## 2 Materials and Methods
### Simulation Details  
In this study, the grid resolution (x-y-z) of 3D simulations was set to 128 \(\times\) 64 \(\times\) 64, and the grid length (\(dx\)) was set to 1 \(\upmu\)m [19]. The orthogonal elliptic fibers were placed in the central region of the calculation domain, and the particle-loaded suspension flow followed the positive direction of the \(x\)-axis, perpendicular to the fibers. The inlet was set as a constant velocity boundary, while the outlet was set as a fully developed boundary, i.e., \(\partial\mathbf{u}/\partial\mathbf{x}=\partial\mathbf{v}/\partial\mathbf{x}=0\); the other four boundaries were assumed to be periodic. Non-equilibrium extrapolation scheme was used here to easily deal with inlet and outlet boundary conditions. Schematic diagrams of the calculation domain are shown in Figure 2, and the parameters of six simulation models are listed in Table 1, in which the packing density (\(\alpha\)) refers to the solid volume fraction and the aspect ratio (\(\epsilon\)) is calculated by dividing the long axis by the short axis of an elliptic cylinder. Models a, b, and c were constructed using different aspect ratios to evaluate the impact of the fiber shape (aspect ratio), whereas models a, d, e, and f were designed to evaluate the impact of the fiber size (packing density). The volume fraction occupied by particles in the fluid was determined to be as low as 6.5 \(\times\) 10\({}^{-6}\), and the particle-particle interactions in the fluid were not considered in this study [44]. The time step (\(\Delta t\)) was 10\({}^{-6}\) s. The kinematic viscosity (\(\
u\)) of the fluid (air) was set to 1.6 \(\times\) 10\({}^{-5}\) m\({}^{2}\)/s, and the density of the fluid (\(\rho_{0}\)) and the particles (\(\rho_{\mathrm{p}}\)) were set to 1 kg/m\({}^{3}\) and 1000 kg/m\({}^{3}\), respectively. Note that the Reynolds number (\(Re=u_{0}d_{f}/\
u\), where \(d_{\mathrm{f}}\) is the equivalent length of long axis) ranged from 0.14 to 0.86, and so the flow was approximately a Stokes flow. The filtration process could be divided into two parts: the simulation of the gas fields and, once the gas fields have reached the stable state, the simulation of gas-particle fields following the injection of particles. During the filtration process, the shape of the filtration medium (containing fibers and deposited particles) changed continuously due to the deposited particles. Once a particle was deposited on the fiber surface, a fluid node was converted to a boundary node, and particles could still move onto fluid and boundary nodes. If the accumulation volume of captured particles achieved 60%, the boundary node became a solid node, which influenced the flow field. Therefore, the flow field would be recalculated if a new solid node was formed. To determine the effects of the fiber parameters, Table 2 summarizes the 11 typical simulation cases of woven fibers considered in this study. The effects of different particle diameters on the continuous formation process of particle dendrites were first investigated (Cases 1-4), and then the effects of the dynamic pressure drop and capture efficiency were examined under diverse operating conditions: (a) different aspect ratios of elliptical fibers (Cases 2, 5, and 6); (b) different packing densities of elliptical fibers (Cases 2, 7-9); and (c) different inlet flow velocities of the fluidizing gas (Cases 2, 10, and 11). When examining the effect of a particular parameter, all other operational parameters were held fixed, thereby allowing the differences to be accurately distinguished. Furthermore, note that Case 2 is considered to be the default condition, and used mesh is shown in Figure 3a, while the clean flow field around the fibers is shown in Figure 3b-d.