‘Carbon boil’ is CO gas bubbling to the liquid steel surface. It is a manifestation of carbon removal from the melt via oxidation. Large C contents, as in steelmaking from pig iron, are removed by oxygen blown through the melt. At very low C levels, CaO, MnO or SiO2 may be used.
It is more of a steelmaking practice than a foundry technique, although I have seen it at larger foundries. In the olden days of open-hearth furnaces, typical C removal rate was 0.12-0.18 wt. % C per hour. Faster rates were obtained by the basic oxygen furnace (BOF) and other top-blown oxygen processes [I think 4x faster]. – The Making, Shaping and Treating of Steel, 9th Edn., p. 374. The oxygen blow also removes excess Mn and Si as slag.
I don’t believe carbon boil has much relevance in stainless steelmaking per se, except as a preparatory steelmaking step. Nearly all SS is made by melting scrap in electric arc furnaces, by either AOD (argon-oxygen) or VOD (vacuum-oxygen) processes. The carbon content is reduced by oxygen blowing, and then the excess oxygen is removed prior to alloying additions. Don’t want to make Cr2O3. C content is determined by analysis rather than visual observation of ‘carbon boil,’ which would be difficult if blowing argon or pulling a vacuum. After removal of the initial, oxidizing slag (which contains P and S impurities as well as CaO, MnO & SiO2), a vacuum is applied or argon is blown through the melt to aid CO and excess O removal. This reduces the amount of CaC2, FeSix or Al needed to deoxidize the melt, minimizing the amount of reducing slag and resulting in a cleaner steel (fewer oxide inclusions). Then, the easily-oxidized Cr is added as FeCr2. [CaC2 can be added to reduce Cr2O3 from slag back into the liquid alloy, but I don’t know if this is much used.]
Hope this helps. My knowledge of steelmaking is rather dated, but the chemistry is unchanged although newer techniques (e.g., methods of applying vacuum) have been adopted.
Ken