# Numerical Study of the Filtration Performance for Electrospun Nanofiber Membranes
## 2 Numerical Simulation Method
### Construction of the Numerical Model
#### 2.3.2 Determination of Voxel Size  
A voxel is the smallest data unit in three-dimensional space, similar to a pixel in a two-dimensional image. It is an abbreviation for \"Volume Element\", representing a cell in a three-dimensional spatial grid, which is usually used to represent certain attributes within the cell, such as density and color. When using GeoDict software to establish the three-dimensional model structure of electrospun nanofiber filtration media, the fiber media  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Sample** & **Fiber Membrane Thickness/mm** & **Sample** & **Fiber Membrane Thickness/mm** \\ \hline
7\% & 0.0150 & 3.0 h & 0.0150 \\
9\% & 0.0150 & 3.5 h & 0.0184 \\
11\% & 0.0150 & 4.0 h & 0.0216 \\
13\% & 0.0150 & 4.5 h & 0.0232 \\
15\% & 0.0150 & 5.0 h & 0.0240 \\ \hline \hline \end{tabular}  
* Note: For PAN concentration samples (7–15%), the electrospinning time = 3 h; for electrospinning time samples (3.0 h–5.0 h), the PAN concentration = 9%.  
\end{table}
Table 2: Model thickness of fiber filter media.  
model is composed of many small cubes, namely voxels [26]. The vertices of each voxel serve as the base points for numerical calculations. Therefore, the size of the voxel directly affects the time consumption of numerical calculations and the accuracy of the results, which requires us to explore the voxel size.  
To eliminate the influence of voxel size on the numerical simulation results of the fiber filtration media model, the filtration pressure drops at six voxel sizes of 10 nm, 15 nm, 25 nm, 50 nm, 75 nm, and 100 nm and were taken as evaluation indicators. The simulated system for voxel size analysis is as follows: 2000 \(\times\) 2000 \(\times\) 500 voxels (X \(\times\) Y \(\times\) Z) with fiber diameter 418 nm and solid volume fraction 11.3% (9% PAN sample). Figure 2 shows the filtration pressure drop under different voxel sizes. When the voxel size changes, the filtration pressure drop changes accordingly. Meanwhile, the x-y plane size of the fiber filter medium model is related to the numerical calculation accuracy, memory and time cost, which needs to be explored and analyzed.  
Meanwhile, the x-y plane size of the fiber filtration media model is also related to the accuracy of numerical calculations, as well as the memory size and time cost required during the calculation process. Therefore, the size of the x-y plane of the model also needs to be explored and analyzed. As shown in Figure 3, six x-y plane sizes of 500 \(\times\) 500 voxels, 1000 \(\times\) 1000 voxels, 1500 \(\times\) 1500 voxels, 2000 \(\times\) 2000 voxels, 2500 \(\times\) 2500 voxels, and 3000 \(\times\) 3000 voxels were set, respectively. During the exploration of x-y plane sizes, the voxel size was fixed at 25 nm (consistent with the optimized voxel size in this study), and the thickness of the simulated system was 0.0150 mm (same as the 9% PAN sample, a representative case with an average fiber diameter of 418 nm and solid volume fraction of 11.3%).  
Based on this, to ensure the accuracy of the numerical simulation results and reduce the consumption of computational resources, in the subsequent numerical simulation calculations, this study plans to set the size of the electrospun nanofiber filtration media model in the x-y plane to 2000 \(\times\) 2000 voxels and the voxel size to 25 nm.  
Figure 2: Pressure drop of different voxel size models (system: 2000 \(\times\) 2000 \(\times\) 500 voxels; fiber diameter = 418 nm; and SVF = 11.3%).