Particular Aspects Concerning Instability at Interface LCAK Steel- Slag (CaO-Al2O3) due to Transfer of Sulphur, Evaluated Using the Model Reichenbach-Linde Adapted

Abstract

Based on the model of Reichembach and Linde, adapted to the interface in the system LCAK steel-(CaO-Al₂O₃) slag at temperature 1873.15 K, it is shown that transfer of sulphur from steel to slag could promote interfacial Marangoni instability, proven by positive and relative small values of Marangoni dimensionless number, related to slag. Positive values of critical Marangoni number have been found in the rage of dimensionless wavenumber a a₀<a<a_∞ , a₀ =2.881255±5·10^-6 and a_∞=3.0058−3.006 (asymptote) for a characteristic length d=100 μm. In the range of values of the dimensionless wavenumber a=2.9−3.0, corresponding to wavelength λ=216.66−209.44 μm, a relation Ma_c,slag = (0.0957a + 0.618 + (1/(L_S·D^*)))·e^{168.69a2-947.51a+1331.7}, containing also the sulphur partition ratio between slag and steel LS and ratio of diffusion coefficients of sulphur in slag and steel D^* , was established giving values of critical Marangoni dimensionless number. Values Ma_c,slag=20−5200 are obtained for L_S=10−1000, supporting the idea that slag is active in the dynamics of interface steel-slag with consequences on the steel quality and kinetics of important processes of refining, contrary to certain evaluations seeming to be insufficiently substantiated. Stationary instability in the form of short wavelength waves could develop in the mentioned conditions or, considering the asymptote found at a_∞=3.0058−3.006 oscillatory waves could develop.