Light from sound

Before Tuesday, I had never heard of “cavitation”. Then I received a breathless email about physics from a biomedical web page which I have never trusted for its science. But during my afternoon walk in the wooded park which graces my neighborhood of Philadelphia, I listened to an incompetent interviewer who seemed to be in over his head. So I was coming to Mark Leclaire, the interviewee, with a good deal of skepticism. But as his story unfolded, my bullshit detector hovered around the zero mark. He referenced high-energy astrophysics, cold fusion, and evolutionary biology, subjects with which I’m tolerably familiar, and I didn’t catch him in a single error.

And so I’ve embarked on a crash course to learn what cavitation is, how it is in evidence all around us, and what may be its technological potential. 

Subtleties of the Second Law

It’s easy to disperse energy, difficult to concentrate it. A cup of hot tea will spontaneously lose its heat to the surrounding room, but you have to do work to concentrate heat energy from the room if you want to warm the tea. If you have one high-energy photon (say, ultraviolet light), its interaction with matter will spontaneously turn it into two low-energy photons (say, infrared); but combining those two IR photons into one UV photon requires some trickery, and maybe some extra work. These are classical applications of the Second Law of Thermodynamics.

Now consider a more subtle case of sound and light. Sound energy comes in “phonons” of very low energy because they are very low frequency as compared to light. (Frequency is related to energy by Planck’s Law, E=hν.) It should be easy to turn light into noise, but hard to turn sound into light. An enormous number of phonons must contribute to a single visible photon.

So it took physicists by surprise when sonoluminescence was discovered experimentally in 1934. Vibrate a beaker of water with ultrasound, turn off the lights, and you can see little flashes of blue. Tiny spots within the water are hotter than the sun.

This sure looks like a violation of the Second Law. Many small quanta of sound are being combined to make one big quantum of light. Mr Sonoluminescence hasn’t actually run afoul of the law, but you might say the judge let him off on a technicality. The sound energy input is not noise, but a coherent, ordered wave. It’s more like kinetic energy, energy of bulk motion, rather than noise. And kinetic energy is pure work, or energy that carries no entropy at all. Still, we wonder how this loophole is exploited. What is the mechanism by which coherent sound energy at low frequency can be turned to enormous temperatures, and thence to light?

There is no scientific consensus on an answer to this question, but there is agreement that it involves cavitation. 

How does water boil?

Water is evaporating all the time, but not necessarily boiling. Water at a given temperature has a given propensity to evaporate, which is reported as a “vapor pressure”. Vapor pressure is the mechanical push of evaporating water. Boiling is what happ ens when the vapor pressure of water is greater than the ambient pressure. 

We commonly boil water by raising the temperature. We notice that on a mountain top, where atmospheric pressure is low, water boils at a lower temperature. That’s because a lower temperature is needed to achieve the lowered pressure that matches atmospheric pressure high above sea level. We can also boil water at room temperature by putting it in a bell jar under a vacuum pump. The pump lowers the ambient pressure so that even the very low vapor pressure of water at room temperature is sufficient.

If you swirl water violently, or pump it rapidly through a narrow valve, or excite it with intense sound waves, there are places in the flow where the water pressure in a small region falls below the vapor pressure at room temperature. So the water boils just in these regions, forming vapor bubbles a millimeter in size or less. These bubbles quickly flow into areas where the pressure is higher and the bubbles collapse. Inevitably, one spot on the surface of the bubble is the weakest, and that’s where the water squirts into the bubble, deforming the bubble into a donut shape, producing a tiny jet. These jets are known to move over very short distances but with tremendous speed. We know how violent they are because of the damage that cavitation causes in pump impellers and boat rotors. 

The rotor is made of stainless steel, or even of super-strong carbon fiber. What is damaging it is just water! How fast do these tiny jets of water have to move to make holes in steel? We begin to see that cavitation is an everyday phenomenon, undeniably real and powerful; but mysterious, and not well-understood from the standpoint of fundamental physics.

Once you have such tremendously powerful jets of water, you can imagine heating a microscopic bubble so hot that it glows with sonoluminescence. But the forces that produce the jet from collapsing mini-bubbles are not so easily understood. The mechanical force of the collapsing bubble is far too small, and the surface tension forces around the bubble are not much bigger. What makes those tiny jets of water move at thousands of miles per hour?

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