## 1 Introduction  
Granular materials are useful in a number of engineering applications, for example, to increase the gas diffusion layer in a proton exchange membrane fuel cell [1], including the capillary pressure effect based on a fractal structure [2]. On the other hand, porous materials are widely used in practice, particularly in fibrous porous media made up of fibers and solid particles [3], as well as for ensuring the effective diffusion through charged porous media [4]. A classifier as a device for the separation of bulk polydispersed mixtures is one of the most commonly used pieces of equipment in any production. A variety of requirements and material properties determine a variety of designs and operating processes of this equipment. Increasing the efficiency of chemical, heat, and mass exchange, as well as thermal and heterogeneous processes in most cases, is achieved using solid materials in a powder-like condition and in a certain granulometric composition. Therefore, classifiers are installed in technological lines aimed at separating granular mixtures into two or more phases. This process is predominantly realized for fine and coarse particles. For this purpose, a pneumatic classification is widely used, and pneumatic classifiers are installed in devices of different designs. The complexity of interactions between gas, solid particles, and functional elements of the apparatus determines the difficulty to describe them, and there is so far an insufficient number of studies on the operating process. Therefore, the development of new designs (more efficient in terms of productivity) with a fundamentally new organization of the operating process should be based on experimental studies and a mathematical synthesis of the obtained results. This fact determines the relevance of this work. Granular materials are separated into fine and coarse fractions mainly under the influence of gravitational and inertial forces in the ascending gas flow in gravitational pneumatic classifiers or centrifugal-type devices [5]. The development and use of pneumatic classifiers in an industry are complicated due to the absence of general approaches for calculation of their parameters, which should be based on reliable mathematical models of the operating process. Consequently, one of the main objectives of recent research is developing a comprehensive approach for modeling the suspended layer when it is transferred from the polydispersed fraction in the apparatus and separated by the turbulent gas flow. Most designs of pneumatic classifiers operate quite efficiently as separators for the removal of fine fractions from granular mixtures with a content of fine fraction in the starting material in a range of 15-20%. When separating binary granular mixtures with an equal content of fine and coarse fractions, the typical pneumatic classifiers provide purity of the obtained fractions of 70-75% maximum. However, technologies requiring a clean separation product are needed for ensuring the efficiency of at least 95%. Therefore, it is necessary to develop new designs of related devices with a fundamentally different organization of pneumatic classification processes and pneumatic enrichment of granular mixtures in order to obtain sufficiently clean separation products. An important objective in the study of pneumatic classification is the development of the mathematical model, which allows determining the concentration of fine particles in a suspended layer of granular material and, consequently, the entrainment of fine particles from this layer [6]. It should be noted that there is a sufficient number of empirical equations to determine the entrainment of a fine fraction from the polydisperse mixture by the gas flow. However, these equations contain empirical constants, the determination of which is highly complicated. Moreover, these constants can be evaluated for a certain design of apparatus only.