Effect of geometric structures on initial filtration and dust loading performance of bimodal coarse fibrous filter media: a numerical study

Effect of geometric structures on initial filtration and dust loading performance of bimodal coarse fibrous filter media: a numerical study | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Effect of geometric structures on initial filtration and dust loading performance of bimodal coarse fibrous filter media: a numerical study Yu Song, Min Du, Yuhai Yan, Jiawei Liu, Rongwu Wang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6799210/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Geometric structure is the most important factor of fibrous filter media affecting its filtration performance, regardless of the fiber type and post-finishing. Bimodal structure design is a common and useful strategy to solve the trade-off among filtration properties, however, its structure-property relationship is not yet clear. In this work, a particle collision model was first developed based on a generated digital twin structure according to the previous experimental work to further implement reliable numerical simulations. Then, in total, 41 individual 3D bimodal filter models were generated, covering 8 types of geometric structures, including fiber morphologies (fiber diameter, blend ratio, cross-section shape, and diameter distribution) and filter structures (basis weight, porosity, bulkiness, and fiber orientation). Dust loading simulations were carried out on these filter models to predict the initial filtration and dust loading performance. Among the above geometric structures, filter bulkiness is the key structural factor to be addressed, because higher bulkiness significantly reduces the resistance and improves the filter lifetime, with only a little penalty in the filtration efficiencies. The findings of this work could contribute to the encyclopedia of filter structure design, and the reported research methodology could also be further applied to other multi-phase filtration and separation fields. Dust loading Geometric structure Filter lifetime Collision Numerical simulation GeoDict Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 1 Introduction Fibrous filters can effectively purify aerosol contaminants and have become essential goods in our daily lives, which protect us in residential environments, automotive/aircraft cabins, office buildings, etc. Each filter has a lifetime which varies from several hours (e.g., PPE masks) to a couple of years (e.g., engine air-intake filters). During the filtration, particles could enter the filter media and clog its pore space, rapidly increasing air resistance and energy consumption, as well as decreasing clean air delivery rate [ 1 , 2 ]. Especially for filters working against dust contaminants, the dust particles typically range from several hundred nanometers to over one hundred microns [ 3 ], which could quickly clog the filters. Therefore, it is important to enhance filter media's comprehensive performance, covering the capability of initial particle capturing, air resistance, and filter lifetime. The trade-off exists among the filtration properties. For instance, fabricating filter media with fine fibers could easily improve filtration efficiency, leading to higher resistance and shorter filter lifetime [ 4 ]. Applying electrostatic charging could improve the efficiency without sacrificing its pressure drop, however, it also decreases the filter lifetime [ 5 , 6 ]. Gradient structural design combines the advantages of multiple filter layers, but it suffers from the complexity of fabrication [ 7 – 9 ]. Nanofibrous filters greatly reduce the pressure drop via the slip effect, while their mass production is still not comparable to conventional methods, even if many of them are commercially available [ 10 , 11 ]. Overall, many filtration solutions have limitations in enhancing the comprehensive filtration performance. One of the most traditional textile wisdom—applying a bimodal fibrous structure, i.e., simply blending two different types of fibers, could be an ideal solution [ 12 ]. Payen et al. [ 13 ] fabricated bimodal hydroentangled nonwoven filters that improved overall filtration performance compared with unimodal fiber composition. Yang et al. [ 14 ] designed bimodal electrospun nanofibrous composite filter media and realized a high quality factor of 0.097 Pa − 1 , considering both the filtration efficiency (99.8%) and pressure drop (65 Pa). Xu et al. [ 15 ] fabricated micro-nano electrospun filter media presenting improved filtration performance compared with microfiber media and nanofiber media. However, the filter lifetime and its evaluation indicator, dust holding capacity (DHC), have not been studied much. Furthermore, the corresponding structure-property relationship and mechanisms of particle dynamics have not been fully understood. To study structure-property relationships, typical research methodologies in the aerosol filtration field include experiments, modeling, and simulations. Fabrication of filter media via the nonwoven process generally changes multiple variables simultaneously. For instance, increasing punching density increases the filter solidity and changes the 3D fiber orientation of a needled felt [ 16 ]; also, increasing the throughput increases both the fiber diameter and filter basis weight of meltblown nonwovens [ 17 ]. From the point of modeling, reported analytical expressions mostly focused on initial filtration performance, such as permeability, filtration efficiency, and pressure drop [ 18 – 20 ], rather than the filter lifetime and dust holding capacity. Furthermore, for polydisperse dust particles, current models mostly focus on the surface filtration or cake filtration stage [ 1 ], rather than addressing the depth filtration stage that largely contributes to the full DHC. Numerical simulation has been an emerging and important technique for dust-loading studies because of its capability in single-variable studies at a relatively low cost and quick response. Azimian et al. [ 3 ] simulated the lifetime of fibrous filter media with homogeneous, linear fiber diameter gradient and exponential fiber diameter gradient, respectively, and discovered that the exponential gradient filter media exhibited the largest DHC. Lee et al. [ 21 ] studied the aerosol loading behaviors of mask filters in various environments and conditions, including NISOH, work areas, classrooms, and offices. A critical work by Pan et al. [ 21 ] performed a numerical study on the effect of structural factors on dust loading performance, including filter thickness, porosity, bulk density, fiber orientation, and gradient design. Overall, further investigations are needed on the relationship between filter structures and dust loading performance. More importantly, numerical simulation is a powerful tool that can reveal the mechanisms of particle dynamics. Regarding particle collision dynamics, many studies used pre-defined constant values of the restitution coefficient for all particle sizes in simulations [ 22 – 24 ]. We recently realized the high-fidelity simulation of initial fractional filtration efficiency by determining the size-dependent fractional restitution coefficient [ 25 ], indicating the significant difference in particle collision behaviors at various particle sizes. Regarding particle deposition dynamics, many studies have proved its importance, as the particle deposition profile and its microstructures directly affect the pressure drop evolution and structure clogging during dust loading [ 26 – 28 ]. The high-fidelity simulation also enabled the structure acquisition and analysis of dynamic particle deposition and filter structure throughout the dust loading process, which experiments could not easily obtain [ 29 , 30 ]. Still, further studies are required to analyze the dust particle collision dynamics with different geometric filter structures and to correlate the particle deposition profiles with dust loading performance. In this work, we generated virtual 3D models of bimodal coarse fibrous filters, covering typical fiber morphologies and filter structures, and further carried out comprehensive numerical investigations on the relationship between filter structures and filtration properties. The collision model was developed to evaluate the initial filtration efficiency, and the particle deposition profiles acquired from the simulated 3D dust-loaded filter structures illustrated the effect of geometric structures on the dust loading performance. This work provides microstructural insights into the lifetime-scale filtration performance. The reported research approach can be further utilized in other multi-phase flow filtration and separations. 2 Numerical simulation 2.1 Boundary conditions and simulation process GeoDict software was used for 3D filter structure generation and numerical simulation of initial filtration and dust loading performance. This powerful tool for 3D structure modeling, multiphase-flow direct numerical simulation, and digital structure analysis has been widely applied and involved in 800 + publications [ 31 ] (accessed on May 1st, 2025). The 3D structure generation was performed using the FiberGeo module. One 3D filter model (Fig. 1 a) was generated with dimensions of 800*800*600 voxel 3 and a voxel length of 1 µm. Furthermore, a 350-voxel inflow region and a 50-voxel outflow region were added to the 3D structure (Fig. 1 a) to prevent flow-channel closure during the dust loading. Periodic boundary conditions were applied in the X-plane and the Y-plane (Fig. 1 b). The dust loading simulation is an iterative process (Fig. 1 c) to save the computation resources and time required for real-time dynamic simulation. Firstly, the flow field in the 3D domain is computed. Then, one batch of dust particles is released at the top of the inflow region and travels across the depth of the 3D domain. Once the collision between particle and fiber occurs, the pre-defined collision model determines if the particle gets captured or continues moving forward. At the end of each batch, captured particles become part of the filter structure and are then involved in the flow field calculation in the following iterations. Eventually, the dust loading process terminates once the targeted pressure drop is reached. 2.2 3D structure design of coarse fibrous filter media To study the structure-property relationship of bimodal coarse nonwoven filter media, firstly, the structure shown in Fig. 1 a was set as a standard model composed of 8.5-µm-thick fine fiber (1.265 g/cm 3 density referring to nylon/polyester fibrillated fiber [ 32 ] and supposing these two components are equally distributed; nylon, 1.14 g/cm 3 , polyester, 1.39 g/cm 3 [ 33 ]) and 20-µm-thick coarse fiber (referring to polyester binder) with a mass blend ratio of 70/30. It had a basis weight of 30 g/m 2 , a solidity of 3.84%, and a bulkiness of 20 cm 3 /g. The fibers were simplified as straight cylinders and were also isotopically distributed in the in-plane (X-Y plane) direction. Furthermore, 3D filter models with various structures were generated by controlling fiber morphologies of the fine fibers including fiber diameter, cross-section shape, blend ratio, and diameter distribution, as well as filter geometries including basis weight, porosity, bulkiness, and in-plane fiber orientation (Fig. 2 ). All 3D structures have a dimension of 800*800 µm 2 in the X-Y plane, with fixed fine fiber density and coarse fiber configurations. 