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A neat party trick (typically for outdoors) is to build a pyramid of tealights, let them burn for a while and then pour a bit of water over it and see a large jet flame shoot out (see e.g. this youtube video).

I was always told that this is caused by the water spreading the liquid wax out allow more of it to burn at the same time, but I am not completely satisfied with that answer because, in my opinion, that cannot explain the large jet flame. Can someone explain why this jet flame occurs? Is it the wax vapour that catches fire, which can form at 370 $^o\ce{C}$, and is this the reason you need to build a close packed pyramid? But what is the role of the water then?

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The wax doesn't need to become gaseous to cause the column of flame (if that's what you were thinking). Water, when in contact with the liquid wax at a couple of hundred degrees above its boiling point, will flash-boil in a very chaotic manner as if it were "exploding" ("transition boiling" in this graph). The water closest to the wax very quickly vaporises and tries to escape, but is temporarily blocked by the layer of liquid water above it, so the system ends up being vigorously churned to make way for the vapour.

The problem is that the turmoil will make tiny liquid wax droplets airborne, as if wax were being shot out of an atomizer, creating a wax aerosol. Suddenly, the same amount of wax has its surface area increased tremendously and is exposed to much more oxygen. Even though the wax in the aerosol quickly loses heat and may become solid again in a fraction of a second, if even a small region of the wax aerosol reaches ignition temperature, the flame quickly propagates as a huge amount of heat is dumped at once in the vicinity and triggers the ignition of all the airborne wax.

This trick is effectively the same as what happens if you try to put out a grease fire with water.

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I think it's a mixture of both.

You can actually get the same sort of flame just using a pyramid of tealights, but it takes a while longer. I think the role of the water is get the process started, throwing around some wax vapour that can then ignite and self-sustain.

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