If you burn carbon, you can just decrease your air input to furnace. It is not done today because it causes lots of CO, which is very poisonous. If you don't care about CO like in this process, you an put O2 sensor (lambda sensor, used in all new cars to alter how much air is used) and almost eliminate oxygen from your output.
It works fine for any degree of oxygen blend too, it just requires proportionally more Gallium. 400 times more or so for atmospheric blend. The problem is the energy required to then reduce the gallium.
I wish it were this simple... but given that there's ~5250 O2 molecules for each CO2 molecule in the air, this will result in the production of 5250x additional CO2 molecules. Our CO2 capture process would then have to be 99.9999% efficient for this to pencil out.
One could mix the incoming air with hydrogen. Igniting that would capture the oxygen in the resultant water. This would allow precipitating it out prior to the mix hitting the gallium. Hydrogen could then be recaptured by using electrolysis on the byproduct water, exhausting the oxygen.
I don't imagine this would be particularly efficient, however.
I don't understand the downvotes. The idea of turning excess oxigen into CO2 which I replied to is plainly stupid just because of this proportion. How much coal (and oxygen) would we use up to bring down CO2 levels to 0.03?
GP proposed to filter out O2 by burning carbon. This will create a CO2-rich gas, perhaps at about 30% (depends of the density of CO2 compared to O2).
GP didn't mean that we deplete oxygen in the athmosphere, but that this is an intermediate step inside the CO2 scrubbing apparatus. Perhaps that's why you got downvotes.
The burnt carbon will be gained back by the Gallium process, however this might not work out anyway because the process needs to be very efficient in filtering out CO2, as someone else already pointed out.
I do wonder if it would be much cheaper to capture CO2 by investing technology and capital into 'building' forests. What if we can irrigate Sahara and cultivate some fast-growing plants like bamboos there? Maybe that has ecological consequences but it doesn't seem to be much different than the agricultural land expansion that has happened in rainforests in the first place.
The sahara seems like a bit of a hassle compared to the taiga (russia to canada). The real problem with growing forests is that they do not store significant amounts of carbon after they reach maturity. They did during the carboniferous, but after fungi figured out how to decompose cellulose they haven't, and wont. Fast growing plants only capture carbon faster, but the total storage would be less per area.
However, we do know of how the deposits of fossil fuels formed in the first place, and most places newer than the carboniferous, formed at the bottom of deep lakes and especially oceans. They form from the anoxic compaction of marine snow. Either during massive algae booms, or more slowly from slightly larger corpses.
This process is slow for several reasons, but a significant, in particular for the latter category, one is the lack of surfaces for attachment on the open ocean.
The creation of large floating artificial coral reefs could provide this, and with it a highly productive rich ecosystem. We could further fertilize these, with iron in particular being rare, but also regular fertilizer.