2.3 Flow field calculation, particle tracking, and collision model The airflow field was computed using the FlowDict module. The airflow was considerably slow, which can be considered as Stokes flow with the Reynolds number close to zero. In this case, the airflow governed by the conservation of mass and momentum (Eq. ( 1 ) and Eq. ( 2 ) [ 35 ]) can be expressed as the Stokes equations. $$\:-\mu\:\varDelta\:\overrightarrow{u}+\nabla\:p=\overrightarrow{f}$$ 1 $$\:\nabla\:·\overrightarrow{u}=0$$ 2 Where µ is the air dynamic viscosity (kg/ms), \(\:\overrightarrow{u}\) denotes the airflow velocity (m/s), p is the pressure (Pa), and \(\:\overrightarrow{f}\) is the external force for the fluid (N). Within one batch, it is assumed that the generated particles could not interact with each other, and the moving particles would not affect the airflow. A combination of the air drag force and Brownian diffusive motion influences the particle movement in the air. Thus, the particle trajectories can be obtained by solving Eq. ( 3 ) [ 36 ]. $$\:m\frac{d\overrightarrow{v}}{dt}=\gamma\:\left(\overrightarrow{u}-\overrightarrow{v}+\sqrt{2D}\frac{d\overrightarrow{W}\left(t\right)}{dt}\right)$$ 3 where \(\:\gamma\:=6\pi\:\mu\:\frac{R}{{C}_{c}}\) indicates the fraction coefficient (kg/s), \(\:D=\frac{KT}{\gamma\:}\) is the particle diffusivity (m 2 /s), \(\:{C}_{c}=1+\frac{\lambda\:}{{d}_{p}}(2.34+1.05{e}^{-0.39\frac{{d}_{p}}{\lambda\:}})\) is the Cunningham correction factor that models the slip effect for tiny particles [ 37 ]. Furthermore, m is the particle mass (kg), dW is 3D Wiener measure ( \(\:\sqrt{s}\) ), R is the particle radius (m), K is the Boltzmann constant (J/K), T is the temperature (K), and λ denotes the mean free path of air molecules which equals 66 nm. The collision model determines the consequent particle motion after the collision with a fiber or deposited particle. The Hamaker model considers that the collision absorbs the particle's kinetic energy and slows it down. After a certain number of collisions, the kinetic energy of a particle would be low enough, which falls below the adhesion force between the particle and fiber (or particle and deposited particle), and then this particle is captured. Such particle-capturing conditions can be expressed using Eq. ( 4 ). $$\:{v}^{2}<\frac{H}{4{\pi\:}\rho\:{\text{a}}_{0}{R}^{2}}$$ 4 Where the restitution coefficient \(\:e=\frac{{v}_{2}}{{v}_{1}}\) (0 < e <1) is used to evaluate the remained kinetic energy of a particle after the collision. e = 0.1 indicates the post-collision velocity after collision ( v 2 ) equals 10% of the pre-collision velocity ( v 1 ). Furthermore, ρ is the particle density (kg/m 3 ), a 0 is the constant of adhesion distance or equilibrium spacing between the particle and the surface, which equals 0.4 nm. H is the Hamaker constant (×10 −20 J). The parameters and values used for the Hamaker constant calculation are listed in Table S1, and their detailed illustrations refer to our previous work [ 25 ]. Key simulation parameters include the face velocity (u) of 20 cm/s and particle concentration (c) of 150 mg/m 3 . The particle size distribution of A2 dust particles is shown in Fig. S1 [ 25 ], and its particle density was set as 1808 kg/m 3 [ 25 ]. Each batch with 45 s releases 108,970 particles on the 3D filter domain. Other parameters are included in Table S2. The simulations were stopped when the pressure drop reached 120 Pa at the cake filtration stage. The simulations were conducted using a high-performance computer with a 13th Gen Intel Core CPU (i7-13700KF, 3.40 GHz, 16 cores) and 128 GB RAM, which enabled the total runtime of dust loading around 5 hr for the 3D filter structure in Fig. 1 a. 3 Results and discussion 3.1 Developing particle collision model based on statistical digital twin The size-dependent fractional particle-fiber restitution coefficient was applied in our previous work [ 25 ] so that the high-fidelity simulation of initial fractional filtration efficiency against A2 dust aerosols was successfully realized. However, in this study, the unpredicted valleys of underestimated filtration efficiency varying from 2.289 µm to 5.051 µm (Fig. S2a and b) were observed using the reported collision model and based on the 3D structure with 8.5-µm-thick fine fiber and 6-µm-thick fine fiber (i.e., 3D structures in Fig. S3a-8.5µm and Fig. S3a-6µm). The key reason was attributed to the fact that the selected Hamaker collision model only considered the kinetic energy loss after each collision, and it ignored the effect of filter structures on the particle collision dynamics. The reported collision model was developed based on a coarse filter structure [ 29 ], with a mono-dispersed fiber diameter distribution and a mean diameter of 12.6 µm. Therefore, in contrast, we selected a fibrous filter media with a broad fiber diameter distribution, considering the roping effect of meltblown nonwovens [ 17 ], in this work to develop a corresponding collision model. With the help of the built-in deep learning model in the FiberFind module of GeoDict software, the statistical digital twin was successfully created (Fig. 3 a and Fig. S5a) with a broad fiber diameter distribution considering the roping effect (Fig. 3 b), which is close to the studied structures in fiber scale and fiber distribution. Its simulated pressure drop (Fig. 3 c) was in good agreement with the experimental result. Then, an updated collision model was developed based on such a statistical digital twin (uniform structure, Fig. S5a (ii)) from the original 3D structure (uniform realistic structure, Fig. S5a (i)). Figure 3 d summarizes the initial fractional efficiencies at various particle-fiber restitution coefficients. A good fit between the experimental results [ 30 ] and simulated results could be achieved as shown in Fig. 3 f by applying the size-dependent fractional particle-fiber (PF) restitution coefficient in Fig. 3 e. Still, the efficiencies at small particles were underestimated. As a result, simulated filtration efficiencies in the following simulations include fractional filtration efficiency and mass filtration efficiency unless otherwise noted. Furthermore, a significant improvement in filtration efficiency (Fig. S5c) can be observed by applying elevated PF restitution coefficients (Fig. S5b). The unusual valley in fractional filtration efficiency no longer exists (Fig. S5d and e). It should still be mentioned that the simulated efficiencies for small particles (R < 1.037 µm) are always underestimated, which also could be found in our previous work [ 25 ] and the study by Maddineni et al. [ 38 ]. Both simulation studies were conducted with the same Palas MFP dust loading equipment and GeoDict simulation software. This discrepancy attributes to the following reasons: (a) the accurate measurement of small particles that exhibit high number fraction but small volume fraction are inherently difficult by current particle counting technology; (b) the voxel size of 1 µm limited the contribution of the Brownian motion to the fractional efficiency for these small particles, as a high-fidelity simulation of aerosol filtration was reported at a voxel length of 50 nm [ 39 ]. It should also be noted that the overestimation for particles (1.982 µm < R 1.037 µm), which occupied 97.9% of the total dust mass (Fig. S1). Then, the fractional particle-fiber restitutions in Fig. 3 e and a particle-particle (PP) restitution coefficient of 0.06 [ 25 ] were applied to all the following dust loading simulations. 3.2 Effect of filter geometries: fiber morphologies 3.2.1 Effect of fiber diameter Fiber diameter ( d ), up to tens of microns and down to several nanometers, is the most basic geometric structure of fibrous filter media that directly determines its filtration performance. Table 1 lists the key structural characteristics of the generated bimodal 3D virtual filters with various fine fiber diameters (Fig. S3a), while maintaining the fixed coarse fiber diameter and the constant filter structures (e.g., basis weight, filter solidity, etc.). The involved fine fiber diameter varies from 17 µm to 6 µm, corresponding to different fibrillation indices of the splitable bicomponent ultrafine fibers [ 32 ], as shown in Fig. 4 a. As the fibrillation index increased, the median pore size ( D 50 ) significantly reduced in Table 1 . The initial particle capturing performance in Fig. 4 b and c indicates that the decreased fine fiber diameter brought higher pressure drop, filtration efficiency, and fractional efficiency at the full particle size range from 0.305 µm to 12.872 µm. The simulated dust loading performance in Fig. 4 d to f depicts that decreased fine fiber diameter led to higher filtration efficiency over time, and higher gravimetric total efficiency, but faster pressure drop increase and lower DHC. Therefore, decreasing the fine fiber diameter in a bimodal filter could effectively increase the particle-capturing capability by sacrificing the filter lifetime due to earlier clogging. This can also be observed in Fig. 4 g, where fewer particles were deposited inside the filter media with a smaller fiber diameter at the end of the filter lifetime. Table 1 Key structural characteristics of virtual filters with various fine fiber diameters. Case d fine , µm d coarse , µm Blend ratio D 50 , µm 1–1 6 20 70/30 50.02 1–2 7 20 70/30 58.29 1–3* 8.5 20 70/30 68.61 1–4 10 20 70/30 77.45 1–5 12 20 70/30 99.74 1–6 17 20 70/30 127.69 * Indicates the case of the filter structure in Fig. 1 a/Fig. S3a-8.5µm. 3.2.2 Effect of fiber blend ratio Blend ratio refers to the mass percentage of two or multiple components, which is one key factor that decides the bimodal configuration of filter media. Table 2 includes the structural characteristics of virtual bimodal 3D filters with various blend ratios (Fig. S3b), while keeping the same fine/coarse fiber diameter and filter basis weight. By adding more coarse fibers, the filter solidity slightly decreased, and the D 50 kept increasing. The initial filtration performance in Fig. 5 a and b also indicates that with the decreasing fine/coarse blend ratio from 90/10 to 30/70, the pressure drop, filtration efficiency, and fractional efficiency all kept decreasing. Furthermore, with a higher percentage of coarse fibers, the pressure drop increases slower (Fig. 5 d) and the DHC increased accordingly (Fig. 5 c), with more particles deposited inside the filter structure at the terminated pressure drop (Fig. 5 f), despite the slowly-increasing dynamic filtration efficiency (Fig. 5 e) and decreased gravimetric efficiency (Fig. 5 c). As a result, adding more coarse fibers in a bimodal filter improves the filtration resistance and extends the filter lifetime at the cost of reduced filtration efficiency. Then, a compromise among these performance indicators could be reached, e.g., optimizing the resistance and lifetime while meeting the required efficiency. Table 2 Key structural characteristics of virtual filters with various blend ratios. Case d fine , µm d coarse , µm Blend ratio α , % D 50 , µm 2 − 1 8.5 20 90/10 3.91 62.68 2–2 8.5 20 80/20 3.88 65.41 2–3* 8.5 20 70/30 3.84 68.61 2–4 8.5 20 60/40 3.80 73.44 2–5 8.5 20 50/50 3.77 77.44 2–6 8.5 20 30/70 3.70 93.03 * Indicates the case of the filter structure in Fig. 1 a/Fig. S3a-8.5µm. 3.2.3 Effect of fiber diameter distribution and fiber cross-section shape Fiber diameter distribution is typically stable and narrow for staple man-made fibers. Broad distributions may result from manufacturing defects such as roping in the meltblowing [ 17 ], and narrower distributions are typically desired to realize better filtration efficiency because coarse fibers make less contributions [ 40 ]. Table S3 lists the key structural characteristics of virtual 3D filters with various fine fiber diameter distributions (Fig. S4a), while keeping the coarse fiber constant. Narrower fine fiber diameter distribution led to a slightly smaller D 50 and higher specific surface area (Table S3), which further resulted in the slightly higher initial pressure drop, filtration efficiency, fractional filtration efficiency (Fig. S6a and b), as well as the slightly higher dynamic filtration efficiency (Fig. S6e) and gravimetric total efficiency (Fig. S6c). However, no clear pattern could be found in the dynamic pressure drop (Fig. S6d), DHC (Fig. S6c), and the particle deposition profiles (Fig. S6f), because such a narrow fiber diameter distribution has little influence on pore structure and its clogging during dust loading. Therefore, narrower fiber diameter distribution affects the initial filtration performance and reduces the particle capturing capability, but has nearly no effect on dust loading properties. The fiber cross-section shape of man-made fibers can be modified using different spinneret orifices to improve thermal insulation, moisture wicking, or particle capturing. Table S4 lists the key structural characteristics of virtual 3D filters with various cross-section shapes of the fine fiber (Fig. S4b), including circular, elliptical, rectangular, angular, trilobal, and quadrilobal. It can be found that the higher specific surface area (Table S4) brought slightly higher initial pressure drop, filtration efficiency, and fractional efficiency (Fig. S7a and b). However, no clear pattern exists for dust loading performance (Fig. S7c to f), because the particle dendrites would quickly form on the fiber surface, so that further challenging particles would not collide with these particle-deposited fibers. Therefore, the profiled fibers with different cross-section shapes only affect the initial filtration performance and do not influence dust loading behaviors. 