Hertha Ayrton in The Electric Arc has a formula that gives an absolute minimum voltage of about 28 VDC. This is a very old book and tough going but the formula is in there. Above that point you need a minimum current as well so it becomes dependent on fault current but reasonable short circuit currents such as 200% of the power supply maximum output quickly show why there are practical limits. Ammerman covers this and more in detail here: DC Arc Models and Incident Energy Calculations. R. Ammerman, T. Gammon, P.K. Sen, J. Nelson. IEEE Transactions on Industry Applications, Vol. 46, No. 5, September/October 2010
Essentially the minimum theoretical arc voltage is around 25-30 VDC but this is with nearly infinite available current and working at a 1 mm gap. One of the more recent papers (referenced above) is the Stokes and Oppelander (1991) work that reviewed a lot of the others and gives a formula for arc voltage as Varc=(20+0.534*L)*I^0.12 where L is the arc gap in millimeters. So if we set the gap to 1 mm then to get to a 50 V arcing fault we'd need 2.435 = I^0.12. Taking the log of both sides we get 0.3865 = 0.12 * log(I) or 3.221 = log(I). Solving finally for I we get 1662 A which is quite a bit more current than most DC power supplies can put out. Don't forget that this is with a ZERO system resistance. The real system would need at least twice that current based on maximum power transfer arguments so we need at least 3324 A to sustain an arc at 50 VDC with no gap at all across air. Welders do not need this much current because the arc is within a metal vapor/liquid. Note that pretty much all the models in the above paper show an absolute theoretical minimum of around 25-30 VDC for arcing no matter how much current is applied even as the arc gap drops. You can run through Ammerman's full theoretical model working it to see where the cutoff is but it's there and there's no way to worry about anything under around 50 V. So the limit in 70E stands.
