A model for slag eyes in steel refining ladles covered with thick slag

During inert gas stirring in steel ladles, the overlying slag is pushed to the side by the rising gas-metal plume, resulting in an open-eye of exposed metal. The present work is devoted to the formation of ladle eyes in a bath covered with a thick slag layer, where the eyes formed are often smaller than the cross-section of the gas-metal plume. The model is developed from fundamental fluid flow considerations by extending the concept of a previous mechanistic-based approach for modeling eye formation in thin slag layers. The present model for the eye size correlates a dimensionless eye area to the density ratio of the liquids and an appropriate Froude number. It is shown that the model is consistent with the experimental results in different gas/liquid/liquid systems. Further, a criterion is deduced for soft bubbling of Argon in the ladle without forming an eye that brings the metal above the slag layer.