3.3 Effect of filter geometries: filter structures 3.3.1 Effect of filter basis weight Basis weight ( W ) refers to the areal density of fibrous media. Table 3 lists the key structural characteristics of virtual 3D filters with various filter basis weights (Fig. S3c). As the basis weight increased from 10 g/m 2 to 60 g/m 2 , the pore size gently decreased (Table 3 ). Higher basis weight significantly increased the filtration efficiency and fractional efficiency in the beginning, followed by a slower increase, while the initial pressure drop increased linearly (Fig. 6 a and b). Furthermore, higher basis weight also increased the evolutional filtration efficiency during dust loading (Fig. 6 e) and gravimetric efficiency (Fig. 6 c). However, except for the filter with 10 g/m 2 basis weight possessed longest filter lifetime due to its low filtration efficiency and slower clogging, the rest filters exhibited similar pressure drop increase rate (Fig. 6 d) and all filter media presented close DHC (Fig. 6 c). The particle deposition profiles in Fig. 6 f and visualized particle deposits in Fig. 6 g demonstrated that all filters had nearly the same particle deposition zone despite their difference in basis weight. Overall, for a bimodal coarse filter media with a certain basis weight and thickness, increasing its basis weight is a method to increase its capability in particle capturing with diminishing returns [ 41 ], but it does not influence the filter lifetime. Table 3 Key structural characteristics of virtual filters with various filter basis weights. Case W , g/m 2 h , µm α , % b , cm 3 /g D 50 , µm 3 − 1 10 200 3.84 20 70.86 3 − 2 20 400 3.84 20 69.73 3–3* 30 600 3.84 20 68.61 3–4 40 800 3.84 20 69.76 3–5 50 1000 3.84 20 65.80 3–6 60 1200 3.84 20 67.98 * Indicates the case of the filter structure in Fig. 1 a/Fig. S3a-8.5µm. 3.3.2 Effect of filter solidity and filter bulkiness Solidity ( α ), also known as solid volume fraction, is defined as the percentage of fiber volume over the total filter volume to evaluate the compactness of filter structures. Table 4 lists the key structural characteristics of virtual 3D filters with various filter solidities at a given filter thickness of 600 µm (Fig. S3d). In Table 4 , D 50 decreased from 130.03 µm to 28.29 µm with the increase in filter solidity from 1.28–15.36%. It quantitatively indicated the rapidly decreasing pore space inside filter media at the fixed dimensions. In addition to the structure change, higher filter solidity significantly increased the initial pressure drop, filtration efficiency, and fractional efficiency (Fig. 7 a and b). Higher solidity also brought higher filtration efficiency over time (Fig. 7 e), and higher gravimetric efficiency (Fig. 7 c), while the pressure drop increased much faster (Fig. 7 d) and the DHC decreased from 90.7 g/m 2 to 14.5 g/m 2 (Fig. 7 c). Microscale particle depositions across filter depth in Fig. 7 f and 3 D visualizations of particle deposits in Fig. 7 g further elucidate that faster clogging occurred in high-solidity filter structure and fewer particles were deposited inside filter media, which led to a lower DHC. Therefore, a compact filter structure with high solidity exhibits high initial and dynamic filtration efficiency due to narrow pore size and a higher chance for particle collisions, but also results in a short filter lifetime owing to the small pore space for dust holding. Table 4 Key structural characteristics of virtual filters with various filter solidities. Case W , g/m 2 h , µm α , % b , cm 3 /g D 50 , µm 4 − 1 10 600 1.28 60 130.03 4 − 2 20 600 2.56 30 92.03 4 − 3* 30 600 3.84 20 68.61 4–4 60 600 7.68 10 45.03 4–5 90 600 11.52 6.67 34.29 4–6 120 600 15.36 5 28.29 * Indicates the case of the filter structure in Fig. 1 a/Fig. S3a-8.5µm. Bulkiness ( b ), also referred to as bulk, loft, and fluffiness [ 42 ], is defined as the total filter volume divided by the filter basis weight. It is typically used to rate the fluffy structure of yarns and fabrics [ 43 ], and is also used to evaluate the compactness of paper-based filter media [ 44 , 45 ]. Table 5 lists the key structural characteristics of virtual 3D filters with various filter bulkiness at a given filter basis weight of 30 g/m 2 (Fig. S3e). As the filter bulkiness increased from 5 cm 3 /g to 60 cm 3 /g, the D 50 increased from 27.52 µm to 124.40 µm. Regarding the filtration performance, higher bulkiness brought slightly lower filtration efficiency but much lower pressure drop (Fig. 8 a). Filter media with higher bulkiness also had lower fractional efficiency (Fig. 8 b), especially for small particles (< 3.28 µm), because their chance of being intercepted by the fiber network was reduced due to the larger pore size of high-bulk filters. Considering these small particles only occupies 20.9% of total dust mass (Fig. S1), the initial mass filtration efficiency slightly dropped from 78.0–70.5% (Fig. 8 a), and the gravimetric efficiency decreased from 94.75–91.75% (Fig. 8 c), as the filter bulkiness increased from 5 cm 3 /g to 60 cm 3 /g. Higher bulkiness also led to much slower pressure drop increase and improved DHC from 30.7 g/m 2 to 109 g/m 2 (Fig. 8 c and d), but resulted in lower evolutionary filtration efficiency (Fig. 8 e), which was all attributed to the slower clogging of the filter structure. Microscale particle depositions in Fig. 8 f indicated that a lot more particles were deposited inside high-bulk filter media, which contributed to its higher DHC. 3D visualizations of particle deposits in Fig. 8 g further explained the reason for prolonged filter lifetime that higher filter bulkiness largely increased the pore space for dust holding, despite the cost of reduced filtration efficiency (Fig. 8 a). Therefore, increasing filter bulkiness could be a good strategy to improve the filter lifetime with a little cost in particle capturing. Table 5 Key structural characteristics of virtual filters with various filter bulkiness. Case W , g/m 2 h , µm α , % b , cm 3 /g D 50 , µm 5 − 1 30 150 15.36 5 27.52 5 − 2 30 200 11.52 6.67 35.24 5 − 3 30 300 7.68 10 44.93 5 − 4* 30 600 3.84 20 68.61 5–5 30 900 2.56 30 80.76 5–6 30 1800 1.28 60 124.40 * Indicates the case of the filter structure in Fig. 1 a/Fig. S3a-8.5µm. 3.3.3 Effect of in-plane fiber orientation In-plane fiber orientation is generally determined by nonwoven processing, e.g., web formation technology and drawing process, and it could affect the filtration performance [ 44 ]. Table S5 lists the key structural characteristics of virtual 3D filters with various in-plane fiber orientations of the fine fiber (Fig. S4c). This table and Fig. S9 indicate that the filter with isotropically-distributed fine fibers (case S3-1) and filter with perpendicular fine/coarse fibers (case S3-2) exhibited the largest D 50 and the largest D 90 , respectively, while parallel fine/coarse fibers (case S3-6) had the smallest D 10 , D 50 , and D 90 . In terms of filtration performance (Fig. S8a to e), parallel orientation led to the highest initial pressure drop, filtration efficiency, and fractional efficiency, fastest pressure drop increase, and highest dynamic filtration efficiency, because of its smallest pore size. In contrast, perpendicular orientation led to contradictory initial and dynamic filtration performance, as well as the highest DHC, due to its large through pores (the largest D 90 ). Isotropic distribution and other cases with cross distributions exhibited interim filtration performance. Particle deposition profiles in Fig. S8f indicated that parallel-oriented filter media had the least volume of particles deposited inside the filter structure, while perpendicular-oriented filter media had the most volume. Overall, the in-plane fiber orientation changes the pore structure of filter media and further affects the filtration performance. 3.4 Implications Significance. This work has significance for both academic and industry readers. (a) For academia, the collision model has been developed based on a 3D filter model with a broad fiber diameter distribution. The obtained model fixed the issue of underestimated filtration efficiency from 2.289 µm to 5.051 µm (Fig. S2a and b) that occurred using our previous collision model [ 25 ]. Therefore, it could provide more reliable information for revealing the initial and clogging mechanisms of particle separation. Furthermore, this study revealed the effect of filter geometries on filtration properties from the microstructural perspective with particle deposition profiles and 3D visualizations, which cannot be easily obtained via experimental methods [ 29 , 30 ]. (b) For industry, such findings could enable more effective proof of concept and provide a much faster turnover of product research and development. Limitations and prospects. (a) A statistical digital twin was used to calibrate the particle-fiber restitution coefficient, powered by the built-in deep-learning model of the FiberFind module. Realistic and uniform structures with better representativeness can be further acquired and incorporated by applying advanced 3D imaging techniques, e.g., FIB-SEM or nano-CT for high-resolution imaging [ 39 ], and synchrotron radiation X-ray CT for large-scale sampling [ 46 , 47 ]. In addition, the method to generate a digital twin with better representativeness is also recommended to be investigated. (b) This work selected the X-Y domain of 800*800 µm 2 , 77.8% larger than 600*600 µm 2 in prior arts [ 25 , 44 ]. Still, an even larger computational domain is recommended in future simulation studies for better reliability. (c) The filter lifetime simulation in this work was based on a partially resolved collision model, as particles < 1 µm were invisible. A fully resolved collision model is suggested and can be realized by selecting a smaller voxel size. Once these small particles become resolved, the particle-particle collision chance would be higher, thus changing the particle-particle restitution coefficient and its corresponding cake structure. (d) Significant differences existed between the restitutions in this work and our previous work, as shown in Fig. S5b. Further investigations are recommended on the effect of filter structures and filtration conditions on particle collision dynamics. (e) With further improvement of the collision model, numerical simulations can provide reliable data for building filter databases, developing mathematical models, and constructing training sets to develop deep learning models for the prediction of filtration performance and multi-phase flow behaviors. 4 Conclusions In this work, 41 individual 3D filter models were generated, covering 8 structural variables that included fiber morphologies (fiber diameter, blend ratio, cross-section shape, and diameter distribution) and filter structures (basis weight, porosity, bulkiness, and fiber orientation). A calibrated particle collision model was developed based on a digital twin model with a similar fiber scale to the generated structures. Dust loading simulations were further conducted using this collision model to study the effect of geometric structures on initial and loading filtration performance. Microscale particle depositions and their 3D visualizations were also analyzed to elucidate the clogging mechanism. The following findings were discovered. Initial filtration performance. Reducing fiber diameter effectively increases particle capturing with increased resistance; adding more coarse fibers improves pressure drop at the cost of filtration efficiency; increasing filter basis weight improves the efficiency with diminishing returns; increasing filter solidity significantly increases both the efficiency and pressure drop; higher filter bulkiness effectively reduces pressure drop while slightly decreases filtration efficiency; narrower fiber diameter distribution, fiber cross-section with higher specific surface area, and parallel fiber orientation lead to slightly higher efficiency and resistance. Dust loading properties. Increasing fiber diameter leads to slower pressure drop increase, lower dynamic efficiency, and higher DHC, while adding more coarse fibers receives the same feedback; reducing the filter solidity significantly increases the filter lifetime at the cost of filtration efficiency, due to improved space for dust holding; however, increasing filter bulkiness obtains the same pattern of results with only a little penalty in dynamic efficiency; perpendicular fiber orientation improves the DHC with slightly lower efficiency; fiber diameter distribution and cross-section shape have no evident influence in the filter lifetime. Declarations Acknowledgment This work was supported by the Shanghai Sailing Program (23YF1400600), the Fundamental Research Funds for the Central Universities (2232025D-11, 2232023G-06). We also appreciate Lei Zhan's help drawing the graphical abstract and Fig.2. References T. Xia, C. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6799210","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":465016891,"identity":"345691c8-8b4e-47a2-9de8-b2e459d2aac9","order_by":0,"name":"Yu Song","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAwElEQVRIiWNgGAWjYPACG8YNIIqHBC1ppGs5TIIW+fbew695287LbpdIYHzwto1B3pyQFoMz59KsedtuG++ckcBsOLeNwXBnAyEtEjlmxkAtiRtuJLBJ87YxJBgcIOSwGWAt50Ba2H8TpYXhRo7xY962A2BbmInSYnDmjBnjnHPJxhvOPGyWnHNOwnADQYe19xh/eFNmJ7vhePJBIMNGnrDDGBjYpCDRwdgAJCQIqwcC5o8/iFI3CkbBKBgFIxYAADoPQj9CPgtZAAAAAElFTkSuQmCC","orcid":"","institution":"Donghua University","correspondingAuthor":true,"prefix":"","firstName":"Yu","middleName":"","lastName":"Song","suffix":""},{"id":465016892,"identity":"3519141a-785b-4c9a-bac7-0387ca5a7240","order_by":1,"name":"Min Du","email":"","orcid":"","institution":"Donghua University","correspondingAuthor":false,"prefix":"","firstName":"Min","middleName":"","lastName":"Du","suffix":""},{"id":465016893,"identity":"c5de31fd-c6e0-42aa-a95d-6abac48392ae","order_by":2,"name":"Yuhai Yan","email":"","orcid":"","institution":"Donghua University","correspondingAuthor":false,"prefix":"","firstName":"Yuhai","middleName":"","lastName":"Yan","suffix":""},{"id":465016894,"identity":"d442cddc-2e94-4e17-83af-c95d2371580f","order_by":3,"name":"Jiawei Liu","email":"","orcid":"","institution":"Donghua University","correspondingAuthor":false,"prefix":"","firstName":"Jiawei","middleName":"","lastName":"Liu","suffix":""},{"id":465016895,"identity":"50573d0b-bdcb-4d95-b874-dfa874068de3","order_by":4,"name":"Rongwu Wang","email":"","orcid":"","institution":"Donghua University","correspondingAuthor":false,"prefix":"","firstName":"Rongwu","middleName":"","lastName":"Wang","suffix":""}],"badges":[],"createdAt":"2025-06-02 06:08:59","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-6799210/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6799210/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":83819592,"identity":"430e635a-8cc8-410d-9c46-fb33eb10be0b","added_by":"auto","created_at":"2025-06-03 08:27:04","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":981015,"visible":true,"origin":"","legend":"\u003cp\u003e(a) 3D filter model, (b) boundary conditions, and (c) simulation process.