# Is there more energy in the collapse of a cavitation bubble than the energy required to create the bubble in the first place?

The following does not include all scientific details and parameters, only a common summary of "thoughts". What is scientifically wrong with this summary?

When you take your beer and tap the top of a friends beer bottle, the beer shoots out the top as the CO2 is taken out of solution and rebounds off the bottom of the bottle. If the liquid in the bottle does not have anything in solution, the tap on the top of the bottle results in the explosion of the bottom of the bottle. This is from the cavitation that was created at the bottom of the bottle, and the pressure wave that propogates through the liquid to collapse the cavitation. When the cavitation collapses, the momentum of the water that has now been shifted down hits the bottom and blows out the bottom of the bottle. It does not seem that the energy imparted with the relatively light tap on the top is enough to violently blow out the bottom of the bottle. Is there more energy in the collapse of a cavitation than the energy required to create the cavitation in the first place? Or is it just the momentum of the liquid that blows out the bottom of the bottle? Pits and dings in metal pump blades are caused by cavitation collapse. What is and where does that power come from?

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## 3 Answers

Just a quick comment on the question about cavitation pitting propellers. Think of the power issue this way: Which hurts more, pinching yourself with your fingers, or pinching yourself with a pair of needle-nosed pliers using exactly the same fingers and force on the handle?

Cavitation is one of many examples of "focusing" or concentrating forces (and through that, energy) in the natural world. The bubble creates a cavity into which the fluid must rush back in, especially if the bubble has very little in it (a vacuum is best). But bubbles curve inward! That means it's like lots of little fire hoses all trying to squirt the same spot, with no where else to go. The pressure can become absolutely astonishing, and it increases more when the bubble is so perfectly spherical that the flows stay synchronized all the way to the very end. When that happens... Pow! It's quite an impact, but one that starts with only a tiny bit of energy in total, just like your fingers on those needle-nosed pliers.

And finally, don't forget needles and knives, which are yet another amazingly common example of how ordinary things we take for granted concentrate forces. A knife cuts because it applies a large force to a very narrow arrow, creating a force so strong that in extreme cases there are very few things that can resist that force. Sharpening a knife becomes an exercise in force physics, concentrating ordinary forces into every-smaller areas to create a blade that can push even through solid steel, if the blade is hard enough.

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The cavitation does not produce more energy than you put in, it just doesn't take a great deal of energy to break glass. It takes a lot of force, but once the two pieces of glass are separated by a few angstroms, the force drops to zero, so the total work done in the process is not very large.

To estimate the energy, multiply the number of atoms on a surface by 1eV, which is a generous bond-energy. This doesn't take into account long-range forces, like Van-Der-Waals attraction, but I assume these effects are not much stronger. A circle of circumference 20cm and width .25 cm has an area of 5cm^2, which is 5*10^16 A^2. This gives a binding energy of the order .01 J, and your hand has plenty more energy than that.

As an aside, regarding the cavitation at the bottom, this is an interplay of the different speed of sound in air vs. glass. When you hit the glass, the sound in the glass reaches the bottom of the glass before the sound wave in the air can transmit the pulse to the water, so that you get an underpressure at the bottom.

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That does seem mighty powerful.

If you can get a system to dump it's energy quickly enough, it will produce violent results. I would guess that whatever is happening, it is a very quick phenomenon, possibly proceeding at the speed of sound. This makes sense, in a way, detonation is a wave-front moving at a high speed, like sound traveling through a material.

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There should be some awesome videos on youtube of making cavitation with sonar. – sonardude Feb 29 '12 at 1:44