When some things are burning, and allowed to burn to completion until the fire or flame burns out, the flame often becomes extra bright for a flash before it completely goes out.
I see this happen when a match is allowed to burn to completion, as well as a cigarette dropped on the ground while still lit. What happens to make the flame brighten just before going out completely ?
Something involving a burning flame, still liberating combustible material as it burns, and running out more rapidly at the end due to the fuel-burn geometry, could produce this effect.
For instance, in a simple solid rocket motor, the combustion area grows as the fuel burns from the inside out. Just before it burns out, the available area hollowed out by the burning of the fuel reaches a maximum diameter, hence a biggest burn.
Alternatively (and I’ve seen this one too) as the heat source diminishes, it may not spread out the combustible material (e.g. gasified wax) as much, which could at the end result in a rich mixture of ready-to-burn material. A little gust of air could cause it to burn very quickly, then there’s no more fuel, so it burns out.
If the flame hits a pocket of vaporized, fast-burning fuel, then it can burn rapidly enough to suck up all the oxygen for a just long enough to let the fuel cool below flashpoint so that it smokes instead of burns.
Flammable solids don’t burn. The heat of the ongoing flame pyrolizes* the solid material into a mixture of gasses that do burn, and incombustible residue that we call “smoke” or “ash”.
So while any fire is burning, part of the energy of combustion is spent heating & pyrolizing the solid material, while the rest is available to the environment as heat & light. The pyrolizing process can be thought of as the “overhead” of an ongoing combustion, just like the energy spent turning camshafts and overcoming friction inside an internal combustion engine is “overhead” that reduces the net power output.
With that background …
Consider what happens in the last couple of minutes or seconds as the available unburned solid fuel runs low and first approaches then hits zero. There is less and less mass remaining to be heated. So for the same size fire, more of the energy is available as sensible heat & light. This effect reaches its apex just as the last bit of solid is heated to combustion temperature, gives off its burnable gasses, which then combust with no more as-yet-unheated solid to need to heat. 100% of the combustion energy is available to (briefly) heat the incandescent gasses we call “flame” to a hotter = brighter & whiter temperature. Bingo: that final flash.
You will notice the opposite effect, a dimming of the final flame, when a small fire fails to ignight larger fuel. The classic example being lighting a small splinter on a large hunk of firewood. The splinter burns well and brightly, but as it’s consumed, the fire just isn’t big enough to heat the nearby bit of larger log enough to pyrolize. In the final moments the tiny fire is spending all its energy against the larger background of cold wood. So it both shrinks in size and declines in brightness until it’s gone.
* See here for more: