## Article  
Lattice Boltzmann Simulation of Non-Steady-State Particulate Matter Filtration Process in Woven Fiber  
**[PERSON] 1**, **[PERSON] 1,** **[PERSON] 1**, **[PERSON] 1** and [PERSON] 1,2**  
experimentally investigated both the pressure drop and capture efficiency in dust-loaded electrostatic filters by replacing the fiber diameter and packing density with equivalent values. Based on previous research, many numerical simulations [10; 11; 12; 13] and experimental measurements [14; 15; 16] have been conducted to study the dynamic dust-loaded processes. Many numerical simulations have investigated different arrangements of fibrous filters and most considered a single-fiber model or a uniform arrangement. The real fibers used in fibrous filtration can be divided into two types: non-woven filter cloth and synthetic woven filter cloth. The true fibrous filtration of real non-woven filters has been intensively studied in recent years [17; 18; 19; 20]. [PERSON] et al. [17] obtained information about the lifetime capture efficiency, pressure drop, and dust loading of a non-woven oil filter. [PERSON] et al. [19] presented quantitative prediction formulas for the normalized pressure drop and normalized capture efficiency of a single fiber, finding that they were exponential and linear functions of the deposited mass, respectively. [PERSON] et al. [21] proposed that there always existed a trade-off between maximizing filtration efficiency and pressure drop for filter cloth, and the measurement and prediction of pressure drop and capture efficiency for many different fabrics could significantly help to make good filters from fabrics. However, different from non-woven filter, there has been very few fundamental filtration models of woven filters, and the underlying connection between pressure drop, capture efficiency, and deposited particles is still unclear. Currently, woven filter cloth is deemed to be one of the most effective air filtration media of all fabric filters due to its mature manufacturing process, high strength, and homogeneous fiber size [22]. As a response to the current COVID-19 pandemic, woven cloth materials have been examined in terms of the protection they provide against the transmission of particles of certain sizes, particularly in the \"Greenfield gap\" from 0.25-0.5 \(\upmu\)m [23; 24; 25]. To date, numerous experimental researchers have investigated the performance of woven cloth in face masks [26; 27; 28; 29; 30]. [PERSON] et al. [26] measured 32 available mask cloth for protection from the COVID-19 virus, and proposed that filtration efficiency and pressure were very relevant to those of single layer. [PERSON] et al. [28] investigated the filtration performance of carbon woven fabric on the removal of PM 1.0 particles. [PERSON] et al. [29] tested various common fabrics for use as cloth masks and presented the filtration efficiency data as a function of aerosol particle size. These experimental studies have examined many macro factors, i.e., particle size, textile parameters, porosity, and electrostatics, which influence the use of the mask and the optimization of the fiber filter. Nevertheless, they ignored the impact of angular distribution of particle dendrites deposited on a fiber. During the dynamic filtration process, the captured particles form branched dendrites, change the flow fluid, and further significantly affect the performance of filtration media in the so-called fiber-dendrite collection stage [19; 31]. Gaining the insights of dendrites growth is beneficial to the in-depth descriptions of the dust-loaded process and further prediction of filtration performance of woven fiber. Many simulations have been successfully conducted to explore the dust-loaded process and provide some details and predictions for the filtration performance of filter cloth [32; 33; 34]. [PERSON] et al. [32] derived mathematical equations for estimating the initial pressure drop (neglecting the dust-loading process) of woven screens. [PERSON] et al.