## Article
[34] proposed a simple modeling approach for the nanoparticle capture efficiency for personal protective woven fiber during clean filtration process. However, they paid attention to the steady-state filtration process (based on classical filtration theories), and very few simulations examined the non-steady-state dust-loaded process and the changed flow field influenced by particle dendrites during the fiber-dendrite collection stage [35; 36; 37]. [PERSON] et al. [35] used direct numerical simulation to investigate the filter resistance on the single fabric layer, and found that the resistance on the first particle layer shows a maximum as particle size corresponds to the pore size. [PERSON] et al. [36] developed a one-dimensional mathematical model for the cake growth on the woven cloth by simply assuming particles accumulated in height, mainly concentrated on the fiber and pore diameters. [PERSON] and [PERSON] [37] simulated the 3D structure of particles depositedon the woven fiber of two orthogonal cylindrical fibers. The authors reported that the changing boundary conditions had almost no influence on the filtration process for smaller particles, although a slight influence was observed for larger particles. In fact, the mass loading on the fiber exhibits a crucial impact on the pressure drop and filtration efficiency. This difference might be because there were too few particles in that study to form large dendritic structures. The dendritic structures on the fiber and the connection between pressure drop, capture efficiency, and particles dendrites have rarely been investigated, which is to be solved in this work. The dynamic evolution of the capture efficiency, pressure drop, and morphologies of particle dendrites is vital in the design and optimization of filters. The aim of this work is to reveal these inherent features of the particulate matter removal process by a general element (two orthogonal fibers) of woven filter cloth. However, the mechanisms of fibrous filtration are rather complex due to the multiple capture mechanisms of solid particles. Fortunately, the lattice Boltzmann-cellular automata (LB-CA) probabilistic model provides a very promising approach for determining these mechanisms [38; 39]. The solid particles are constrained to only move on the same regular lattices as the fluid particles, and their transport probabilities to neighboring nodes depend on the local fluid flow and other external forces subject to solid particles [40]. The LB-CA models can consider the effect of Brownian diffusion and the drag force due to their stochastic nature in treating particle motion, and the interaction between gas-solid flow and unsteady geometric boundary, such as the captured particles dendrites, can be easily realized, which have been successfully used to simulate the dynamic filtration process of a single fiber and multi-fibers with parallel and staggered fiber arrangements [19; 40; 41]. As seen in Figure 1, the woven filter cloth consists of many fibers arranged using different weaving methods (e.g., plain weave, twill weave, and satin weave), and various weaving patterns are commonly characterized by the same micro-structure formed by two orthogonal fibers [28; 42]. Therefore, two (single-layer) orthogonal fibers can be recognized as a general element of three kinds of woven filter cloths. Hence, we use 3D LB-CA simulations to examine the filtration process under various conditions and to investigate the formation of particle dendrites. Since the branched dendrites change the flow fluid and significantly affect the filtration performance in the fiber-dendrite collection stage, we first investigate the angular distribution of particle dendrites. Then, the impacts of aspect ratio and packing density of elliptical fibers on the non-steady-state filtration process are examined; it is then proposed the formula that the logarithmic scaling of pressure drop (\(\Delta P/\Delta P_{0}\)) and the normalized capture efficiency (\(\eta/\eta_{0}\)) are linear functions of the mass of deposited particles (\(M\)).