Integrating Calphad and finite volume method for predicting non-equilibrium solidification of lithium metasilicate

Abstract Efficient recycling of lithium metasilicate (Li 2 SiO 3 ) from lithium-containing slag via a pyrometallurgical route demands a comprehensive understanding of its solidification process in the slag reactor. A simulation framework is developed to predict the heterogeneous phase distribution of Li 2 SiO 3 , the temperature and velocity fields considering density changes in the solidifying melt, on the apparatus scale. This framework integrates thermodynamic models via calculation of phase diagrams with the enthalpy-porosity technique and the volume of fluid method within a finite volume approach, ensuring thermodynamic consistency and adherence to mass balance. Thus, the formation of Li 2 SiO 3 from the liquid slag composed of Li 2 O-SiO 2 is described in space and temporal fields. Thereby, the interrelationship between the temperature field, enthalpy field, velocity field, and phase distribution of Li 2 SiO 3 is revealed. It is shown that the lower temperature on reactor boundaries prompts the earlier formation of Li 2 SiO 3 in the vicinity of the boundaries, which subsequently induces a downward flow due to the higher density of Li 2 SiO 3 . The predicted global mass fraction of Li 2 SiO 3 under non-equilibrium conditions is 11.5 wt % lower than that calculated using the global equilibrium assumption. This demonstrates the global non-equilibrium behavior on the process scale and its consequences on slag solidification.