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-6799210/v1/84c1fe837c16a5d522525ef5.png"},{"id":83819706,"identity":"79cdb6c4-1bef-48df-8f9e-b1d629be1508","added_by":"auto","created_at":"2025-06-03 08:35:04","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":1100299,"visible":true,"origin":"","legend":"\u003cp\u003eOverview of major filter geometric structures. Fiber morphologies: fiber diameter, blend ratio, cross-section shape [34], and fiber diameter distribution. Filter structures: basis weight, porosity, bulkiness, and in-plane fiber orientation.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-6799210/v1/e3218961ba50068e28fac32e.png"},{"id":83819596,"identity":"64bf8f34-8a11-4867-a72f-4418d6856628","added_by":"auto","created_at":"2025-06-03 08:27:04","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":643844,"visible":true,"origin":"","legend":"\u003cp\u003eCreation of statistical digital twin and collision model development. (a) Creating a statistical digital twin of the nonwoven filter media via deep learning considering the roping effect (some roping fibers are marked with orange dashed circles in the SEM image), (b) comparison of manually-counted single fiber diameter distribution and deep learning-powered roping fiber diameter distribution, (c) comparison of pressure drop. (d) Simulated filtration efficiency at various particle-fiber (PF) restitution coefficients based on statistical digital twin, (e) fractional PF restitution coefficient, (f) experimental vs. simulated fractional filtration efficiency.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-6799210/v1/7d980f1feaca5ecf90eeed57.png"},{"id":83819597,"identity":"d54e086f-9721-44dd-93c2-08b4c1009f91","added_by":"auto","created_at":"2025-06-03 08:27:04","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":993900,"visible":true,"origin":"","legend":"\u003cp\u003eEffect of fine fiber diameter. (a) Initial filtration efficiency and pressure drop, (b) initial fractional efficiency. (c) Dust holding capacity and gravimetric total efficiency at 120 Pa, (d) pressure drop evolution, and (e) filtration efficiency evolution during dust loading, and (f) particle deposition profile across filter depth.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-6799210/v1/7ebd8e5e1191200ea376261c.png"},{"id":83819603,"identity":"4af0215c-f313-4fbf-a0e2-ac55eefa92fa","added_by":"auto","created_at":"2025-06-03 08:27:04","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":570978,"visible":true,"origin":"","legend":"\u003cp\u003eEffect of blend ratio. (a) Initial filtration efficiency and pressure drop, (b) initial fractional efficiency. (c) Dust holding capacity and gravimetric total efficiency at 120 Pa, (d) pressure drop evolution, and (e) filtration efficiency evolution during dust loading, and (f) particle deposition profile across filter depth.\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-6799210/v1/32583c02e2ed903191d52aa4.png"},{"id":83819599,"identity":"45d2f740-c009-4f17-b9d6-4e75ec227984","added_by":"auto","created_at":"2025-06-03 08:27:04","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":1174613,"visible":true,"origin":"","legend":"\u003cp\u003eEffect of filter basis weight. (a) Initial filtration efficiency and pressure drop, (b) initial fractional efficiency. (c) DHC and gravimetric total efficiency at 120 Pa, (d) pressure drop evolution and (e) filtration efficiency evolution during dust loading, (f) particle deposition profile across filter depth, and (g) visualizations of particle depositions inside filter media and particle deposits alone.\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-6799210/v1/7013601c3812d207ddede4d4.png"},{"id":83819708,"identity":"35d76a82-0036-440f-97bc-45b0e3dc94ad","added_by":"auto","created_at":"2025-06-03 08:35:04","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":1211037,"visible":true,"origin":"","legend":"\u003cp\u003eEffect of filter solidity. (a) Initial filtration efficiency and pressure drop, (b) initial fractional efficiency. (c) Dust holding capacity and gravimetric total efficiency at 120 Pa, (d) pressure drop evolution and (e) filtration efficiency evolution during dust loading, (f) particle deposition profile across filter depth, and (g) visualizations of particle depositions inside filter media and particle deposits alone.\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-6799210/v1/60b9eb0039a591e14740265f.png"},{"id":83819709,"identity":"af7986d1-3d88-4892-a3fe-6727495140a0","added_by":"auto","created_at":"2025-06-03 08:35:04","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":1371608,"visible":true,"origin":"","legend":"\u003cp\u003eEffect of filter bulkiness. (a) Initial filtration efficiency and pressure drop, (b) initial fractional efficiency. (c) Dust holding capacity and gravimetric total efficiency at 120 Pa, (d) pressure drop evolution and (e) filtration efficiency evolution during dust loading, (f) particle deposition profile across filter depth, and (g) visualizations of particle depositions inside filter media and particle deposits alone.\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-6799210/v1/aa0b29f55f00ab9fda791436.png"},{"id":83820473,"identity":"06435a9c-1560-420a-a046-989f200e09db","added_by":"auto","created_at":"2025-06-03 08:43:10","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":9663289,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6799210/v1/55057fe9-f93f-4df9-9b23-abf6ece23032.pdf"},{"id":83819605,"identity":"5c1d6579-02c5-4083-b219-4ce9a1108127","added_by":"auto","created_at":"2025-06-03 08:27:04","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":2749047,"visible":true,"origin":"","legend":"","description":"","filename":"SupplementaryInformation.docx","url":"https://assets-eu.researchsquare.com/files/rs-6799210/v1/bc30e875bb6b3dd7d191c369.docx"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003e\u003cstrong\u003eEffect of geometric structures on initial filtration and dust loading performance of bimodal coarse fibrous filter media: a numerical study\u003c/strong\u003e\u003c/p\u003e","fulltext":[{"header":"1 Introduction","content":"\u003cp\u003eFibrous filters can effectively purify aerosol contaminants and have become essential goods in our daily lives, which protect us in residential environments, automotive/aircraft cabins, office buildings, etc. Each filter has a lifetime which varies from several hours (e.g., PPE masks) to a couple of years (e.g., engine air-intake filters). During the filtration, particles could enter the filter media and clog its pore space, rapidly increasing air resistance and energy consumption, as well as decreasing clean air delivery rate [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. Especially for filters working against dust contaminants, the dust particles typically range from several hundred nanometers to over one hundred microns [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e], which could quickly clog the filters. Therefore, it is important to enhance filter media's comprehensive performance, covering the capability of initial particle capturing, air resistance, and filter lifetime.\u003c/p\u003e \u003cp\u003eThe trade-off exists among the filtration properties. For instance, fabricating filter media with fine fibers could easily improve filtration efficiency, leading to higher resistance and shorter filter lifetime [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. Applying electrostatic charging could improve the efficiency without sacrificing its pressure drop, however, it also decreases the filter lifetime [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. Gradient structural design combines the advantages of multiple filter layers, but it suffers from the complexity of fabrication [\u003cspan additionalcitationids=\"CR8\" citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. Nanofibrous filters greatly reduce the pressure drop via the slip effect, while their mass production is still not comparable to conventional methods, even if many of them are commercially available [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. Overall, many filtration solutions have limitations in enhancing the comprehensive filtration performance.\u003c/p\u003e \u003cp\u003eOne of the most traditional textile wisdom\u0026mdash;applying a bimodal fibrous structure, i.e., simply blending two different types of fibers, could be an ideal solution [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. Payen et al. [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e] fabricated bimodal hydroentangled nonwoven filters that improved overall filtration performance compared with unimodal fiber composition. Yang et al. [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e] designed bimodal electrospun nanofibrous composite filter media and realized a high quality factor of 0.097 Pa\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, considering both the filtration efficiency (99.8%) and pressure drop (65 Pa). Xu et al. [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e] fabricated micro-nano electrospun filter media presenting improved filtration performance compared with microfiber media and nanofiber media. However, the filter lifetime and its evaluation indicator, dust holding capacity (DHC), have not been studied much. Furthermore, the corresponding structure-property relationship and mechanisms of particle dynamics have not been fully understood.\u003c/p\u003e \u003cp\u003eTo study structure-property relationships, typical research methodologies in the aerosol filtration field include experiments, modeling, and simulations. Fabrication of filter media via the nonwoven process generally changes multiple variables simultaneously. For instance, increasing punching density increases the filter solidity and changes the 3D fiber orientation of a needled felt [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]; also, increasing the throughput increases both the fiber diameter and filter basis weight of meltblown nonwovens [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. From the point of modeling, reported analytical expressions mostly focused on initial filtration performance, such as permeability, filtration efficiency, and pressure drop [\u003cspan additionalcitationids=\"CR19\" citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e], rather than the filter lifetime and dust holding capacity. Furthermore, for polydisperse dust particles, current models mostly focus on the surface filtration or cake filtration stage [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e], rather than addressing the depth filtration stage that largely contributes to the full DHC.\u003c/p\u003e \u003cp\u003eNumerical simulation has been an emerging and important technique for dust-loading studies because of its capability in single-variable studies at a relatively low cost and quick response. Azimian et al. [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e] simulated the lifetime of fibrous filter media with homogeneous, linear fiber diameter gradient and exponential fiber diameter gradient, respectively, and discovered that the exponential gradient filter media exhibited the largest DHC. Lee et al. [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e] studied the aerosol loading behaviors of mask filters in various environments and conditions, including NISOH, work areas, classrooms, and offices. A critical work by Pan et al. [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e] performed a numerical study on the effect of structural factors on dust loading performance, including filter thickness, porosity, bulk density, fiber orientation, and gradient design. Overall, further investigations are needed on the relationship between filter structures and dust loading performance.\u003c/p\u003e \u003cp\u003eMore importantly, numerical simulation is a powerful tool that can reveal the mechanisms of particle dynamics. Regarding particle collision dynamics, many studies used pre-defined constant values of the restitution coefficient for all particle sizes in simulations [\u003cspan additionalcitationids=\"CR23\" citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]. We recently realized the high-fidelity simulation of initial fractional filtration efficiency by determining the size-dependent fractional restitution coefficient [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e], indicating the significant difference in particle collision behaviors at various particle sizes. Regarding particle deposition dynamics, many studies have proved its importance, as the particle deposition profile and its microstructures directly affect the pressure drop evolution and structure clogging during dust loading [\u003cspan additionalcitationids=\"CR27\" citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e]. The high-fidelity simulation also enabled the structure acquisition and analysis of dynamic particle deposition and filter structure throughout the dust loading process, which experiments could not easily obtain [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e, \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]. Still, further studies are required to analyze the dust particle collision dynamics with different geometric filter structures and to correlate the particle deposition profiles with dust loading performance.