## 3 Results and Discussion
### Discussions  
The impacts of the particle sizes (from 0.2-2 \(\upmu\)m), aspect ratio (from 1-3), packing density (from 2.5-10%), and inlet fluid velocity (0.1-0.3 m/s) are well determined during the fiber-dendrite collection processes. Figure 15 shows the number distribution of deposited particles on the leeward and windward sides of fiber surfaces under 11 different cases (Table 2). It is found that with the increase in particle diameter, more particles are deposited on the windward sides of fiber surfaces (Cases 1-4). It is because the morphologies of particle dendrites depend on the dominant filtration mechanism [19]. Brownian diffusion is important to the dendrites structure of fine particles (i.e., \(d_{\text{p}}\) = 0.2 \(\upmu\)m, windward particle proportion is 0.55), while the interception effect is enhanced for larger particles (i.e., \(d_{\text{p}}\) = 2 \(\upmu\)m, windward particle proportion is 0.70). As for the different aspect ratios of elliptical fibers (Cases 2, 5, and 6), it can be seen in Figure 15 that fine particles are peculiarly prone to collide and make contact with the woven fibers with higher aspect ratio. It is in consistent with the particle distribution in Figure 7 that more particles deposit on the end of elliptical long axis. The growth of dendrites structures significantly decreases the cross-sectional area of fiber media, leading to the rapid increase in pressure drop and capture efficiency during the fiber-dendrite collection stage. In terms of the woven fibers with same aspect ratio but different packing densities (Cases 2, 7-9), the windward particle proportion is slightly increased from 0.57 to 0.62 due to the decrease in cross-sectional area of the fiber media. Figure 10 shows that dendrites structures on windward sides are nearly the same, which cannot significantly change the flow field. The higher slope \(k\) of fibers with larger packing density mainly comes from the remarkable reduction in fluid cross-sectional area as dendrites grow. Finally, the similar particle distributions under different inlet flow velocities of the fluidizing gas (Cases 2, 10, and 11) well explain the same trend of dynamic pressure drop and capture efficiency in Section 3.2.3. Figure 14: (**a**) Logarithmic scaling of the normalized pressure drop and (**b**) dynamic changes in normalized capture efficiency with different inlet fluid velocities. It can be concluded that the normalized pressure drop (\(\Delta P/\Delta P_{0}\)) is an exponential function of the mass of deposited particles (\(M\)), taking the form \(\ln(\Delta P/\Delta P_{0})=kM+b\), which is in agreement with the results of single fiber [19]. Our results imply that the slope \(k\) is positively correlated to the fiber perimeter but is independent of the inlet fluid velocity. That is, the fiber shape and size have a vital impact on the normalized pressure drop, and so woven fibers with a larger aspect ratio or packing density will lead to a higher rate of increase in the normalized pressure drop. This can be explained by the reduced cross-sectional area of flow fluid, which is caused by different particle dendrites on the woven fiber. As for the capture efficiency, it is found that the normalized capture efficiency (\(\eta/\eta_{0}\)) is a linear function of \(M\) that can be expressed as \(\eta/\eta_{0}=\lambda M+\gamma\). Fibers with a larger aspect ratio or packing density will lead to a larger rate of increase in the normalized collection efficiency, whereas the inlet fluid velocity again has no obvious impact. Note that the slope \(\lambda\) cannot keep rising as the packing density increases, and so it is not advisable to increase the packing density too much in the design of filtration media. Furthermore, once the aspect ratio of woven fibers exceeds 1.6, \(\lambda\) becomes more likely to grow linearly. Figure 15 shows that the windward particle proportions for case 2, 5, and 6 are 0.54, 0.57, and 0.63, respectively.