A procedural model is urgently required for optimization of slag foaming in metallurgical processes. Through physical modeling following the similarity criterion of the Morton number (Mo), this paper investigates the effects of superficial gas velocity, dynamic viscosity, and surface tension on the foaming height. From the physical modeling results, several dimensionless numbers relevant to the slag foaming were identified, and this includes the Reynolds number (Re), Weber number (We), Froude number (Fr), and Mo. In addition, the relationships between Mo and Re for the various types of slag foaming were derived via dimensional analysis. Furthermore, assuming that these dimensionless numbers follow a power law, correlations of foaming height as a function of the slag physical properties and the superficial gas velocity were obtained based on the physical modeling results. Consequently, this study proposes a dynamic mathematical model for predicting the liquid height variation with time during slag foaming according to the gas balance.

迫切需要一个过程模型来优化冶金过程中的矿渣泡沫。通过遵循Morton数（Mo）相似性准则的物理建模，研究了表观气体速度，动态粘度和表面张力对泡沫高度的影响。从物理模拟结果，相关的泡沫渣几无量纲数进行了鉴定，这包括雷诺数（重新），韦伯数（我们），弗劳德数（星期五），和莫。另外，之间的关系的Mo和重新用于不同类型的熔渣起泡的推导经由多方面分析。此外，假设这些无量纲数遵循幂定律，则基于物理建模结果，可以得出泡沫高度与炉渣物理性能和表观气体速度之间的关系。因此，本研究提出了一种动态数学模型，用于根据气体平衡预测炉渣发泡过程中液体高度随时间的变化。