Abstract:Flotation is a process in which micro-scale mineralization （collision，adhesion，and detachment） occurs locally during the macro-scale movement of bubbles and particles in a fluid. A complete flotation kinetics process should encompass the multiphase hydrodynamics process dominated by the movement of particles and bubbles，as well as the mineralization kinetics process centered on particle-bubble interactions. The flotation of fine particles is strongly dependent on the turbulent environment. However，due to disciplinary barriers，classical microscopic flotation kinetics models are difficult to apply to fine particle flotation because they do not fully consider the characteristics of micro-turbulence. Traditional multiphase flow models are also difficult to apply to mineral flotation systems as they fail to adequately account for the physicochemical factors involved in flotation. This paper systematically summarizes the key mathematical models dominated by hydrodynamics in the flotation process of fine minerals，including the drag coefficient model between bubbles and fluid，the drag coefficient model between particles and fluid，and the particle-bubble collision model. Meanwhile，focusing on key points such as interface properties，flotation solution chemistry，and turbulent flow，it analyzes the applicability of existing models and the progress made by researchers （including our team） in addressing the insufficient applicability of current models. For example，a gas-liquid drag coefficient model considering the effects of surfactants and particle loading，a liquid- solid drag coefficient model considering the fine-scale effect and surface hydrophobic effect，and explorations in the modification of particle-bubble turbulent collision models have been established. Flotation hydrodynamics research that fully considers micro-scale turbulence characteristics and is deeply coupled with interface physicochemistry， as well as the model research paradigm combining CFD （Computational Fluid Dynamics） and AI （Artificial Intelligence），are important challenges for breakthroughs in flotation basic theory.