# Numerical Study of the Filtration Performance for Electrospun Nanofiber Membranes
## 1 Introduction  
With the acceleration of industrialization and the continuous growth of urban populations, air pollution is becoming more and more serious. Atmospheric particulate matter (PM) is considered to be harmful to health [1], especially fine particulate matter (PM\({}_{2.5}\)) in the air, which poses a huge threat to human health [2, 3, 4]. When humans inhale air, they also inhale the particulate matter in it. After these particles enter the respiratory system, they diffuse into the blood vessels, causing damage to the cardiovascular system and inflicting significant harm on the human body [5, 6, 7]. Due to its small particle size, difficulty in sedimentation, and strong penetrability, it is challenging to control. Among various treatment methods, filtration technology has received widespread attention because of its advantages such as simple operation, wide application, and low energy consumption [8, 9]. In recent years, electrospinning technology has gained extensive attention and applicationin the field of air filtration because it can be used to prepare nanofiber membranes with a high specific surface area and high porosity.  
However, traditional experimental methods have problems such as a high cost and long cycle in studying the filtration performance of nanofiber membranes. As an efficient research method, numerical simulation can predict and analyze the filtration performance under different conditions in a short time so as to guide the actual production design. [PERSON] et al. [10] used OpenForm to numerically simulate the gas-solid flow characteristics of particles in fiber media and revealed the influencing mechanism of fiber structure on airflow distribution and particle trajectory. This study provides a theoretical basis for understanding the gas-solid two-phase flow of traditional fiber filter media, but it is mainly aimed at the conventional fiber arrangement structure and has not yet involved the special pore structure of submicron nanofiber membranes.  
Electrospinning, as a novel nanofiber preparation method, shows great potential in air filtration due to its advantages of simple operation, low cost, and controllable fiber morphology. The technology relies on an electrostatic interaction to prepare fibers: during the process, polymer solutions or melts are extruded and subjected to a high-voltage electric field [11; 12; 13], forming a cone-shaped jet that stretches into filaments with nano-scale diameters [14; 15]. Electrospun nanofiber membranes exhibit significant advantages in high-efficiency and low-resistance filtration, including porous structures, high specific surface areas, and multifunctional fiber surfaces--properties that make them ideal for capturing fine particulate matter. Relevant studies have demonstrated their applications in oil-water separation [16], nanofiltration [17], and pressure drop prediction [18], further confirming their versatility. They concluded that the pressure drop prediction model incorporating the air slip effect reduces the relative error to less than 8% for nanofibers with diameters \(\leq 500\) nm, providing a more accurate prediction method for nanofiber filter design.  
This study is based on the actual polydisperse electrospun nanofiber filter materials. Starting from the determination of the structural parameters of the electrospun nanofiber filter materials, the three-dimensional structure of the electrospun nanofiber membrane is reconstructed using the GeoDict simulation software to establish a three-dimensional model that is closer to the structure of the actual filter material. Numerical simulations are carried out on the filtration resistance and filtration efficiency of the corresponding model. The correlation between the experimental results and the simulation results of the electrospun nanofiber membrane is fully compared, and the applicability of the numerical models for nanofiber membrane structure and performance prediction in evaluating the filtration efficiency of electrospun nanofibers is systematically investigated.