What is the physical mechanism of an iron spark? What propels it? How does it form a microsphere? Why do sparks shoot away from the steel wool?
Hypothesis: It seems like a spark there is like a micro rocket, a tiny bit of fuel that is burning on one side, so it gets propelled away. The burning can't combust the entire thing, but produces enough heat to entirely melt what remains. Surface tension forms a sphere, and it solidifies in a fraction of a second.
But how does the rocket form?
What's the exact limiting mechanism that stops larger pieces of steel combusting?
Once again, Mick, great experiments!!!
If you look on the internet you can find some sites making experiements with steel wool, too, e.g., here one for kids:
http://www.bbc.co.uk/bang/handson/steel_wool.shtml
From there I got also the idea of igniting it with a battery, but other places have the battery ignition, too, including survival sites,
It appears the ignition of steel wool is quite common in student chemistry labs, as the wool after burning is heavier than before. This is counter-intuitive to usual concepts of combustion, but it becomes clear when looking at the chemical reaction:
4 Fe + 3 O2 → 2 Fe2O3,
which is exothermic. It has no gas as product, so gas produced from the reaction as a propellent is ruled out.
The iron gets oxidized to
Iron(III)oxid. So the spheres we obtain are Iron(III)oxid, which becomes rust only upon hydration. Before hydration it does not look red but still shiny metallic. Its crystalline form is
Hematite.
So is it clear whether we are looking for microspheres of iron or of iron(III)oxid?
The reaction rate is limited by the amount of oxygen available compared to the surface.this is also an explanation why macroscopic pieces of iron do not burn, because the low surface-to-volume ratio inhibits the reactants to come into contact sufficiently, and the energy produced by the reaction is not self-sustained.
You can compare that with wood wool, which burns quite rapidly (and also similarily to steel wool) when ignited:
[the wood wool is right]
Compare that if you try to ignite a bulk piece of wood which has been planed and smoothed; it wont ignite readily. And if you manage to ignite it eventually, it will probably not burn self-sustained but go out. Only when you put the wood piece into the glow of a fire (initiated by smaller pieces of wood) that was burning for a while, it will ignite in a self-sustained way.
So it is all about the surface-to-volume ratio that lets iron burn.*
The difference in the surface-to-volume ration also might be an explanation for the two different processes Mick observed:
- smaller strands have a favourable surface-to-volume ratio for a higher combustion rate transversal to the strand, so the iron gets hot quick and forms a drop of molten iron at the end of the string, still attached. The heat produced in the drop can be conducted along the strand, and if the conduction is quicker than the reaction rate progressing of combustion along the strand the drop detaches and you get a small microsphere.
- bigger strands have a lower combustion rate transversally, so do not produce so much heat, but still enough to form a drop of molten iron at its end. However, heat conductivity progresses here slower than the combustion along the string, so that the drop can grow while it walks along the strand.
This is just a hypotheses by me, but it can be tested by burning single strands with different thicknesses.
To the question why sparks shoot away from the steel wool. I guess this results form a difference of temperature between two sides of a molten microsphere. The gas molecules that come into contact with the hotter side get more kinetic energy than those on the colder side, thus producing more pressure on that side. This pressure difference is enough to propel the microspheres for tens of centimetres.
This could also explain curved trajectories by assuming that the microsphere got some angular momentum either from the start right away or after some collision.
The effect is quite similar to that in the (misnamed)
light mill, where the gas particles bouncing away from the hotter plate propel the mill:
* Just an idea: Maybe the energies of the plane crash / fire were sufficient to get the iron ignition started. So perhaps the CTs were right about flows of molten iron from the Twin Towers?? 

On the other hand, this was surely checked before… [deleted after discussion with Mick, see posts below]