Distribution Of Particles Research Articles

Anti-symmetric and positivity preserving formulation of a spectral method for Vlasov-Poisson equations

We analyze the anti-symmetric properties of a spectral discretization for the one-dimensional Vlasov-Poisson equations. The discretization is based on a spectral expansion in velocity with the symmetrically weighted Hermite basis functions, central finite differencing in space, and an implicit Runge Kutta integrator in time. The proposed discretization preserves the anti-symmetric structure of the advection operator in the Vlasov equation, resulting in a stable numerical method. We apply such discretization to two formulations: the canonical Vlasov-Poisson equations and their continuously transformed square-root representation. The latter preserves the positivity of the particle distribution function. We derive analytically the conservation properties of both formulations, including particle number, momentum, and energy, which are verified numerically on the following benchmark problems: manufactured solution, linear and nonlinear Landau damping, two-stream instability, bump-on-tail instability, and ion-acoustic wave.

A high-order fully Lagrangian particle level-set method for dynamic surfaces

We present a fully Lagrangian particle level-set method based on high-order polynomial regression. This enables meshfree simulations of dynamic surfaces, relaxing the need for particle-mesh interpolation. Instead, we perform level-set redistancing directly on irregularly distributed particles by polynomial regression in a Newton-Lagrange basis on a set of unisolvent nodes. We demonstrate that the resulting particle closest-point (PCP) redistancing achieves high-order accuracy for 2D and 3D geometries discretized on irregular particle distributions and has better robustness against particle distortion than regression in a monomial basis. Further, we show convergence in classic level-set benchmark cases involving ill-conditioned particle distributions, and we present an example application to multi-phase flow problems involving oscillating and dividing droplets.

Impact of deposition parameters on the optical properties of Fe2O3 thin films prepared by SILAR method

In order to explore the structures, morphology, and optical features of Fe2O3 nanofilms, the successive ionic layer adsorption and reactions (SILARs) technique was utilized to deposit the nanofilms onto glassy slides at varying concentrations of the precursor. Three precursor concentrations (0.025, 0.05 and 0.075) M were used. Analysis using X-ray diffraction (XRD) presented the crystalline structure of the Fe2O3 thin films. Field emission-scanning electron microscopy (FE-SEM) was used to evaluate the morphological features of the films. The results demonstrate that the surfaces of the films are nonporous and that there is a good distribution for spherical nanosize particles. The number of cycles is another important parameter that has been tested and its effect on the optical properties of prepared films was evaluated. The optical properties like optical absorption and energy gaps are affected directionally by changing the concentration and cycle numbers during the preparation. The latest objective of our study is to determine the role of precursor concentrations and deposition cycles in preparing thin films that have electronic applications such as sensors and solar cells.

Whole Process Analysis and Fate Behavior of Microplastics in Urban Wastewater Treatment Plants, Including their Occurrence Forms, Components, and Removal Efficiency

Microplastics are among the most difficult new pollutants to remove in wastewater treatment plants. In order to explore the occurrence form, size distribution, composition, removal efficiency, migration law, and fate behavior characteristics of microplastic particles in sewage plants, taking a sewage treatment plant in Hohhot as an example, a total of 17 sampling sites were set up. The LAS X software counted the shape, abundance, and size of microplastics and conducted a full-process analysis. The results showed that： fibrous microplastics had the highest abundance and widest distribution and were the main form of existence, accounting for 61.8% of the total abundance； the size of microplastics ranged mainly between 0 and 1.00 mm, and among the four sizes, the abundance of microplastics 0.25 to 0.50 mm in China was the highest, accounting for 32.9%. Among the eight types of plastic components detected, polyester substances （PET, PBT）, cellulose, and polypropylene （PP） were the main components, accounting for 25%, 21%, and 17%, respectively. The influent abundance of the sewage plant was （73 ±5） n·L-1, the effluent abundance was （14 ±2） n·L-1, and the overall removal rate was （80.8 ±12.1）%. Among the three treatment stages of the sewage plant, only the primary treatment played a role in removal, and the abundance of microplastics surged in the secondary treatment. Different structures playing a major role in the removal of microplastics were fine grids （49.2 ±7.4）% and secondary sedimentation tanks （92.4 ±13.9）%. Microplastics mainly existed in the form of fibers, fragments, and films. The proportion of fibers was approximately 70%, and the size of fragments was mainly concentrated between 0.50 and 5.00 mm. Most fragments were in the range of 5.00 mm, accounting for 50%, making them the main form apart from fibrous. The film-like size was mostly concentrated in the range of less than 0.50 mm, accounting for more than 10%. Therefore, improving the removal of small-sized fibrous and film-like microplastics and large-sized fragmented microplastic particles can effectively reduce the pollution risk of microplastics in the environment caused by sewage plant drainage.

