Research Association, which acts as liaison between NASA and the academic community.

He is associate editor of the Journal of Fluid Mechanics, co-author of more than 60 published articles, and mentor to countless Cornell students, both undergraduate and graduate. “Basically, Professor Steen taught me how to be a scientist,” says John Faria, who went to work for Steen as a sophomore and continued until he graduated in 2005. “Before I came here, I didn’t know how to make a convincing scientific argument, and the only experiments I’d done were in chemistry lab, where we knew exactly what results we were supposed to get. With Professor Steen, for the first time, I didn’t know the outcome. And whenever I ran into a problem, he was able to help me work through it.”

Steen has always enjoyed working with undergraduates and generally has three or four working as part of his research group. (“You can try some of your riskiest ideas with undergrads,” he says, “because their diplomas don’t depend on the idea working out and they’re some of the best brainstormers you’ll ever find.”) Faria, who begins medical school this fall, tells the story of successfully reverse engineering a bubble toy that Steen’s younger daughter brought home from a birthday party. When he showed the results to Steen, “he was ten times more excited than me. He just jumped out of his chair, landed on the floor, and kept staring at this bubble. And that’s the attitude he carried throughout the whole lab.”

“Paul gives his students a lot of freedom,” says Vogel, who has spent the last three years working with Steen as a post-doc, collaborating closely on both the droplet switch and casting by design. “He’s very easygoing, with a very laid-back approach. He’s very good at boiling down complicated problems into a relatively simple theoretical framework. And it’s nice to work with someone who has faith that you’ll produce great things.”

For Steen’s two daughters, 15-year-old Ana, whose passion is ballet, and 13-year-old Frances, who’s currently studying classical guitar, the idea of walking on a ceiling is more than great — it’s cool. As a family, Steen, his wife, Kyra Stephanoff, and the girls spend summers bicycling through the watersheds of Central New York and winters cross-country skiing around the Finger Lakes. It reminds Steen of his own childhood, playing in the woods, and in the quiet moments between hills, gives him a chance to think through those next obstacles: a more uniform array of switches and a smoother ribbon of aluminum.

“I get an incredible thrill from doing this work,” says Steen. “It’s still amazing to me that we have this way of connecting numbers to physical phenomena. The range of predicting and understanding instabilities is just a fundamental fascination for me. And underneath it all, I like the idea of taking a mathematical proof and seeing it connect with something we can all use.” 

Steen has received a grant from DARPA (Defense Advanced Research Projects Agency)  to demonstrate “capillarity-based reversible super-adhesion.” This is a direct application of the parallel action of surface tension (capillarity) inspired by the palm beetle, and the idea can be illustrated with a bank of soap bubbles or liquid droplets controlled by electro-osmotic droplet switches. Steen, principal investigator on the project, is working with Vogel, who is principal scientist. Shakti Technologies of Palo Alto, Calif., will fabricate the prototype device.