To date, the main problem in the development of the mineral resource base has been the deterioration in the quality and technological properties of processed minerals. This has led to a significant decrease in the efficiency of traditional beneficiation techniques. These techniques are unable to meet industry standards in terms of the content of useful components, processing complexity, and environmental requirements.

The key factors determining the technological complexity of processing strategic raw minerals include: the dispersed connection between minerals of valuable components and waste rock, high complexity and variability in material composition, and the complexity of the morphology and separation of ore bodies involved in the processing. All these aspects significantly affect the efficiency of beneficiation processes and profitability of the final product.

The main directions for solving this problem are improving flotation beneficiation processes. The flexibility and versatility of flotation technologies allows increasing their efficiency through improving reagent regimes and intensification methods with the preceding grinding stage. Confirmation of the effectiveness of these solutions is possible through the use of complex numerical criteria based on experimental and theoretical studies of the physical and chemical properties of raw materials.

For numerical evaluation of the intensifying impacts during the grinding process, a semi-empirical criterion has been proposed, which characterizes the proportionality between the required specific energy for destruction and the relative reduction in the characteristic fineness of the product. This criterion is based on interpreting the Gibbs–Helmholtz equation in terms of the equivalence of energies expended on reducing the fineness and forming a new surface area. In grinding operations, the increase in the newly formed surface area is proportional to the energy spent breaking a certain amount of material, as described by Bond's law.

To establish the influence of variations in grinding and flotation technologies on beneficiation efficiency, a method for characterizing the distribution of materials by flotability has been proposed. This method allows for the numerical characterization of changes in the flotation ability of materials. The method is based on a probabilistic-kinetic approach to studying flotation, and it involves abstractly allocating flotability classes to materials according to their flotation properties. Each fraction of material is assigned a flotability value, which is proportional to the flotation constant rate of that fraction. The flotation index value represents the proportionality between the flotation recovery probability and the constant value of the fraction's flotation rate. Initial data for determining flotability functions are obtained from experimental studies of flotation kinetic enrichment using the γ model. The values of the flotation function characterize the distribution of materials into certain flotation classes and collectively represent a step function with an exponent b.

Thus, the criterion for intensifying the grinding process's efficiency will allow us to justify the most cost-effective ratio of particle size and energy consumption for the proposed ore preparation solutions. Parameters of floatability functions will allow estimating the effectiveness of new reagent regimens on the flotability of various ore components. Establishing correlations between these parameters will enable us to characterize the impact of intensified grinding on the efficiency of flotation processes.

This work was carried out within the grant of the Russian Science Foundation (Project № 23-47-00109).