Unbalanced Optimal Transport For Stochastic Particle Tracking

Non-invasive flow measurement techniques, such as particle tracking velocimetry, resolve 3D velocity fields by pairing tracer particle positions in successive time steps. These trajectories are crucial for evaluating physical quantities like vorticity, shear stress, pressure, and coherent structures. Traditional approaches deterministically reconstruct particle positions and extract particle tracks using tracking algorithms. However, reliable track estimation is challenging due to measurement noise caused by high particle density, particle image overlap, and falsely reconstructed 3D particle positions. To overcome this challenge, probabilistic approaches quantify the epistemic uncertainty in particle positions, typically using a Gaussian probability distribution. However, the standard deterministic tracking algorithms relying on nearest-neighbor search do not directly extend to the probabilistic setting. Moreover, such algorithms do not necessarily find globally consistent solutions robust to reconstruction errors. This paper aims to develop a globally consistent nearest-neighborhood algorithm that robustly extracts stochastic particle tracks from the reconstructed Gaussian particle distributions in all frames. Our tracking algorithm relies on the unbalanced optimal transport theory in the metric space of Gaussian measures. Specifically, we optimize a binary transport plan for efficiently moving the Gaussian distributions of reconstructed particle positions between time frames. We achieve this by computing the partial Wasserstein distance in the metric space of Gaussian measures. Our tracking algorithm is robust to position reconstruction errors since it automatically detects the number of particles that should be matched through hyperparameter optimization. Notably, our tracking algorithm also readily applies to the standard deterministic PTV case. Finally, we validate our method using an in vitro flow experiment using a 3D-printed cerebral aneurysm.

Hygroscopic Mg–Al LDHs composite microspheres for highly efficient hyperspectral camouflage in the VIS and NIR wavebands

In order to enhance the hyperspectral camouflage efficacy of stealth coatings against a natural vegetative backdrop, LiCl, known for its significant hygroscopic properties, was incorporated into green Mg–Al layered double hydroxide (Mg–Al LDHs) material. Micron-sized composite microspheres were subsequently synthesized via the spray-drying granulation technique. The structure, morphology, and chemical composition of these microspheres were thoroughly characterized by X-ray diffraction, scanning electron microscopy, laser particle size analysis, nitrogen adsorption–desorption isotherms, and Fourier-transform infrared spectroscopy. The effect of LiCl content on the moisture absorption capacity and near-infrared reflectance spectra of the microspheres was systematically evaluated. We found that incorporating an optimal amount of LiCl into the internal pores of the Mg–Al LDHs microspheres did not compromise their smooth surface morphology and uniform particulate distribution. Notably, when the LiCl content was 10%, the maximum saturation moisture uptake ratio of the coating increased to 0.75 g/g. This hygroscopicity significantly enhanced the absorption and scattering of near-infrared radiation by the coating while concurrently improving its ability to modulate the shape and reflectance of both the visible and near-infrared spectral curves. Spectral congruence between the synthetic coating and natural green foliage was quantified at 97.41%. Moreover, this performance was maintained over 10 cycles of programmed drying and re-humidification, and the coating consistently demonstrated stable hygroscopic properties and sustained over 95% spectral congruence. These optimized artificial coatings were found to effectively confuse hyperspectral classification algorithms, thus blending seamlessly into a natural foliage backdrop. This study provides a new method for regulating VIS and NIR spectral (visible–near infrared spectrum) features, which will be critical for applications in advanced hyperspectral camouflage materials.

