## 3 Results and Discussion  
### Particle Dendrites of the Woven Fibers  
Figure 5 illustrates the growth process of the dendrite structures (green spots) of Case 2 during the whole filtration process. The diameter of the particles was set to 0.4 \(\upmu\)m, which is in the Greenfield gap, and the dominant capture mechanism was Brownian diffusion. The dendrite growth exhibits three stages in this dynamic process, similar to previous results [19]. In the initial stage of nearly \"clean\" fibers [from Figure 5a,b], the predominant diffusion leads to an isotropic distribution of particles around the surface of the fibers. As the number of captured particles increases [Figure 5c], the particle dendrites develop many branches with high fractal dimension distributed in the radial direction, leading to changes in the flow field. Finally, the particle dendrites become so large that more and more particles become prone to being deposited on either end of the elliptical long axis [Figure 5d]. Additionally, the shape and number of dendrite-like clusters of two fibers are apparently analogous, and the fluid particles struggle to migrate to the leeward side of the fibers during the dust loading process.  
Figure 4: (**a**) Grid sensitivity verification of Case 2; (**b**) comparison between simulated penetration and experimental values [37].  
Figure 5: Growth process of dendrite structures of Case 2: (**a**) number of captured particles is 9176; (**b**) number of captured particles is 25,407; (**c**) number of captured particles is 58,442; (**d**) number of captured particles is 132,253.  
The particle dendrites are dependent on the particle size. Figure 6 exhibits the morphologies (five views) of the dendrite structures for particles of different diameters (0.2-2 \(\upmu\)m). The dendrite structures resting on the woven fibers are similar to those on a single fiber for particles in the Greenfield gap. Generally, the dominant capture mechanism is diffusion when the particle diameter is less than 0.5 \(\upmu\)m [31]. As shown in Figure 6a,b, in terms of small particles (i.e., \(d_{\mathrm{p}}\) = 0.2 \(\upmu\)m or 0.4 \(\upmu\)m), the particles are relatively uniformly distributed and rest on any part of the fiber surface. With rising particle diameter, the diffusion mechanism becomes weaker, and hence interception and inertia impaction become more significant, resulting in an increasing number of particles being deposited on the lateral sides and front sides of the fibers. When the particle diameter reaches 1 \(\upmu\)m, the Brownian force is rather weak, and the structures of particle deposition are a combination of the dendrites expected from interception particles [Figure 6c]. This means that particles with a larger size led to a less uniform angular distribution. As for the largest particles (\(d_{\mathrm{P}}\) = 2 \(\upmu\)m), which are in the inertial impaction dominant regime, most are deposited on the windward side of the fiber, producing slender clusters that grow in the opposite direction to the flow [Figure 6d]. This might be because large particles do not fully comply with the streamlines and instead tend to move in a straight path, and so relatively few particles of large size will reach the rear side of the horizontal fiber.