The purpose now is to oxidize the carbon, too, without reducing the phosphorus and sulphur and causing them to return to the iron.

We want the pure iron to begin crystallizing out of the bath like butter from the churning buttermilk.
More and more of the carbon gas comes out of the puddle, and as it bubbles out the charge is agitated by its escape and the "boil" is in progress.

It is not real boiling like the boiling of a teakettle.

When a teakettle boils the water turns to bubbles of vapor and goes up in the air to turn to water again when it gets cold.

But in the boiling iron puddle a chemical change is taking place.