\u003c/p\u003e \u003cp\u003eIn this work, we generated virtual 3D models of bimodal coarse fibrous filters, covering typical fiber morphologies and filter structures, and further carried out comprehensive numerical investigations on the relationship between filter structures and filtration properties. The collision model was developed to evaluate the initial filtration efficiency, and the particle deposition profiles acquired from the simulated 3D dust-loaded filter structures illustrated the effect of geometric structures on the dust loading performance. This work provides microstructural insights into the lifetime-scale filtration performance. The reported research approach can be further utilized in other multi-phase flow filtration and separations.\u003c/p\u003e"},{"header":"2 Numerical simulation","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Boundary conditions and simulation process\u003c/h2\u003e \u003cp\u003eGeoDict software was used for 3D filter structure generation and numerical simulation of initial filtration and dust loading performance. This powerful tool for 3D structure modeling, multiphase-flow direct numerical simulation, and digital structure analysis has been widely applied and involved in 800\u0026thinsp;+\u0026thinsp;publications [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e] (accessed on May 1st, 2025).\u003c/p\u003e \u003cp\u003eThe 3D structure generation was performed using the FiberGeo module. One 3D filter model (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea) was generated with dimensions of 800*800*600 voxel\u003csup\u003e3\u003c/sup\u003e and a voxel length of 1 \u0026micro;m. Furthermore, a 350-voxel inflow region and a 50-voxel outflow region were added to the 3D structure (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea) to prevent flow-channel closure during the dust loading. Periodic boundary conditions were applied in the X-plane and the Y-plane (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eb).\u003c/p\u003e \u003cp\u003eThe dust loading simulation is an iterative process (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ec) to save the computation resources and time required for real-time dynamic simulation. Firstly, the flow field in the 3D domain is computed. Then, one batch of dust particles is released at the top of the inflow region and travels across the depth of the 3D domain. Once the collision between particle and fiber occurs, the pre-defined collision model determines if the particle gets captured or continues moving forward. At the end of each batch, captured particles become part of the filter structure and are then involved in the flow field calculation in the following iterations. Eventually, the dust loading process terminates once the targeted pressure drop is reached.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 3D structure design of coarse fibrous filter media\u003c/h2\u003e \u003cp\u003eTo study the structure-property relationship of bimodal coarse nonwoven filter media, firstly, the structure shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea was set as a standard model composed of 8.5-\u0026micro;m-thick fine fiber (1.265 g/cm\u003csup\u003e3\u003c/sup\u003e density referring to nylon/polyester fibrillated fiber [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e] and supposing these two components are equally distributed; nylon, 1.14 g/cm\u003csup\u003e3\u003c/sup\u003e, polyester, 1.39 g/cm\u003csup\u003e3\u003c/sup\u003e [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e]) and 20-\u0026micro;m-thick coarse fiber (referring to polyester binder) with a mass blend ratio of 70/30. It had a basis weight of 30 g/m\u003csup\u003e2\u003c/sup\u003e, a solidity of 3.84%, and a bulkiness of 20 cm\u003csup\u003e3\u003c/sup\u003e/g. The fibers were simplified as straight cylinders and were also isotopically distributed in the in-plane (X-Y plane) direction.\u003c/p\u003e \u003cp\u003eFurthermore, 3D filter models with various structures were generated by controlling fiber morphologies of the fine fibers including fiber diameter, cross-section shape, blend ratio, and diameter distribution, as well as filter geometries including basis weight, porosity, bulkiness, and in-plane fiber orientation (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). All 3D structures have a dimension of 800*800 \u0026micro;m\u003csup\u003e2\u003c/sup\u003e in the X-Y plane, with fixed fine fiber density and coarse fiber configurations.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3 Flow field calculation, particle tracking, and collision model\u003c/h2\u003e \u003cp\u003eThe airflow field was computed using the FlowDict module. The airflow was considerably slow, which can be considered as Stokes flow with the Reynolds number close to zero. In this case, the airflow governed by the conservation of mass and momentum (Eq.\u0026nbsp;(\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e) and Eq.\u0026nbsp;(\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e2\u003c/span\u003e) [\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e]) can be expressed as the Stokes equations.\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:-\\mu\\:\\varDelta\\:\\overrightarrow{u}+\\nabla\\:p=\\overrightarrow{f}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:\\nabla\\:\u0026middot;\\overrightarrow{u}=0$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere \u003cem\u003e\u0026micro;\u003c/em\u003e is the air dynamic viscosity (kg/ms), \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\overrightarrow{u}\\)\u003c/span\u003e\u003c/span\u003e denotes the airflow velocity (m/s), \u003cem\u003ep\u003c/em\u003e is the pressure (Pa), and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\overrightarrow{f}\\)\u003c/span\u003e\u003c/span\u003e is the external force for the fluid (N).\u003c/p\u003e \u003cp\u003eWithin one batch, it is assumed that the generated particles could not interact with each other, and the moving particles would not affect the airflow. A combination of the air drag force and Brownian diffusive motion influences the particle movement in the air. Thus, the particle trajectories can be obtained by solving Eq.\u0026nbsp;(\u003cspan refid=\"Equ3\" class=\"InternalRef\"\u003e3\u003c/span\u003e) [\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e].\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\:m\\frac{d\\overrightarrow{v}}{dt}=\\gamma\\:\\left(\\overrightarrow{u}-\\overrightarrow{v}+\\sqrt{2D}\\frac{d\\overrightarrow{W}\\left(t\\right)}{dt}\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\gamma\\:=6\\pi\\:\\mu\\:\\frac{R}{{C}_{c}}\\)\u003c/span\u003e\u003c/span\u003e indicates the fraction coefficient (kg/s), \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:D=\\frac{KT}{\\gamma\\:}\\)\u003c/span\u003e\u003c/span\u003e is the particle diffusivity (m\u003csup\u003e2\u003c/sup\u003e/s), \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{C}_{c}=1+\\frac{\\lambda\\:}{{d}_{p}}(2.34+1.05{e}^{-0.39\\frac{{d}_{p}}{\\lambda\\:}})\\)\u003c/span\u003e\u003c/span\u003e is the Cunningham correction factor that models the slip effect for tiny particles [\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e]. Furthermore, \u003cem\u003em\u003c/em\u003e is the particle mass (kg), \u003cem\u003edW\u003c/em\u003e is 3D Wiener measure (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\sqrt{s}\\)\u003c/span\u003e\u003c/span\u003e), \u003cem\u003eR\u003c/em\u003e is the particle radius (m), K is the Boltzmann constant (J/K), T is the temperature (K), and \u003cem\u003eλ\u003c/em\u003e denotes the mean free path of air molecules which equals 66 nm.\u003c/p\u003e \u003cp\u003eThe collision model determines the consequent particle motion after the collision with a fiber or deposited particle. The Hamaker model considers that the collision absorbs the particle's kinetic energy and slows it down. After a certain number of collisions, the kinetic energy of a particle would be low enough, which falls below the adhesion force between the particle and fiber (or particle and deposited particle), and then this particle is captured. Such particle-capturing conditions can be expressed using Eq.\u0026nbsp;(\u003cspan refid=\"Equ4\" class=\"InternalRef\"\u003e4\u003c/span\u003e).\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$\\:{v}^{2}\u0026lt;\\frac{H}{4{\\pi\\:}\\rho\\:{\\text{a}}_{0}{R}^{2}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere the restitution coefficient \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:e=\\frac{{v}_{2}}{{v}_{1}}\\)\u003c/span\u003e\u003c/span\u003e (0\u0026thinsp;\u0026lt;\u0026thinsp;\u003cem\u003ee\u003c/em\u003e\u0026lt;1) is used to evaluate the remained kinetic energy of a particle after the collision. \u003cem\u003ee\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.1 indicates the post-collision velocity after collision (\u003cem\u003ev\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e) equals 10% of the pre-collision velocity (\u003cem\u003ev\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e). Furthermore, \u003cem\u003eρ\u003c/em\u003e is the particle density (kg/m\u003csup\u003e3\u003c/sup\u003e), a\u003csub\u003e0\u003c/sub\u003e is the constant of adhesion distance or equilibrium spacing between the particle and the surface, which equals 0.4 nm. \u003cem\u003eH\u003c/em\u003e is the Hamaker constant (\u0026times;10\u003csup\u003e\u0026minus;20\u003c/sup\u003e J). The parameters and values used for the Hamaker constant calculation are listed in Table S1, and their detailed illustrations refer to our previous work [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eKey simulation parameters include the face velocity (u) of 20 cm/s and particle concentration (c) of 150 mg/m\u003csup\u003e3\u003c/sup\u003e. The particle size distribution of A2 dust particles is shown in Fig. S1 [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e], and its particle density was set as 1808 kg/m\u003csup\u003e3\u003c/sup\u003e [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]. Each batch with 45 s releases 108,970 particles on the 3D filter domain. Other parameters are included in Table S2. The simulations were stopped when the pressure drop reached 120 Pa at the cake filtration stage. The simulations were conducted using a high-performance computer with a 13th Gen Intel Core CPU (i7-13700KF, 3.40 GHz, 16 cores) and 128 GB RAM, which enabled the total runtime of dust loading around 5 hr for the 3D filter structure in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea.\u003c/p\u003e \u003c/div\u003e"},{"header":"3 Results and discussion","content":"\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Developing particle collision model based on statistical digital twin\u003c/h2\u003e \u003cp\u003eThe size-dependent fractional particle-fiber restitution coefficient was applied in our previous work [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e] so that the high-fidelity simulation of initial fractional filtration efficiency against A2 dust aerosols was successfully realized. However, in this study, the unpredicted valleys of underestimated filtration efficiency varying from 2.289 \u0026micro;m to 5.051 \u0026micro;m (Fig. S2a and b) were observed using the reported collision model and based on the 3D structure with 8.5-\u0026micro;m-thick fine fiber and 6-\u0026micro;m-thick fine fiber (i.e., 3D structures in Fig. S3a-8.5\u0026micro;m and Fig. S3a-6\u0026micro;m). The key reason was attributed to the fact that the selected Hamaker collision model only considered the kinetic energy loss after each collision, and it ignored the effect of filter structures on the particle collision dynamics. The reported collision model was developed based on a coarse filter structure [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e], with a mono-dispersed fiber diameter distribution and a mean diameter of 12.6 \u0026micro;m. Therefore, in contrast, we selected a fibrous filter media with a broad fiber diameter distribution, considering the roping effect of meltblown nonwovens [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e], in this work to develop a corresponding collision model.\u003c/p\u003e \u003cp\u003eWith the help of the built-in deep learning model in the FiberFind module of GeoDict software, the statistical digital twin was successfully created (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea and Fig. S5a) with a broad fiber diameter distribution considering the roping effect (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eb), which is close to the studied structures in fiber scale and fiber distribution. Its simulated pressure drop (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ec) was in good agreement with the experimental result. Then, an updated collision model was developed based on such a statistical digital twin (uniform structure, Fig. S5a (ii)) from the original 3D structure (uniform realistic structure, Fig. S5a (i)).