## 3 Results  
Motion simulation was performed for grain mixtures of wheat: bulk density 750 kg\(\cdot\)m\({}^{-3}\), calculated value of flow viscosity \(\mu_{0}\) = 0.1 Pa\(\cdot\)s, equivalent impurity diameter \(d_{p}\) = 0.002 m, average impurity particle density \(\rho_{p}\) = 400 kg\(\cdot\)m\({}^{-3}\). The selected values of density \(\rho\) at numerical miscalculations were accepted under the condition of basic humidity of grain mix of wheat of 14%. It was not difficult to take into account the change in moisture content of the grain mixture and grain density of the main crop and impurities, conducting additional experiments. The numerical calculation of the system of Equations (5) and (6) obtained the trajectories of particles of the grain mixture (Figure 5). Initially, the particles of the grain mixture move downward under the action of gravity. Impurities, whose velocity of floating was less than airspeed, changed the direction of movement and began to move upwards. For such particles \(F/m>g\). Other heavier particles of grain mixtures moved downwards. For them \(F/m<g\). According to previous studies [10; 11; 29; 30; 31], the following structural and technological parameters were adopted for the developed pneumatic separation duct: the slope angle of the scaley surface (\(\theta\)) was 40\({}^{\lx@math@degree}\), its length 0.5 m, the airflow velocity on the scaly surface 3 m\(\cdot\)s\({}^{-1}\), the airflow velocity in the vertical ducts V= 6 m\(\cdot\)s\({}^{-1}\), duct width 0.05 m. The results of mathematical modeling of the dynamics of components of grain mixtures in the vertical duct in the form of trajectories of impurity particles are presented in Figure 6.  
The analysis of trajectories (Figure 6) revealed the influence of the coordinates of the location of the impurity particles on the thickness of the mixture layer and on the efficiency of its selection. The effective separation of light impurity particles located in the middle and above the middle of the grain mixture layer was also determined. To determine the influence of the properties of particles of lightweight impurities on the dynamics of their motion in the vertical duct, we differentiated their introduction by the thickness of the layer. A laboratory facility was used for experimental studies (Figures 2 and 3). Due to its transparent wall, the location of a given particle of lightweight impurities in the work area was determined and the trajectory of its motion was also defined (Figures 7 and 8). Figure 8: The trajectories of the grain mixture particles in the vertical duct at the initial coordinate: 1—y\({}_{0}\) = 0.05 m; 2—y\({}_{0}\) = 0.04 m; 3—y\({}_{0}\) = 0.03 m; 4—y\({}_{0}\) = 0.02 m; 5—y\({}_{0}\) = 0.01 m; 6—y\({}_{0}\) = 0 m; (H = 0.05 m; 1 = 7 m:s^-1; d\({}_{\rm p}\) = 0.002 m; \(\rho_{\rm p}\) = 700 kg m\({}^{-3}\)); —the upper boundary of the grain layer; —trajectories of impurities. Figure 6: The trajectories of impurity particles in the vertical duct (d\({}_{\rm p}\) = 0.001 m; \(\rho_{\rm p}\) = 600 kg m\({}^{-3}\)): 1—trajectories of impurity; 2—the upper boundary of the grain layer; 3—the impurity trajectory without considering the effect of the grain layer. The dependence analysis (Figures 7 and 8) confirmed the results of mathematical modeling and determined the presence of redistribution of light impurity particles in the working zone of the vertical pneumatic separation duct. It was established (Figure 8) that particles of lightweight impurities with lower density crossed the upper boundary of the grain mixture much earlier (by 40-90%) and had time to stand out at the initial coordinate within the layer. At the initial arrangement of the particles of light impurities inside and in the upper sub-layers, their separation was observed along the width of a given vertical duct. It was proved that the location of particles of lightweight impurities in the lower sub-layers of the grain mixture creates problems with their redistribution in the layer and separation.