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We all know that fire spreads quickly in some materials,and in others doesn't.

Why? How is fire spreading at atomic level? Is the velocity of spreading constant?

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Fire happens on the molecular level, I would claim. Fire is the process of oxidation. Materials like hydrogen or carbon will form bonds with oxygen. This will release energy in form of heat. However, there is a certain energy of activation needed to split the $\mathrm{O_2}$ molecule and also to get the oxidized substance split from its bonds. This energy needs to be supplied from outside will be given back in the chain reaction.

The spreading will work by heating the environment and enabling the oxidation reaction. From there, it depends on the chemical properties of the material, the density, whether there is wind. The velocity of spreading is probably more or less constant if the fire reached the full scale. Until then, it will probably accelerate spreading due to overall heating of the environment up to combustion temperature and also non-linear effects like chimneys.

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