## 2 Literature Review  
The simplest pneumatic classifiers with vertical channels are not widely used since they do not provide the required separation efficiency [7]. In such devices, a raw material is loaded into the working volume, causing an increase in gas-dispersed flow density. Consequently, the mixture has poor contact with the gas flow. Therefore, the coarse fraction entrains the fine fraction, which decreases the efficiency of fractional separation. Further development of such devices was presented by zigzag pneumatic classifiers [8; 9], wherein centrifugal forces arise due to the gas flow turns, causing particle circulation. This effect reduces flow density and, consequently, increases the efficiency of the classification process. However, this type of pneumatic classifier was modernized, and the new design has a vertical channel with a rectangular cross-section, in which blind shelves are installed at two angles to the gas flow [10; 11]. However,blind shelves significantly increase the hydraulic resistance of the device and turbulize the flow, which increases entrainment of a coarse fraction into the cyclone. The device with inclined perforated shelves allows implementing an active aerodynamic mode of suspending the granular layer. Consequently, entrainment of the coarse fraction and energy costs of the pneumatic classification process are reduced. The apparatus of this design enables effectively removing the fine fraction of less than 1 mm from the polydisperse mixture of granular mineral fertilizers [12]. Pneumatic classifiers with a fluidized bed of the granular layer and perforated grate [13; 14] are mainly intended for separation of the bulk product in order to separate particles less than 0.5 mm from the layer. This allows extending the separation possibility to significantly increase the gas flow rate, which leads to increased energy costs. Pneumatic classifiers based on the action of centrifugal forces are mainly used for separation of fine materials with a particle size less than 0.04-0.05 mm [15; 16]. Their main disadvantage is the content of a significant amount (about 20-25%) of fine particles and the presence of a coarse fraction in the final product. Moreover, centrifugal turbo-air classifiers are highly complicated [17; 18]. Thus, a rhomb-shaped pneumatic classifier is a relatively new device, which is applied in the technology of producing organic mineral fertilizers [19]. Due to the absence of internal contact elements, the rhomb-shaped pneumatic classifiers have a minimized hydraulic resistance. Moreover, a relatively high degree of product separation in such an apparatus is achieved by cyclic loading of raw material into the apparatus, thereby creating a rotating vortex layer; accordingly, prolongation of the contact of particles with the gas flow is efficiently provided. Complicated nonlinear dependencies describing the mass transfer process can be numerically calculated using the artificial intelligence systems based on the generalized approach presented in Reference [20]. Additionally, research work [21] was devoted to decreasing the complexity of the practical use of empirical constants and their applicability to specific conditions. However, the mechanism of particle transportation in a fluidized bed depends on a number of hydrodynamic effects, including collisions of particles, and on the characteristics of both solid particles and suspended layer. Moreover, the use of a graphical method for calculating the process of pneumatic classification using separation curves is proposed in Reference [22]. Unfortunately, in this case, computer realization is not possible. Due to the abovementioned issues, the aim of this article is to develop a reliable mathematical model of the pneumatic classification process for polydisperse mixtures of granular material in a rhomb-shaped apparatus.