\u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ed summarizes the initial fractional efficiencies at various particle-fiber restitution coefficients. A good fit between the experimental results [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e] and simulated results could be achieved as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ef by applying the size-dependent fractional particle-fiber (PF) restitution coefficient in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ee. Still, the efficiencies at small particles were underestimated. As a result, simulated filtration efficiencies in the following simulations include fractional filtration efficiency and mass filtration efficiency unless otherwise noted. Furthermore, a significant improvement in filtration efficiency (Fig. S5c) can be observed by applying elevated PF restitution coefficients (Fig. S5b). The unusual valley in fractional filtration efficiency no longer exists (Fig. S5d and e). It should still be mentioned that the simulated efficiencies for small particles (R\u0026thinsp;\u0026lt;\u0026thinsp;1.037 \u0026micro;m) are always underestimated, which also could be found in our previous work [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e] and the study by Maddineni et al. [\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e]. Both simulation studies were conducted with the same Palas MFP dust loading equipment and GeoDict simulation software. This discrepancy attributes to the following reasons: (a) the accurate measurement of small particles that exhibit high number fraction but small volume fraction are inherently difficult by current particle counting technology; (b) the voxel size of 1 \u0026micro;m limited the contribution of the Brownian motion to the fractional efficiency for these small particles, as a high-fidelity simulation of aerosol filtration was reported at a voxel length of 50 nm [\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e]. It should also be noted that the overestimation for particles (1.982 \u0026micro;m\u0026thinsp;\u0026lt;\u0026thinsp;R\u0026thinsp;\u0026lt;\u0026thinsp;3.28 \u0026micro;m) [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e] no longer occurred in this work. Overall, the collision model developed in this study worked well for the large dust particles (R\u0026gt;1.037 \u0026micro;m), which occupied 97.9% of the total dust mass (Fig. S1). Then, the fractional particle-fiber restitutions in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ee and a particle-particle (PP) restitution coefficient of 0.06 [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e] were applied to all the following dust loading simulations.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Effect of filter geometries: fiber morphologies\u003c/h2\u003e \u003cdiv id=\"Sec9\" class=\"Section3\"\u003e \u003ch2\u003e3.2.1 Effect of fiber diameter\u003c/h2\u003e \u003cp\u003eFiber diameter (\u003cem\u003ed\u003c/em\u003e), up to tens of microns and down to several nanometers, is the most basic geometric structure of fibrous filter media that directly determines its filtration performance. Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e lists the key structural characteristics of the generated bimodal 3D virtual filters with various fine fiber diameters (Fig. S3a), while maintaining the fixed coarse fiber diameter and the constant filter structures (e.g., basis weight, filter solidity, etc.). The involved fine fiber diameter varies from 17 \u0026micro;m to 6 \u0026micro;m, corresponding to different fibrillation indices of the splitable bicomponent ultrafine fibers [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e], as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ea. As the fibrillation index increased, the median pore size (\u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003e50\u003c/em\u003e\u003c/sub\u003e) significantly reduced in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. The initial particle capturing performance in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eb and c indicates that the decreased fine fiber diameter brought higher pressure drop, filtration efficiency, and fractional efficiency at the full particle size range from 0.305 \u0026micro;m to 12.872 \u0026micro;m. The simulated dust loading performance in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ed to f depicts that decreased fine fiber diameter led to higher filtration efficiency over time, and higher gravimetric total efficiency, but faster pressure drop increase and lower DHC. Therefore, decreasing the fine fiber diameter in a bimodal filter could effectively increase the particle-capturing capability by sacrificing the filter lifetime due to earlier clogging. This can also be observed in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eg, where fewer particles were deposited inside the filter media with a smaller fiber diameter at the end of the filter lifetime.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eKey structural characteristics of virtual filters with various fine fiber diameters.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCase\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003ed\u003c/em\u003e\u003csub\u003e\u003cem\u003efine\u003c/em\u003e\u003c/sub\u003e, \u0026micro;m\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003ed\u003c/em\u003e\u003csub\u003e\u003cem\u003ecoarse\u003c/em\u003e\u003c/sub\u003e, \u0026micro;m\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBlend ratio\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003e50\u003c/em\u003e\u003c/sub\u003e, \u0026micro;m\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u0026ndash;1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e70/30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e50.02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u0026ndash;2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e70/30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e58.29\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u0026ndash;3*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e8.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e70/30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e68.61\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u0026ndash;4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e70/30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e77.45\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u0026ndash;5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e70/30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e99.74\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u0026ndash;6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e70/30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e127.69\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e* Indicates the case of the filter structure in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea/Fig. S3a-8.5\u0026micro;m.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section3\"\u003e \u003ch2\u003e3.2.2 Effect of fiber blend ratio\u003c/h2\u003e \u003cp\u003eBlend ratio refers to the mass percentage of two or multiple components, which is one key factor that decides the bimodal configuration of filter media. Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e includes the structural characteristics of virtual bimodal 3D filters with various blend ratios (Fig. S3b), while keeping the same fine/coarse fiber diameter and filter basis weight. By adding more coarse fibers, the filter solidity slightly decreased, and the \u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003e50\u003c/em\u003e\u003c/sub\u003e kept increasing. The initial filtration performance in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ea and b also indicates that with the decreasing fine/coarse blend ratio from 90/10 to 30/70, the pressure drop, filtration efficiency, and fractional efficiency all kept decreasing. Furthermore, with a higher percentage of coarse fibers, the pressure drop increases slower (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ed) and the DHC increased accordingly (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ec), with more particles deposited inside the filter structure at the terminated pressure drop (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ef), despite the slowly-increasing dynamic filtration efficiency (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ee) and decreased gravimetric efficiency (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ec). As a result, adding more coarse fibers in a bimodal filter improves the filtration resistance and extends the filter lifetime at the cost of reduced filtration efficiency. Then, a compromise among these performance indicators could be reached, e.g., optimizing the resistance and lifetime while meeting the required efficiency.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eKey structural characteristics of virtual filters with various blend ratios.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCase\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003ed\u003c/em\u003e\u003csub\u003e\u003cem\u003efine\u003c/em\u003e\u003c/sub\u003e, \u0026micro;m\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003ed\u003c/em\u003e\u003csub\u003e\u003cem\u003ecoarse\u003c/em\u003e\u003c/sub\u003e, \u0026micro;m\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBlend ratio\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003eα\u003c/em\u003e, %\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003e50\u003c/em\u003e\u003c/sub\u003e, \u0026micro;m\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u0026thinsp;\u0026minus;\u0026thinsp;1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e8.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e90/10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3.91\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e62.68\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u0026ndash;2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e8.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e80/20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3.88\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e65.41\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u0026ndash;3*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e8.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e70/30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3.84\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e68.61\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u0026ndash;4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e8.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e60/40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3.80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e73.44\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u0026ndash;5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e8.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e50/50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3.77\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e77.44\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u0026ndash;6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e8.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e30/70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3.70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e93.03\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e* Indicates the case of the filter structure in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea/Fig. S3a-8.5\u0026micro;m.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section3\"\u003e \u003ch2\u003e3.2.3 Effect of fiber diameter distribution and fiber cross-section shape\u003c/h2\u003e \u003cp\u003eFiber diameter distribution is typically stable and narrow for staple man-made fibers. Broad distributions may result from manufacturing defects such as roping in the meltblowing [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e], and narrower distributions are typically desired to realize better filtration efficiency because coarse fibers make less contributions [\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e]. Table S3 lists the key structural characteristics of virtual 3D filters with various fine fiber diameter distributions (Fig. S4a), while keeping the coarse fiber constant. Narrower fine fiber diameter distribution led to a slightly smaller \u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003e50\u003c/em\u003e\u003c/sub\u003e and higher specific surface area (Table S3), which further resulted in the slightly higher initial pressure drop, filtration efficiency, fractional filtration efficiency (Fig. S6a and b), as well as the slightly higher dynamic filtration efficiency (Fig. S6e) and gravimetric total efficiency (Fig. S6c). However, no clear pattern could be found in the dynamic pressure drop (Fig. S6d), DHC (Fig. S6c), and the particle deposition profiles (Fig. S6f), because such a narrow fiber diameter distribution has little influence on pore structure and its clogging during dust loading. Therefore, narrower fiber diameter distribution affects the initial filtration performance and reduces the particle capturing capability, but has nearly no effect on dust loading properties.\u003c/p\u003e \u003cp\u003eThe fiber cross-section shape of man-made fibers can be modified using different spinneret orifices to improve thermal insulation, moisture wicking, or particle capturing. Table S4 lists the key structural characteristics of virtual 3D filters with various cross-section shapes of the fine fiber (Fig. S4b), including circular, elliptical, rectangular, angular, trilobal, and quadrilobal. It can be found that the higher specific surface area (Table S4) brought slightly higher initial pressure drop, filtration efficiency, and fractional efficiency (Fig. S7a and b). However, no clear pattern exists for dust loading performance (Fig. S7c to f), because the particle dendrites would quickly form on the fiber surface, so that further challenging particles would not collide with these particle-deposited fibers. Therefore, the profiled fibers with different cross-section shapes only affect the initial filtration performance and do not influence dust loading behaviors.