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In this study, the electronic structure of the galena surface was investigated using the first-principle calculation. The results of band structure, density of states, Mulliken population distribution, and frontier orbital analysis showed that galena was the p-type semiconductor of the direct band gap. During the formation of galena crystals, the 3p orbital of the S and the 6p orbital of the Pb played a primary role. Additionally, S atoms in galena quickly lose electrons and are oxidized, while Pb readily reacts with anions. The results of surface structure and electronic properties, such as surface relaxation, surface state energy levels, electronic density of states, and atomic charge distribution showed that the electronics in the 6p orbital of the Pb are transferred to the 3p orbital of the S in galena crystal. They caused the change of atomic valence states in lattice surfaces. The total electron number of the outermost surface layer was also higher than the bulk, giving the galena surface the properties of electron enrichment. This research is of great significance for developing new galena flotation reagents and for further in-depth exploration of the adsorption of reagents on the galena surface.

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Flotation kinetic models can be applied to describe the flotation process and to predict mineral recoveries. However, the size composition of the target minerals in the feed ore fluctuates considerably, resulting in insufficient accuracy with flotation kinetic models. There have been many studies that focus on the investigation of flotation kinetics with different particle sizes, while the optimization methods for flotation kinetic models based on particle size effects have not been reported. In this paper, flotation tests, optical microscope observations, and particle size analysis were used to identify the reasons for the decrease in accuracy of the flotation kinetic model due to changes in the composition of molybdenite particle size. Additionally, an optimization method for the flotation kinetic model was developed based on the particle size effect. The test results show that the accuracy of the flotation kinetic model for fixed particle size minerals is very high, but the predicted results for flotation recoveries of different particle size mineral mixtures have large deviations. The poor accuracy might be due to the autogenous carrier effect caused by the particle size composition fluctuating considerably. The optimization method for the flotation kinetic model is based on the particle size effect. The model can accurately describe the flotation process of molybdenite with different size compositions of molybdenite and predict the flotation recovery of molybdenite.