Estimation of Metal Drop Size on a Reducing Gas Bubble during Oxide Melt Bubbling

In this paper, we use the metal-phase formation model to estimate the drop size formed on individual bubbles of the reducing gas during the oxide melt bubbling. The model includes the following stages: the bubble formation upon gas injection into the melt, metal reduction on the bubble surface, and its drop concentration in the stern. We present equations that estimate the limiting sizes of a gas bubble (\(R_{{\text{b}}}^{{{\text{cr}}}}\)) and a drop (\(r_{{\text{d}}}^{{{\text{cr}}}}\)) moving in an oxide melt without defragmentation. The critical sizes of a gas bubble (\(R_{{\text{b}}}^{{{\text{cr}}}}\)) moving in an oxide melt without defragmentation were calculated using the densities (ρ kg/m³) and surface tension (σ, mJ/m²) of B₂O₃–CaO and B₂O₃–CaO–CuO melts that are, respectively, described by the equations: σ₁ = 87.0 + 0.242T , ρ₁ = 3.26 × 10³ – 0.91T, σ₂ = 10.8 + 0.178T, ρ₂ = 3.19 × 10³ – 0.70T in the temperature range of 1373–1673 K. Depending on the temperature, the critical bubble radius varies from 0.047 to 0.053 m in the B₂O₃–CaO–CuO melt and 0.06–0.081 m in the B₂O₃–CaO melt. Depending on the CO amount introduced at various temperatures, the change in the copper oxide content in the B₂O₃–CaO–CuO melt was determined by calculating the thermodynamic equilibrium to describe the features of oxide melt bubbling by various reducing gases. Based on the obtained data, the copper amount produced from the interaction of Cu₂O in the melt with a single CO bubble was calculated depending on the copper oxide content and the CO amount in the bubble. The correlation dependences of the drop size on the Cu₂O content in the melt (\({{C}_{{{\text{C}}{{{\text{u}}}_{{\text{2}}}}{\text{O}}}}}\), %), temperature (T, К), and the CO amount in the bubble (n_CO, mol) were obtained by statistical data processing.