# Numerical Study of the Filtration Performance for Electrospun Nanofiber Membranes
## 2 Numerical Simulation Method
### Construction of the Numerical Model
#### 2.3.1 Obtaining the Simulation Parameters of the Fiber Filtration Medium  
In order to effectively replace extensive experimental measurements with numerical simulations, this study comprehensively compares the correlation between experimental and simulation results of electrospun nanofiber membranes. Additionally, it systematically investigates the applicability of the numerical fiber structure model and the mathematical performance calculation model in predicting the filtration performance of electrospun nanofibers. Starting from the random distribution of fibers, the FiberGeo module creates virtual fiber filtration medium materials. The structural performance parameters required for the formation of the fiber materials include the dimensions of the fiber filtration medium sample, such as the fiber diameter, the proportion of the diameter distribution, the planar dimension, the thickness of the filtration medium, and the solid volume fraction (as shown in Figure 1). For the electrospun nanofiber membranes prepared with different PAN concentrations, as the PAN concentration increases, the fiber diameter in the obtained nanofiber membranes increases significantly. The average fiber diameters of the electrospun nanofiber membranes with electrospinning solution concentrations of 7%, 9%, 11%, 13%, and 15% (electrospinning time: 4 h) increase sequentially from 280 nm to 418 nm, 740 nm, 1200 nm, and 1300 nm. Fiber diameter was determined by analyzing SEM images using ImageJ software (version 1.53t). For each sample, 50 randomly selected fibers were measured to ensure statistical reliability. Membrane thickness was measured using an electronic micrometer (5205-25) at five random locations, and the average value was reported. For the electrospun nanofiber membranes prepared with different electrospinning durations, due to certain slight differences in the actual experimental conditions each time, even under the same PAN electrospinning solution concentration and electrospinning parameters, there are still certain differences in the fiber diameters of the prepared electrospun nanofiber membranes. The average fiber diameters of the electrospun nanofiber membranes with electrospinning times of 3 h, 3.5 h, 4 h, 4.5 h, and 5 h (PAN concentration: 11 wt%) are 418 nm, 394 nm, 390 nm, 400 nm, and 396 nm, respectively. Each measurement was repeated three times with a standard deviation of less than 5%. In the surface morphology test of the fiber membrane, we randomly selected 50 nanofibers from each sample group, measured their diameters, calculated the proportion of corresponding fiber diameters, and preliminarily characterized the fiber filtration medium samples. The obtained data were sequentially imported into the Diameter option and the Count option in the FiberGeo module to determine the fiber diameter and the proportion of the diameter distribution of the fiber filtration medium [24]. These structural parameters are crucial for characterizing the filtration performance of the fiber medium, which encompasses filtration efficiency, pressure drop, and dust holding capacity [26]. Electrospinning parameters were optimized based on experimental results: applied voltage of 18 kV, needle-to-collector distance of 13 cm, solution flow rate of 0.0013 mm/s, collector rotation speed of 200 r/min, and ambient conditions maintained at 35 \({}^{\circ}\)C and 30% relative humidity. PAN solutions with concentrations ranging from 7% to 15% (\(w/w\)) were prepared by stirring at 60 \({}^{\circ}\)C for 6 h. After electrospinning, all samples were dried at 80 \({}^{\circ}\)C for 24 h  
Figure 1: FiberGeo module creates a virtual fiber filter media material flow diagram. to remove residual solvent. However, the electrospun nanofiber membranes prepared with different electrospinning durations have obvious differences due to the time gap. The thicknesses of the fiber filtration media with electrospinning times of 3 h, 3.5 h, 4 h, 4.5 h, and 5 h are 0.0150 mm, 0.0184 mm, 0.0216 mm, 0.0232 mm, and 0.0240 mm, respectively.