**4. Conclusions**

Numerical simulations using a multi-phase SPH method were performed on two immiscible high-temperature melts dripping through a coke-packed bed during an ironmaking blast furnace process, namely, a binary trickle flow in which liquid iron and molten slag dripped simultaneously. The advantage of this method is the direct estimation of the transient three-dimensional behavior of multi-phase flow based on body forces considering the force acting between different phases, including complex dispersed phases. The present detailed analysis helps in the rationalization of the unexplained transient behavior of liquid iron and molten slag presented by previous experiments. In particular, the effect of coke surface wettability for molten slag on binary trickle flow was investigated.

The flow behavior of liquid iron is influenced by the presence of slag in coke surfaces with different coke wettability. If the coke surface has poor wettability and contains molten slag, the molten slag drops along the molten iron. However, a coke surface with good wettability retains molten slag owing to a higher attractive force acting between the coke and slag rather than an interfacial force of attraction acting between the iron and slag. Although the molten slag dripping rate is lower than that of the liquid iron because of high viscosity and low density, the coke bed surface is wet by slag immediately and facilitates the sliding of the liquid iron. These results demonstrate that the static hold-up of molten slag may promote the smooth dripping of liquid iron. As predicted by novel findings presented in this study, when the low reducing agent ratio operation is realized, increases in the amount of liquid iron and molten slag passing through a unit volume of coke bed finally influence the amount of stagnant melt behavior in the coke bed through a mechanism in which the descent velocity of each melt depends on coke-slag wettability. Through this analysis, the mechanism underlying the simultaneous trickle flow of liquid iron-molten slag behaviors, as described in conventional research, can be explained from a unified point of view.

**Author Contributions:** Data curation, S.N., H.N., T.K. (Tatsuya Kikuchi), S.I., and S.U.; funding acquisition, S.N. and K.-i.O.; investigation, K.-i.O. and S.S.; methodology, S.N. and T.K. (Tatsuya Kon); software, S.N. and T.K. (Tatsuya Kon); validation, T.K. (Tatsuya Kon); visualization, T.K. (Tatsuya Kon); writing—original draft, S.N.; and writing—review and editing, S.N., H.N., K.T. and R.O.S. All authors have read and agreed to the published version of the manuscript.

**Funding:** This study was funded by the Steel Foundation for Environmental Protection Technology (SEPT), Japan, grant number C-41-52, and supported by the Japan Society for the Promotion of Science (JSPS) KAKENHI, grant number 15H04168.

**Acknowledgments:** The authors thank Shinsuke Taya, Kentaro Baba, Azuma Hirai, Akihisa Ito, and Miho Hayasaka for their support with the construction of the computing environment at Tohoku University, IMRAM.

**Conflicts of Interest:** The authors declare no conflict of interest.

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