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003e3.3 Effect of filter geometries: filter structures\u003c/h2\u003e \u003cdiv id=\"Sec13\" class=\"Section3\"\u003e \u003ch2\u003e3.3.1 Effect of filter basis weight\u003c/h2\u003e \u003cp\u003eBasis weight (\u003cem\u003eW\u003c/em\u003e) refers to the areal density of fibrous media. Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e lists the key structural characteristics of virtual 3D filters with various filter basis weights (Fig. S3c). As the basis weight increased from 10 g/m\u003csup\u003e2\u003c/sup\u003e to 60 g/m\u003csup\u003e2\u003c/sup\u003e, the pore size gently decreased (Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e). Higher basis weight significantly increased the filtration efficiency and fractional efficiency in the beginning, followed by a slower increase, while the initial pressure drop increased linearly (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ea and b). Furthermore, higher basis weight also increased the evolutional filtration efficiency during dust loading (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ee) and gravimetric efficiency (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ec). However, except for the filter with 10 g/m\u003csup\u003e2\u003c/sup\u003e basis weight possessed longest filter lifetime due to its low filtration efficiency and slower clogging, the rest filters exhibited similar pressure drop increase rate (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ed) and all filter media presented close DHC (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ec). The particle deposition profiles in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ef and visualized particle deposits in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eg demonstrated that all filters had nearly the same particle deposition zone despite their difference in basis weight. Overall, for a bimodal coarse filter media with a certain basis weight and thickness, increasing its basis weight is a method to increase its capability in particle capturing with diminishing returns [\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e], but it does not influence the filter lifetime.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eKey structural characteristics of virtual filters with various filter basis weights.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCase\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003eW\u003c/em\u003e, g/m\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003eh\u003c/em\u003e, \u0026micro;m\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003eα\u003c/em\u003e, %\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003eb\u003c/em\u003e, cm\u003csup\u003e3\u003c/sup\u003e/g\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003e50\u003c/em\u003e\u003c/sub\u003e, \u0026micro;m\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u0026thinsp;\u0026minus;\u0026thinsp;1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e200\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3.84\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e70.86\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u0026thinsp;\u0026minus;\u0026thinsp;2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e400\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3.84\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e69.73\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u0026ndash;3*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e600\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3.84\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e68.61\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u0026ndash;4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e800\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3.84\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e69.76\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u0026ndash;5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3.84\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e65.80\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u0026ndash;6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e60\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1200\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3.84\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e67.98\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e* Indicates the case of the filter structure in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea/Fig. S3a-8.5\u0026micro;m.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec14\" class=\"Section3\"\u003e \u003ch2\u003e3.3.2 Effect of filter solidity and filter bulkiness\u003c/h2\u003e \u003cp\u003eSolidity (\u003cem\u003eα\u003c/em\u003e), also known as solid volume fraction, is defined as the percentage of fiber volume over the total filter volume to evaluate the compactness of filter structures. Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e lists the key structural characteristics of virtual 3D filters with various filter solidities at a given filter thickness of 600 \u0026micro;m (Fig. S3d). In Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, \u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003e50\u003c/em\u003e\u003c/sub\u003e decreased from 130.03 \u0026micro;m to 28.29 \u0026micro;m with the increase in filter solidity from 1.28\u0026ndash;15.36%. It quantitatively indicated the rapidly decreasing pore space inside filter media at the fixed dimensions. In addition to the structure change, higher filter solidity significantly increased the initial pressure drop, filtration efficiency, and fractional efficiency (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003ea and b). Higher solidity also brought higher filtration efficiency over time (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003ee), and higher gravimetric efficiency (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003ec), while the pressure drop increased much faster (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003ed) and the DHC decreased from 90.7 g/m\u003csup\u003e2\u003c/sup\u003e to 14.5 g/m\u003csup\u003e2\u003c/sup\u003e (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003ec). Microscale particle depositions across filter depth in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003ef and \u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eD visualizations of particle deposits in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003eg further elucidate that faster clogging occurred in high-solidity filter structure and fewer particles were deposited inside filter media, which led to a lower DHC. Therefore, a compact filter structure with high solidity exhibits high initial and dynamic filtration efficiency due to narrow pore size and a higher chance for particle collisions, but also results in a short filter lifetime owing to the small pore space for dust holding.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eKey structural characteristics of virtual filters with various filter solidities.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCase\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003eW\u003c/em\u003e, g/m\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003eh\u003c/em\u003e, \u0026micro;m\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003eα\u003c/em\u003e, %\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003eb\u003c/em\u003e, cm\u003csup\u003e3\u003c/sup\u003e/g\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003e50\u003c/em\u003e\u003c/sub\u003e, \u0026micro;m\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4\u0026thinsp;\u0026minus;\u0026thinsp;1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e600\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e60\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e130.03\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4\u0026thinsp;\u0026minus;\u0026thinsp;2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e600\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e2.56\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e92.03\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4\u0026thinsp;\u0026minus;\u0026thinsp;3*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e600\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3.84\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e68.61\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4\u0026ndash;4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e60\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e600\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e7.68\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e45.03\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4\u0026ndash;5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e600\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e11.52\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e6.67\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e34.29\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4\u0026ndash;6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e120\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e600\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e15.36\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e28.29\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e* Indicates the case of the filter structure in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea/Fig. S3a-8.5\u0026micro;m.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eBulkiness (\u003cem\u003eb\u003c/em\u003e), also referred to as bulk, loft, and fluffiness [\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e], is defined as the total filter volume divided by the filter basis weight. It is typically used to rate the fluffy structure of yarns and fabrics [\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e], and is also used to evaluate the compactness of paper-based filter media [\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e, \u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e]. Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e lists the key structural characteristics of virtual 3D filters with various filter bulkiness at a given filter basis weight of 30 g/m\u003csup\u003e2\u003c/sup\u003e (Fig. S3e). As the filter bulkiness increased from 5 cm\u003csup\u003e3\u003c/sup\u003e/g to 60 cm\u003csup\u003e3\u003c/sup\u003e/g, the \u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003e50\u003c/em\u003e\u003c/sub\u003e increased from 27.52 \u0026micro;m to 124.40 \u0026micro;m. Regarding the filtration performance, higher bulkiness brought slightly lower filtration efficiency but much lower pressure drop (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003ea). Filter media with higher bulkiness also had lower fractional efficiency (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003eb), especially for small particles (\u0026lt;\u0026thinsp;3.28 \u0026micro;m), because their chance of being intercepted by the fiber network was reduced due to the larger pore size of high-bulk filters. Considering these small particles only occupies 20.9% of total dust mass (Fig. S1), the initial mass filtration efficiency slightly dropped from 78.0\u0026ndash;70.5% (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003ea), and the gravimetric efficiency decreased from 94.75\u0026ndash;91.75% (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003ec), as the filter bulkiness increased from 5 cm\u003csup\u003e3\u003c/sup\u003e/g to 60 cm\u003csup\u003e3\u003c/sup\u003e/g. Higher bulkiness also led to much slower pressure drop increase and improved DHC from 30.7 g/m\u003csup\u003e2\u003c/sup\u003e to 109 g/m\u003csup\u003e2\u003c/sup\u003e (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003ec and d), but resulted in lower evolutionary filtration efficiency (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003ee), which was all attributed to the slower clogging of the filter structure. Microscale particle depositions in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003ef indicated that a lot more particles were deposited inside high-bulk filter media, which contributed to its higher DHC. 3D visualizations of particle deposits in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003eg further explained the reason for prolonged filter lifetime that higher filter bulkiness largely increased the pore space for dust holding, despite the cost of reduced filtration efficiency (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003ea). Therefore, increasing filter bulkiness could be a good strategy to improve the filter lifetime with a little cost in particle capturing.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u0026nbsp;\u003ctable id=\"Tab9\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eKey structural characteristics of virtual filters with various filter bulkiness.