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The area of the contact surface of phases is one of the main hydrodynamic indicators determining the separation and heat and mass transfer equipment calculations. Methods of evaluating this indicator in the separation of multicomponent two-phase systems were considered. It was established that the existing methods for determining the interfacial surface are empirical ones, therefore limited in their applications. Consequently, the use of the corresponding approaches is appropriate for certain technological equipment only. Due to the abovementioned reasons, the universal analytical formula for determining the interfacial surface was developed. The approach is based on both the deterministic and probabilistic mathematical models. The methodology was approved on the example of separation of two-phase systems considering the different fractional distribution of dispersed particles. It was proved that the area of the contact surface with an accuracy to a dimensionless ratio depends on the volume concentration of the dispersed phase and the volume of flow. The separate cases of evaluating the contact area ratio were considered for different laws of the fractional distribution of dispersed particles. As a result, the dependence on the identification of the abovementioned dimensionless ratio was proposed, as well as its limiting values were determined. Finally, a need for the introduction of the correction factor was substantiated and practically proved on the example of mass-transfer equipment.

The design of a multistage cooler with several inclined perforated shelves for cooling granular fertilizers is presented and explained in the article. It is proved that such device has certain technical and energy advantages compared with typical designs of coolers. For this purpose, physical modeling of the hydrodynamic structure of the fluidized bed in the shelf apparatus was carried out. The formation of hydrodynamic regimes that differ in their hydrodynamic structure depending on the design parameters of the shelf contact elements is justified. A mathematical model of the kinetics of cooling granules in a fluidized bed is developed, which makes it possible to determine the cooling time of granules and calculate the temperature profile in a suspended layer. The optimal design parameters of the shelf cooler were experimentally determined, at which the granules are intensively cooled to the technologically required temperature. The results of experimental studies are presented, which confirm the efficiency of granular fertilizers cooling in multistage shelf apparatus with less energy consumption.