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The NASA has conducted an experiment in space (Flame Extinguishment Experiment (FLEX)) where they'd initiate a combustion in microgravity in order to test the effectiveness of different fire suppressants.

There's footage of the experiment, I think these images are fascinating, https://www.youtube.com/watch?v=qQQ1OHW1_F4 .

=> Can anyone make an educated description of the phenomenon ?

The combustion forms sorts of a bubble of plasma, there seems to be several phases in the reaction, at least an equilibrium phase and an out-of-equilibrium phase, a hot transient "flame" and a colder one (the slower combustion of heptane droplets used in the experiment, cf link below), etc...

=> Is there any representation or model in physics that predicts the distribution of energy or mass throughout such processes ?

You can find more details on the experiment here https://www.nasa.gov/mission_pages/station/research/experiments/666.html#overview

Edit note: I am not a physicist and can't recognize any more relevant tags for the post; please feel free to edit

Latest Edit: See the cold flame in the link below, at 4min05sec: https://www.youtube.com/watch?v=CE7Nz78rkfQ&t=195s

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There is no up or down in micro-gravity environments. This means that a flame on the space station forms a spherical "bubble", where the reaction products (e.g., CO2 and water) must diffuse outwards, past the flame front, while oxygen diffuses inward as it supports combustion. Any disturbances to this bubble, as seen in the video, will disturb the flame front, and allow more oxygen into the bubble.

For earth-bound flames, the results are quite different. Flame combustion products are very hot, which means that they have a low density compared to the air around them. Because of this, the combustion products rapidly rise, and fresh air rushes in to take their place. This speeds up combustion and produces turbulence, which is why the flame flickers. In addition, there is no "competition" between combustion products flowing outward as fresh air flows inward, so the combustion is much more vigorous than in the micro-gravity environment.

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