# Knotty Thrills

• Posted 07.17.14
• NOVA

The problem of how to tie a knot out of a fluid had eluded scientists for a century and a half. Then, using a 3D printer, bubble mist, and a scaled-down version of a laser light show, three physicists from the University of Chicago did it. And the results are mesmerizing.

Running Time: 05:40

## Transcript

ARI: I want to tell you about a few guys who cracked a really hard, 150-year-old puzzle.

Here are the guys.

And here's the puzzle:

How do you tie a knot in a fluid? I don't mean, how do you tie a knot in a piece of string that's submerged in a fluid. I mean, how do you tie a knot out of the fluid itself?

Now, you may be puzzled with another question right now—who cares?

First answer—just wait, the end result is gorgeous.

Second answer—look up—and imagine that you want to build a plane that flies more efficiently and uses less fuel. You want the plane to move through the air with as little disturbance as possible.

IRVINE: Boeing, if they're designing a new airplane, they do a lot of computer design, but at the end of the day, they build a model, and they put it in a wind tunnel, and they test it.

ARI: In other words, says William Irvine, when air or water, or any fluid actually, flows around an object, we can't predict what that flow looks like very well. So we use models and lots of trial and error. But if we could actually predict the flow, then we could make better airplane wings and propellers without as many duds along the way. Not to mention more aerodynamic buildings and more hydrodynamic ships.

Now, the reason we can’t make good predictions is that fluid flow gets complicated fast.

But what if there were some way to simplify things…by focusing on a single quantity that explains and predicts the complexity?

Well, that quantity might just be something called knottedness—which is how tangled up or swirly a fluid is.

This fluid here has very low knottedness, whereas this fluid has high knottedness.

And knottedness might be really special because maybe, just maybe, it’s the kind of thing that’s "conserved." Which means that the amount of knottedness you start with is the same amount that you end up with—it might just not look the same.

Conserved quantities are powerful things in physics because they give you a way of taking a complex system and reducing it to a few simple rules. There’s conservation of energy and conservation of momentum. And maybe, says Irvine, there’s conservation of knottedness.

IRVINE: If you can prove that, it’s like finding a whole lens through which to look at the world. Then it can give you a very, very powerful tool to understand all sorts of problems.

ARI: And so here’s the puzzle: To test this idea, that knottedness is conserved, you have to be able to tie a knot out of a fluid and watch what happens to that knot. But for 150 years, no one knew how to do it—until Irvine and Dustin Kleckner showed up on the scene.

KLECKNER: Yeah, a really important part of the process was having a 3D printer available to us down the hall.

ARI: Here's what they made on that 3D printer—an assortment of three-dimensional knots.

KLECKNER: The way that the experiment works. Essentially, we have this frame that we're attaching the knot to, and this thing is gonna get immersed into the fluid, like this.

SCHEELER: So in order to visualize, we use tiny microbubbles, so.

ARI: Martin Scheeler sprays a fine mist of bubbles onto the submerged 3D printed knot.

KLECKNER: And then it gets accelerated very rapidly by this pneumatic cylinder right here. This—so that’s me pressurizing the canister, and once we do that, we can fire it by just releasing this switch right here. Ok, so you ready for this? One, two, three…[Bang!]

SCHEELER: And there she goes.

ARI: "She" being a knot of air that's been launched into the water. Here's that same thing as a video. It's remarkable. After working on this 150-year-old problem for a year-and-a-half, they did it. They made a knot out of air.

Can you tell me about how you celebrated?

IRVINE: Have we ever had a party? Maybe it's time to have a party.

KLECKNER: It's hard to identify the clear-cut moment because you always think, like, I could be doing this better. There's always a bit of hesitation.

ARI: Did you guys at least hug?

KLECKNER: I don't know if we hugged, but we probably had a beer, though.

IRVINE: Yes.

KLECKNER: And you know, I also think, like, the mark of a successful experiment is that it raises more questions than it answers.

ARI: One of those big unanswered questions is whether these fluid knots actually conserve their knottedness. Take this knot here, and watch what happens to it over time. It breaks apart into separate rings. It's as though the knot has untied itself.

IRVINE: But in practice, that's not really the beginning and end of the story.

ARI: Perhaps, says Irvine, the knottedness is being transferred internally, like a piece of rope whose strands are twisted up before being woven together. It'll take a while before this work influences the shape of an airplane wing or ship hull or propeller blade. In the meantime, Irvine's elated that he’s glimpsing a part of the physical universe that we just hadn’t been able to witness before…that of fluid knots.

IRVINE: They have just tremendous amount of structure to them—there's little wiggles and bigger wiggles, and they sort of dance around each other in a way you can’t just guess intuitively. To us, that's part of the beauty of it. You look at it, and it's always a little bit mysterious. And every time you try to figure out one of the mysteries, it offers more.

ARI: These knots give life to a fluid. And for Irvine, the questions they shed are too beautifully entangling to escape.

## Credits

### PRODUCTION CREDITS

Written & Produced by
Ari Daniel
Narrated by
Ari Daniel
Original Footage

### MEDIA CREDITS

Knot Experiment Videos
William Irvine & Dustin Kleckner
Laboratory Photographs
Bill Healy & Martin Scheeler
Old World Map
Public Domain/Gerard van Schagen via Wikimedia Commons
Special Thanks
The Choueiter Family & Gather Here

### IMAGE

(main image: Two Fluid Knots)
William Irvine & Dustin Kleckner

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