Modeling electrochemical transport of ions in the molten CaF₂-FeO slag operating under a DC voltage

Electrically resistive CaF2-based slags are extensively used in many metallurgical processes such as electroslag remelting (ESR). Chemical and electrochemical reactions as well as transport of ions in the molten slag (electrolyte) are critical phenomena for those processes. In this paper, an electrochemical system including two parallel, planar electrodes and a completely dissociated electrolyte operating under a DC voltage is modeled. The transport of ions by electro-migration and diffusion is modeled by solving the Poisson-Nernst-Planck (PNP) equations using the Finite Volume Method (FVM). The non-linear Butler-Volmer equations are implemented to describe the boundary condition for the reacting ions at the electrode-electrolyte interface. Firstly, we study a binary symmetrical electrolyte, which was previously addressed by Bazant et al. (2005), to verify the numerical model. Secondly, we employed the model to investigate our target CaF2-FeO system. The electrolyte is consisted of reacting (Fe2+) and non-reacting (Ca+2, O2-, F-) ions. Spatial distributions of concentrations of ions, charge density, and electric potential across the electrolyte at steady state are analyzed. It is found that the Faradaic reaction of the ferrous ion (Fe2+) has negligible impact on the electric potential field at very low current density (<1 A m-2). The strong impact of electric double layer (EDL) capacitance on the system behavior is addressed throughout our analysis. Furthermore, a linear relationship among activation (surface) overpotential and current density (<1600 A m-2) is observed. The simulation results helps to explain some phenomena observed in the ESR process. The higher melt rate for an anodic ESR electrode than a cathodic one is linked to the interfacial potential drop. It is found that the anodic potential drop near the anode is larger than the cathodic voltage drop near the cathode. The results are tested against an experiment.