\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eCase\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003eW\u003c/em\u003e, g/m\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003eh\u003c/em\u003e, \u0026micro;m\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003e\u0026alpha;\u003c/em\u003e, %\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003eb\u003c/em\u003e, cm\u003csup\u003e3\u003c/sup\u003e/g\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003e50\u003c/em\u003e\u003c/sub\u003e, \u0026micro;m\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5\u0026thinsp;\u0026minus;\u0026thinsp;1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e150\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e15.36\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e27.52\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5\u0026thinsp;\u0026minus;\u0026thinsp;2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e200\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e11.52\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.67\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e35.24\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5\u0026thinsp;\u0026minus;\u0026thinsp;3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e300\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e7.68\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e44.93\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5\u0026thinsp;\u0026minus;\u0026thinsp;4*\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e600\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e3.84\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e68.61\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5\u0026ndash;5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e900\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.56\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e80.76\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5\u0026ndash;6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1800\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.28\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e60\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e124.40\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003e\u003c/p\u003e\n\u003cp\u003e* Indicates the case of the filter structure in Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ea/Fig. S3a-8.5\u0026micro;m.\u003c/p\u003e\n\u003cdiv id=\"Sec15\" class=\"Section3\"\u003e\n \u003ch2\u003e3.3.3 Effect of in-plane fiber orientation\u003c/h2\u003e\n \u003cp\u003eIn-plane fiber orientation is generally determined by nonwoven processing, e.g., web formation technology and drawing process, and it could affect the filtration performance [\u003cspan class=\"CitationRef\"\u003e44\u003c/span\u003e]. Table S5 lists the key structural characteristics of virtual 3D filters with various in-plane fiber orientations of the fine fiber (Fig. S4c). This table and Fig. S9 indicate that the filter with isotropically-distributed fine fibers (case S3-1) and filter with perpendicular fine/coarse fibers (case S3-2) exhibited the largest \u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003e50\u003c/em\u003e\u003c/sub\u003e and the largest \u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003e90\u003c/em\u003e\u003c/sub\u003e, respectively, while parallel fine/coarse fibers (case S3-6) had the smallest \u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003e10\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003e50\u003c/em\u003e\u003c/sub\u003e, and \u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003e90\u003c/em\u003e\u003c/sub\u003e. In terms of filtration performance (Fig. S8a to e), parallel orientation led to the highest initial pressure drop, filtration efficiency, and fractional efficiency, fastest pressure drop increase, and highest dynamic filtration efficiency, because of its smallest pore size. In contrast, perpendicular orientation led to contradictory initial and dynamic filtration performance, as well as the highest DHC, due to its large through pores (the largest \u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003e90\u003c/em\u003e\u003c/sub\u003e). Isotropic distribution and other cases with cross distributions exhibited interim filtration performance. Particle deposition profiles in Fig. S8f indicated that parallel-oriented filter media had the least volume of particles deposited inside the filter structure, while perpendicular-oriented filter media had the most volume. Overall, the in-plane fiber orientation changes the pore structure of filter media and further affects the filtration performance.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec16\" class=\"Section2\"\u003e\n \u003ch2\u003e3.4 Implications\u003c/h2\u003e\n \u003cp\u003eSignificance. This work has significance for both academic and industry readers. (a) For academia, the collision model has been developed based on a 3D filter model with a broad fiber diameter distribution. The obtained model fixed the issue of underestimated filtration efficiency from 2.289 \u0026micro;m to 5.051 \u0026micro;m (Fig. S2a and b) that occurred using our previous collision model [\u003cspan class=\"CitationRef\"\u003e25\u003c/span\u003e]. Therefore, it could provide more reliable information for revealing the initial and clogging mechanisms of particle separation. Furthermore, this study revealed the effect of filter geometries on filtration properties from the microstructural perspective with particle deposition profiles and 3D visualizations, which cannot be easily obtained via experimental methods [\u003cspan class=\"CitationRef\"\u003e29\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e30\u003c/span\u003e]. (b) For industry, such findings could enable more effective proof of concept and provide a much faster turnover of product research and development.\u003c/p\u003e\n \u003cp\u003eLimitations and prospects. (a) A statistical digital twin was used to calibrate the particle-fiber restitution coefficient, powered by the built-in deep-learning model of the FiberFind module. Realistic and uniform structures with better representativeness can be further acquired and incorporated by applying advanced 3D imaging techniques, e.g., FIB-SEM or nano-CT for high-resolution imaging [\u003cspan class=\"CitationRef\"\u003e39\u003c/span\u003e], and synchrotron radiation X-ray CT for large-scale sampling [\u003cspan class=\"CitationRef\"\u003e46\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e47\u003c/span\u003e]. In addition, the method to generate a digital twin with better representativeness is also recommended to be investigated. (b) This work selected the X-Y domain of 800*800 \u0026micro;m\u003csup\u003e2\u003c/sup\u003e, 77.8% larger than 600*600 \u0026micro;m\u003csup\u003e2\u003c/sup\u003e in prior arts [\u003cspan class=\"CitationRef\"\u003e25\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e44\u003c/span\u003e]. Still, an even larger computational domain is recommended in future simulation studies for better reliability. (c) The filter lifetime simulation in this work was based on a partially resolved collision model, as particles\u0026thinsp;\u0026lt;\u0026thinsp;1 \u0026micro;m were invisible. A fully resolved collision model is suggested and can be realized by selecting a smaller voxel size. Once these small particles become resolved, the particle-particle collision chance would be higher, thus changing the particle-particle restitution coefficient and its corresponding cake structure. (d) Significant differences existed between the restitutions in this work and our previous work, as shown in Fig. S5b. Further investigations are recommended on the effect of filter structures and filtration conditions on particle collision dynamics. (e) With further improvement of the collision model, numerical simulations can provide reliable data for building filter databases, developing mathematical models, and constructing training sets to develop deep learning models for the prediction of filtration performance and multi-phase flow behaviors.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"4 Conclusions","content":"\u003cp\u003eIn this work, 41 individual 3D filter models were generated, covering 8 structural variables that included fiber morphologies (fiber diameter, blend ratio, cross-section shape, and diameter distribution) and filter structures (basis weight, porosity, bulkiness, and fiber orientation). A calibrated particle collision model was developed based on a digital twin model with a similar fiber scale to the generated structures. Dust loading simulations were further conducted using this collision model to study the effect of geometric structures on initial and loading filtration performance. Microscale particle depositions and their 3D visualizations were also analyzed to elucidate the clogging mechanism. The following findings were discovered.\u003c/p\u003e \u003cp\u003eInitial filtration performance. Reducing fiber diameter effectively increases particle capturing with increased resistance; adding more coarse fibers improves pressure drop at the cost of filtration efficiency; increasing filter basis weight improves the efficiency with diminishing returns; increasing filter solidity significantly increases both the efficiency and pressure drop; higher filter bulkiness effectively reduces pressure drop while slightly decreases filtration efficiency; narrower fiber diameter distribution, fiber cross-section with higher specific surface area, and parallel fiber orientation lead to slightly higher efficiency and resistance.\u003c/p\u003e \u003cp\u003eDust loading properties. Increasing fiber diameter leads to slower pressure drop increase, lower dynamic efficiency, and higher DHC, while adding more coarse fibers receives the same feedback; reducing the filter solidity significantly increases the filter lifetime at the cost of filtration efficiency, due to improved space for dust holding; however, increasing filter bulkiness obtains the same pattern of results with only a little penalty in dynamic efficiency; perpendicular fiber orientation improves the DHC with slightly lower efficiency; fiber diameter distribution and cross-section shape have no evident influence in the filter lifetime.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAcknowledgment\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis work was supported by the Shanghai Sailing Program (23YF1400600), the Fundamental Research Funds for the Central Universities (2232025D-11, 2232023G-06). We also appreciate Lei Zhan\u0026apos;s help drawing the graphical abstract and Fig.2.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eT. Xia, C. Chen, Evolution of pressure drop across electrospun nanofiber filters clogged by solid particles and its influence on indoor particulate air pollution control, J. Hazard. Mater. 402 (2021) 123479. https://doi.org/10.1016/j.jhazmat.2020.123479.\u003c/li\u003e\n\u003cli\u003eW. Zhang, S. Deng, S. Zhang, Z. Yang, Z. Lin, Energy consumption performance optimization of PTFE HEPA filter media during dust loading through compositing them with the efficient filter medium, Sustain. Cities Soc. 78 (2022) 103657. https://doi.org/10.1016/j.scs.2021.103657.\u003c/li\u003e\n\u003cli\u003eM. Azimian, C. K\u0026uuml;hnle, A. Wiegmann, Design and Optimization of Fibrous Filter Media Using Lifetime Multipass Simulations, Chem. Eng. 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Wang, Synchrotron X-ray computed tomography analysis of the morphological characterization of aluminum alloy powders produced by gas atomization, Powder Technol. 429 (2023). https://doi.org/10.1016/j.powtec.2023.118904.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Donghua University","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Dust loading, Geometric structure, Filter lifetime, Collision, Numerical simulation, GeoDict","lastPublishedDoi":"10.21203/rs.3.rs-6799210/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6799210/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eGeometric structure is the most important factor of fibrous filter media affecting its filtration performance, regardless of the fiber type and post-finishing. Bimodal structure design is a common and useful strategy to solve the trade-off among filtration properties, however, its structure-property relationship is not yet clear. In this work, a particle collision model was first developed based on a generated digital twin structure according to the previous experimental work to further implement reliable numerical simulations. Then, in total, 41 individual 3D bimodal filter models were generated, covering 8 types of geometric structures, including fiber morphologies (fiber diameter, blend ratio, cross-section shape, and diameter distribution) and filter structures (basis weight, porosity, bulkiness, and fiber orientation). Dust loading simulations were carried out on these filter models to predict the initial filtration and dust loading performance. Among the above geometric structures, filter bulkiness is the key structural factor to be addressed, because higher bulkiness significantly reduces the resistance and improves the filter lifetime, with only a little penalty in the filtration efficiencies. The findings of this work could contribute to the encyclopedia of filter structure design, and the reported research methodology could also be further applied to other multi-phase filtration and separation fields.\u003c/p\u003e","manuscriptTitle":"Effect of geometric structures on initial filtration and dust loading performance of bimodal coarse fibrous filter media: a numerical study","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-06-03 08:26:59","doi":"10.21203/rs.3.rs-6799210/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"f6f3c280-d28c-4abb-8774-113b15252a0d","owner":[],"postedDate":"June 3rd, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-06-03T08:26:59+00:00","versionOfRecord":[],"versionCreatedAt":"2025-06-03 08:26:59","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6799210","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6799210","identity":"rs-6799210","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}