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I am looking for a liquid that illuminates when vibrations are added.

It does not have to be strictly chemical, it might as well be something else as well.

Maybe a crystal in powder form mixed with some kind of oil, or even algae in a thick:ish liquid.

Does such a liquid exist?

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    $\begingroup$ If you want a pure liquid to emit light, you'll probably have to vibrate it at very high frequencies with ultrasound, creating sonoluminescence, which AFAIK is not entirely understood yet but does not seem to be a chemical phenomenon. Perhaps a more exotic possibility would be a piezophototronic solid. $\endgroup$ – Nicolau Saker Neto Apr 15 '15 at 22:50
  • $\begingroup$ @NicolauSakerNeto interesting. At what frequencies are we talking here? $\endgroup$ – vaid Apr 15 '15 at 22:54
  • $\begingroup$ Well by definition ultrasound means 20 kHz and above. It seems that the exact value used can fluctuate between 20 kHz and 60 kHz (simply because lower frequency ultrasound is easier to produce, I assume), varying with parameters such as the nature of the liquid under sonication and the resonant frequency of the container. I don't really know much about sonoluminescence, but there's a lot you can find on it, if you're curious. The light is incredibly weak and brief, though, so don't expect much. $\endgroup$ – Nicolau Saker Neto Apr 15 '15 at 23:06
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    $\begingroup$ Dioxetanes emit light when energy (heat) is applied. I also think that @NicolauSakerNeto 's comment is right on target. Sonication (a way of supplying energy) can cause cavitation (bubble formation and collapse) in many liquids. Upon bubble collapse, light can be released. $\endgroup$ – ron Apr 16 '15 at 0:04
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    $\begingroup$ You could look up triboluminescence, this would fit your description. $\endgroup$ – porphyrin Jun 25 '19 at 11:02
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Find compounds that emit light under photolysis.

As that may involve radical production pathways, one can also try to apply sonolysis to the same compounds as:

H2O (with dissolved O2, N2,..) + Sonolysis -> *H + *OH

Reference source: 'Free radical formation from sonolysis of water in the presence of different gases'), to quote:

"In this case, O2 reacts with •H to form •OH, indicating that the presence of dissolved O2 in water sonolysis gives additional amount of •OH. "

Also:

H2O2 + Sonolysis -> *OH + *OH

Apparently, with applications, see, 'Bactericidal effect of hydroxyl radicals generated by the sonolysis and photolysis of hydrogen peroxide for endodontic applications'.

where it is likely that one may be able to replicate to varying degrees the action of light treatment.

Here is a source example citing the action of reactive oxygen species (ROS), which can be created by the UV photolysis of, for example, H2O2 (or sonolysis per reference above):

"In biological systems much attention is focused on the two free radicals, superoxide anion and hydroxyl radical....The generation processes of ROS can be monitored using luminescence. Because of the very weak native luminescence of ROS, both luminol and lucigenin have been used in the past to give measurable signals. However, the luminescence of these two substances is very small compared to that of Pholasin®, which allows precise analysis on very small samples."

So, perhaps try performing a sonolysis of, say, luminol or lucigenin, in H2O2 might be interesting.

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