Capillary Interaction Between Arbitrarily-Shaped Inclusions at the Gas/Steel Interface

The dynamic behavior of non-metallic inclusions at the bubble/steel interface or at the slag/steel interface is of particular importance for inclusion removal, and therefore, clean steel production. The attractive long-range force between inclusions is believed to be a kind of capillary force, which arises from the interface deformation due to the presence of the particles. The model developed by Kralchevsky and Paunov (K-P model) for floating spheres is widely applied to explain this long-range force. To apply the K-P model, non-spherical particles are usually simplified as spheres with an equivalent radius or effective radius. However, this simplification may introduce significant errors. A quantitative study of the capillary force between disc-like inclusions by the K-P model, our recently developed sub-particle model and the analytical solution shows that the attractive force calculated from the K-P model deviates from the analytical solution by one order of magnitude, and the degree of the deviation depends on the disc height. The meniscus deformation and the capillary force calculated from the sub-particle model agree well with the analytical solution. In addition, the anisotropic character of interaction between elliptical discs is captured by the sub-particle model.