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Description
The behavior of nonmetallic inclusions (NMs) on gas bubble surfaces has received increasing attention due to its importance in clean steel production. Agglomeration of NMs at the gas/steel interface is usually observed because of capillary attractions. The Kralchevsky–Paunov (K-P) model is often employed to calculate this capillary force quantitatively. In the K-P model calculation, nonspherical particles are simplified into spheres with an equivalent or effective radius. However, this simplification may introduce significant errors. In the present work, a numerical sub-particle model is developed to study gravity-induced capillary interaction between inclusions. This model is an extension of the K-P model from floating spheres to more complex shapes. In the model, the parent inclusions are reconstructed by close-packed smaller spheres (sub-particles) into a parcel resembling the inclusion closely. The capillary interaction between the parent inclusions is represented by the pairwise summation of direct interaction between constituent sub-particles. The capillary interaction between sub-particles is assumed to have a similar form between floating spheres in the K-P model. The net capillary ‘charge’ of a sub-particle parcel is considered to be identical to its parent particle. As a case study, capillary interactions between a pair of round discs and elliptical discs are investigated. For round discs varied with thickness, predictions from the sub-particle model are consistent with the analytical solutions with errors less than 5%, in contrast to the simplified K-P model that can be off by an order of magnitude. For elliptical discs, however, no exact analytical solution is available. Here also the difference between the force calculated with the simplified K-P model and the sub-particle model is substantial and is aggravated with increasing aspect ratio. Moreover, the sub-particle model captures the anisotropy of the interaction.