# Numerical Study of the Filtration Performance for Electrospun Nanofiber Membranes
## 3 Results and Discussion
### Resistance Simulation and Analysis of Electrospun Nanofiber Membrane Model  
Filtration resistance is the pressure difference at a specific flow rate [27], which refers to the hindering force encountered when the gas passes through the electrospun nanofiber filter material during the filtration process. It reflects the blocking degree of the filter medium material to the fluid flow. To evaluate the accuracy of the numerical simulation method in predicting the filtration resistance of the material, the FlowDict module was employed to simulate the flow field, with the surface velocity set to 6.89 cm/s to determine the filtration resistance of the filter material. By simulating the filtration resistance of fibers with different diameters and thicknesses at a fixed surface flow rate of 6.89 cm/s, these simulation results were compared with experimental measurements and predictions from empirical equations. The simulation results were compared with experimental measurements (filtration resistance determined using a differential pressure transducer with an accuracy of \(\pm\)0.1 Pa) and predictions from empirical equations (Davies Equation (6), Happel Equation (7), and Kuwabara Equation (8)). Combined with Figures 6 and 7, it is evident that the filtration resistance values calculated via numerical simulation for all electrospun nanofiber filter media are generally higher than the experimental measurements, with deviations typically within 20%. Figure 6: Experimental measurement, numerical simulation, and empirical formula calculation results of filtration resistance of filter media with different spinning solution concentrations [19; 20; 21]. Figure 7: Experimental measurement, numerical simulation, and empirical formula calculation results of filtration resistance of filter media at different spinning times [19; 20; 21]. This discrepancy (simulated resistance exceeding experimental values by 15-20%) stems from two interconnected modeling assumptions. First, the numerical framework assumes that all fibers are perpendicularly aligned to the airflow (x-y plane), overlooking the presence of z-direction fibers (parallel to the flow) that scanning electron microscopy (SEM) confirms in actual electrospun membranes [28]. Second, [PERSON] et al. [29] experimentally validated that fibers aligned parallel to the airflow reduce the pressure drop by approximately 30% compared to perpendicularly aligned fibers, owing to their smaller frontal area. Consequently, the model's exclusion of these low-resistance z-direction fibers leads to an overestimation of the effective fiber surface area interacting with the airflow, directly accounting for the observed systematic deviation in filtration resistance. This mechanism is consistent with the trends observed across all sample configurations (Figure 6), where simulated values consistently exceed experimental measurements. Therefore, as observed from the diagrams, both the simulation results and empirical calculation values for all fiber filter materials are higher than the experimental measurements. Among these, the numerical simulation results of the fiber filter media exhibit the best agreement with the experimental results.The experimentally measured values, numerical simulation values, and empirical formula calculation values of the filtration resistance of fiber membranes with different spinning solution concentrations and different spinning times are shown in Tables 3 and 4. Based on this, combined with the FlowDict module in GeoDict software, the electrospun nanofiber filter material model generated by the parametric model establishment method is used to simulate the flow field. This method can accurately predict the filtration resistance of the electrospun nanofiber membrane. Therefore, this method is suitable for studying the correlation between filtration resistance and fiber structure in electrospun nanofiber filter materials and provides guidance for the development of electrospun nanofiber materials.