Thermodynamic theory of flotation for a complex multiphase solid–liquid system and high-entropy flotation

The flotation of complex solid–liquid multiphase systems involves interactions between multiple components, which is the core problem faced by flotation theory. Meanwhile, the combined use of multi-component flotation reagents to improve mineral flotation has become an important issue in studies on the efficient utilization of refractory mineral resources. However, studying the flotation of complex solid–liquid systems is extremely difficult and no systematic theory has been developed to date. In addition, the physical mechanism associated with combining reagents to improve the flotation effect has not been unified, which limits the development of flotation theory and the progress of flotation technology. In this study, we applied thermodynamics theory to a solid–liquid flotation system and used changes in entropies and Gibbs free energies of the reagents adsorbed on the mineral surface to establish thermodynamic-equilibrium equations that describe interaction between various material components, while also introducing adsorption equilibrium-constants for the flotation reagents adsorbed on the mineral surface. The homogenization effect on the mineral surface in the pulp solution was found to be determined by the chemical potentials of the material components of the various mineral surfaces required to maintain balance. The flotation effect can be improved through synergy between multi-component flotation reagents, its physical essence is the thermodynamic law that the number of components of flotation reagents on the mineral surface increases, the surface adsorption entropy changes increases, and the Gibbs free energy of adsorption decreases. Based on the results obtained using flotation thermodynamics theory, we established high-entropy flotation theory and a technical method, in which increasing the types of flotation reagent adsorbed on the mineral surface, enhancing the adsorption entropy change of the flotation reagents, reducing the Gibbs free energy change, and improving the adsorption efficiency and stability of the flotation reagents, improves refractory-mineral flotation.