# Analysis of Feed Inlet and Optimal Feeding Amount of Waste Ground Film Impurity Removal Equipment
## 2 Materials and Methods
### CFD-DEM Fluid-Solid Coupling Simulation Analysis  
#### 2.2.1 Principle of Agglomeration and Depolymerization of Membrane Hybrids  
As shown in Figure 6, the residual film was not recovered earlier during the operation. It was entangled and mixed with straw in the soil. The soil particles and liquid droplets combined to form a strong, wet clod and adhered to each other via the straw and the film. When the water in the soil evaporated, the soil, straw, and film agglomerated into a whole. The recovered residual film was mixed with a large amount of this film-soil-cotton stalk mixture agglomerate [14].  
As the device was rotated, the residual film-impurity mixture collided with the wall of the drum screen, and the agglomerates were depolymerized, thus achieving the effect of separating the residual film and impurities. When the maximum collision force, \(F_{\text{cmax}}\), was greater than the maximum viscous force, \(F_{\text{rnn}}\), the agglomerates were broken. The relationship between them was given using Equation (1):  
\[F_{\text{cmax}}>F_{\text{rnn}} \tag{1}\]  
Soil, straw, and residual film agglomerates collided with the wall of the trommel screen inside the device. The maximum collision force in the collision was expressed using Equation (2):  
\[\left\{\begin{array}{l}F_{\text{cmax}}=0.2516\left[\left(\frac{\pi e^{6}\rho _{p}}{k^{2}}\right)\left(\frac{d_{1}^{3}d_{2}^{3}}{d_{1}^{3}+d_{2}^{3}}\right) \left(\frac{2d_{1}d_{2}}{d_{1}+d_{2}}\right)\right]^{\frac{1}{5}}\\ k=\frac{E}{1-v^{2}}\end{array}\right. \tag{2}\]  
where \(d_{1}\) and \(d_{2}\) are particle sizes (m); when \(d_{2}\) was much larger than \(d_{1}\), it was considered to be a collision between the agglomerate and wall; \(k\) is the elastic deformation coefficient of the particle (Pa); \(\rho_{p}\) is the density of the agglomerate (kg/m\({}^{3}\)); \(v\) is the relative collision velocity of the agglomerate and wall of the drum sieve (m/s); \(v\) is [PERSON]'s ratio; and \(E\) is [PERSON]'s modulus of elasticity (Pa).  
When the agglomerate collided with the wall, the constituent particles tended to move relative to each other and were subjected to both tangential and normal viscous forces. The distance between the agglomerate and the wall was rather small; thus, the tangential viscous force was much smaller than the normal viscous force. Therefore, the tangential viscous force was excluded when considering the force of the collision process [15]. The normal viscous force was given using Equation (3):  
Figure 5: Operating principle of the tumbler screen-type film miscellaneous wind separator.  
Figure 6: Membrane heterogeneous mixture agglomeration principle.  
\[F_{vm}=6\pi\mu R^{*}v_{n}\frac{R^{*}}{\hbar} \tag{3}\]  
where \(\mu\) is the dynamic viscosity (N-s/m\({}^{2}\)); \(v_{n}\) is the normal relative motion velocity of the agglomerate and the wall (m/s); \(\hbar\) is the distance from the surface of the agglomerate to the surface of the tremmel screen (m); and \(R^{*}\) is the folding radius, where \(\frac{1}{R^{*}}=\frac{1}{R_{1}}+\frac{1}{R_{2}}\); \(R_{1}\) and \(R_{2}\) are the equivalent radii of the agglomerate and the wall of the tremmel screen, respectively, and \(R_{2}\) can be increased to infinity.  
Equations (2) and (3) were used to obtain the collision force between the agglomerates; the surface of the drum screen increased with an increase in the relative collision velocity. Therefore, among the film-hybrid wind separators, enhancing the relative collision velocity between the residual film-impurity mixture and the tremmel screen facilitated disaggregation.