mdlake.net

Don’t ask the twisty paths I took to reach this video, but the link labeled “corn starch comes alive” at HAMNCHEEZ.com is amazing. (Warning! This site has a lot of vulgarity mixed with its cooler entries. That's why I don't add a direct link here.) Basically, these guys at a fluid dynamics lab at the University of Texas at Austin mix some corn starch into a Petri dish full of water, and vibrate the dish at various frequencies to demonstrate some interesting wave forms.

First the dish is made to produce some standing waves, shaping the surface of the mixture like a brain coral. While the visual image is striking, there’s no real mystery here; it’s just a function of resonance. For the uninitiated, resonance is a sort of “piling up” of waves. If you paddle on the edge of a pool, waves spread out from the point where you touch the surface. As the waves hit the sides of the pool, they bounce back and begin crossing over one another. Where two peaks meet, you momentarily get a very high wave; where two troughs meet, you get a particularly low trough; where a peak and trough meet, they cancel each other out, leaving a momentary stillness at that point. But if you paddle at just the right frequency for the size of the pool, and the pool has a shape that allows it, those peaks and troughs keep meeting at the same places, and some areas of the pool wave like made while others remain dead still. This alignment of a wave with its own reflection is called resonance, and that’s what the Petri dish is doing. But the demonstration gets more complicated.

Using a straw to blow a pea-sized depression in the surface, the presenter shows how a hole in the fluid can be part of the stable wave form: the starch mixture doesn’t flow back together, but maintains that dent right in the middle. I was surprised to learn that this form could be stable, but I have faith that I could work out the math behind it, with a lot of time and my old 8.03 book handy. Differential equations can be complicated and waves can take a lot of shapes.

Then there’s a clip showing the interactions of three such holes: cohesion and gravity cause two of the holes to pull together, but the vibrations of the dish force them away from each other; they seem to bounce off one another. I can’t confidently explain why, though I can offer a few plausible guesses. Maybe small holes are stable, but a larger hole isn’t. Maybe the holes can only exist in certain areas of the wave form, and when they drift too far, they move back toward the center. If that’s true, the holes aren’t reacting to one another at all, but simply pushing away from an unstable point somewhere between.

Up until this point, the movie is fairly familiar ground for me. I may not be able to explain it in detail, but it still makes some kind of sense. But the movie finishes with something that, frankly, boggles my mind. At 120Hz, the presenter blows another hole in the starch mixture and steps back. Briefly, the hole expands, and it looks like the walls of the hole will widen to the edge of the dish. Instead, the walls then climb out of the mixture, much higher than they were blown by the straw, and begin to grow and split into a writhing mass of shapes, maybe half an inch high, which spread to cover the entire dish. Okay, so the energy for this lifelike behavior comes from the persistent vibration, but…what the hell? I would never have believed it possible without seeing it, and nothing in my physics or differential equations classes ever prepared me to explain something like this. I’m not even sure I could absorb an explanation were it given to me.