Sorry, but your explanation to the foam creation doesn't make sense to me. First of all, OP told us:
Using sodium bicarb as a catalysis...the water over time deveopes a thick layer of white foam that floats on top of the water.
Over time, so it is building up, it is not a thing present all the time, it is not a thing that appears at the very beginning. It is not kind of a short lasting foam you are probably referring to (at least that's what I can guess form your description).
Second, amount of bicarbonate in the solution is limited, so (assuming it is a simple acid base reaction) it will be a problem only at the very beginning. Again, from the description it is not.
Third, overvoltage has to be taken into account when designing cell and calculating its parameters, no doubts about it, but we are talking about using voltages that should be easily able to overcome the problem. That means that the main limiting factor is the solution resistance which limits current we can use.
Finally, you suggest that H
+ is produced by the reaction of Fe
3+ with water:
It's CO2 caused by the reaction of localised hydronium ions (caused by the reaction of ferric ions with water) at the anode with the bicarb.
While it is very likely that electrode corrodes, it is not a fast process, so amount of H
+ produced will be low, for sure not high enough to make bicarbonate react as fast as you seem to suggest. We have several processes taking place, let's concentrate on two of them. On the anode dissolution of iron, followed by the carbon dioxide evolution:
Fe -> Fe
3+ + 3e
- (not necesarilly one step, but it doesn't matter for our calculations)
Fe
3+ + 3H
2O -> Fe(OH)
3 + 3H
+ (probably much more complicated, as there are many complexes involved)
3H
+ + 3HCO
3- -> 3H
2O + 3CO
2bottom line is - 1 electron used for corrosion, one molecule of carbon dioxide.
On the cathode:
2H
+ + 2e
- -> H
22 electrons, one molecule of evolving gas.
Even assuming that there are no other reactions but iron dissolution occuring on the anode, amount of carbon dioxide evolving will be only twice larger than the amount of hydrogen evolving. This is not as huge difference in speed as you suggest, and that's only assuming there is no oxygen evolving at the anode at all. There is oxygen evolving and anode corrosion is a slow process, so amount of carbon dioxide evelving should be much, much lower.