## 4 Methodology
### Measurement Method of Material Suspension Velocity  
In the state of material suspension, force analysis is based on the principle of force balance. The analysis reveals that the material's downward gravity equals the upward buoyancy provided by the air and the combined effect of vertical upward air resistance. Correction factors are introduced to solve for the suspension velocity of non-spherical materials. The calculation methods include the equivalent particle size method and the suspension velocity zoning calculation method. These methods involve selecting appropriate air resistance coefficients and incorporating material and airflow parameters into the force balance equation to calculate the suspension velocity. This provides a theoretical calculation value for the material suspension velocity. The calculation formula for this process is as follows:  
\[\left\{\begin{array}{l}G_{1}=F_{\mathrm{Z}}+F_{\mathrm{f}}\\ F_{\mathrm{Z}}=\frac{1}{2}C_{\mathrm{q}}P_{\mathrm{q}}SV_{f}^{2}\end{array}\right. \tag{7}\]  
where \(G_{1}\) denotes the gravitational force of the material, and it is measured in [PERSON]'s (N); \(F_{Z}\) denotes the gravitational force of the material, and it is measured in Newton (N); \(F_{f}\) denotes the gravitational force of the material, and it is measured in [PERSON]'s (N); \(C_{q}\) denotes the gravitational force of the material, and it is measured in [PERSON]'s \(P_{q}\) denotes the gravitational force of the material, and it is measured in [PERSON]'s (kg/m\({}^{3}\)); \(S\) denotes the gravitational force of the material, and it is measured in [PERSON]'s (m\({}^{2}\)); \(V_{f}\) denotes the gravitational force of the material, and it is measured in [PERSON]'s (\(V_{f}\)).  
Replace and organize Equation (7) to derive the theoretical calculation formula of material suspension velocity as:  
\[\mathrm{v_{f}}=\sqrt{\frac{2(G_{1}-F_{\mathrm{f}})}{C_{\mathrm{q}}P_{\mathrm{ q}}S}} \tag{8}\]  
The windward force area when the residual film is suspended can be calculated as follows:  
\[\left\{\begin{array}{l}G_{2}=P_{M}\mathrm{r_{1}}\mathrm{r_{2}}\mathrm{hg}\\ F_{MF}=\mathrm{r_{1}}\mathrm{r_{2}}\mathrm{hP_{q}}\mathrm{g}\\ S_{M}=\mathrm{r_{1}}\mathrm{r_{2}}\end{array}\right. \tag{9}\]  
where \(G_{2}\)--residual film gravity, N, \(P_{M}\)--density of residual film, kg/m\({}^{3}\), \(\mathrm{r_{1}}\)--Residual film length, m, \(\mathrm{r_{2}}\)--Residual film width, m, h--Thickness of residual film, m, g--Gravity acceleration, m/s\({}^{2}\), \(F_{M}\)--Air buoyancy of residual film, N, \(S_{M}\)--windward area of residual film, m\({}^{2}\).  
By substituting Equation (9) into Equation (8) and deriving, the formula for calculating the suspension velocity is obtained as follows:  
\[V_{Mf}=\sqrt{\frac{2\times 10^{6}(hgp_{M}-hp_{q}g)}{C_{q}p_{q}}}, \tag{10}\]  
It is known that the density of the residual film is 1.32 \(\times\) 10\({}^{3}\) kg/m\({}^{3}\), the thickness is \(8.6\times 10^{-6}\) m, the acceleration of gravity is 9.81 m/s\({}^{2}\), and the density of the air is approximately 1.21 \(\times\) 10\({}^{3}\) kg/m\({}^{3}\). Referring to reference [14], the drag coefficient of air is determined to be 0.75. By substituting the above parameters into the equation, the suspension velocity of the residual film is calculated as 2 m/s. The suspension velocity of cotton stalks is reported to be 6 m/s by substituting the same parameters into the equation [26].  
During the above demonstration process, the suspension velocity of the residual film and the cotton stalks differ significantly, so the difference in their suspension velocity is utilized to separate the film.