Crack Initiation in Compacted Graphite Iron with Random Microstructure: Effect of Volume Fraction and Distribution of Particles.

Thanks to the distinctive morphology of graphite particles in its microstructure, compacted graphite iron (CGI) exhibits excellent thermal conductivity together with high strength and durability. CGI is extensively used in many applications, e.g., engine cylinder heads and brakes. The structural integrity of such metal-matrix materials is controlled by the generation and growth of microcracks. Although the effects of the volume fraction and morphology of graphite inclusions on the tensile response of CGI were investigated in recent years, their influence on crack initiation is still unknown. Experimental studies of crack initiation require a considerable amount of time and resources due to the highly complicated geometries of graphite inclusions scattered throughout the metallic matrix. Therefore, developing a 2D computational framework for CGI with a random microstructure capable of predicting the crack initiation and path is desirable. In this work, an integrated numerical model is developed for the analysis of the effects of volume fraction and nodularity on the mechanical properties of CGI as well as its damage and failure behaviours. Finite-element models of random microstructure are generated using an in-house Python script. The determination of spacings between a graphite inclusion and its four adjacent particles is performed with a plugin, written in Java and implemented in ImageJ. To analyse the orientation effect of inclusions, a statistical analysis is implemented for representative elements in this research. Further, Johnson-Cook damage criteria are used to predict crack initiation in the developed models. The numerical simulations are validated with conventional tensile-test data. The created models can support the understanding of the fracture behaviour of CGI under mechanical load, and the proposed approach can be utilised to design metal-matrix composites with optimised mechanical properties and performance.

Performance Requirements and Optimum Mix Proportion of High-Volume Fly Ash 3D Printable Concrete

In this study, a procedure for mixture design was proposed with the aim of meeting the requirements of extrudability, buildability, and shape stability in 3D printable concrete. Optimum water/binder ratio, sand/binder ratio, binder type, utilization ratio, aggregate particle distribution and quantity, and type and utilization ratio of chemical admixtures were determined for 3D printable concrete in terms of print quality and shape stability criteria. A total of 32 different mixtures were produced. It was determined that mixtures produced using a binder content with approximately 40% fly ash, a w/b ratio of 0.35, and aggregates with Dmax of 1 mm exhibit acceptable characteristics. Investigations were also conducted into the thixotropic behavior, rheological characteristics, and mechanical properties of the mixes that were deemed acceptable. As a result, it was determined that the increase in the amount of fly ash usage positively affected the buildability of the printed layers. Additionally, the dynamic yield stress ranging from 114 to 204 Pa, viscosity ranging from 22 to 43 Pa.s, and structural build-up value ranges suitable for the production of 3D printable concrete mixtures were determined.

Biochemical Evaluation and Structural Characteristics of Copper Coating Cellulose Nonwovens Prepared by Magnetron Sputtering Technology

The research aimed to enhance the aqua-jet/spunlace cellulose nonwoven fabric by deposition of copper coating by magnetron sputtering technology. Plasma technology facilitated the efficient distribution of copper particles on the surface of the cellulose nonwoven fabric, while maintaining free airflow and eliminating the need for additional layers. New cellulose-copper composites exhibit potential in biomedical applications, while minimizing their impact on biological processes such as blood plasma coagulation. Consequently, they can be utilized in the production of dressings, bandages, and other medical products requiring effective protection against bacterial infections. The cellulose-copper composite material was subjected to the physiochemical and biological investigations. The physiochemical analysis included the elemental analysis of composites, their microscopic analysis and the surface properties analysis (specific surface area and total pore volume). The biological investigations consisted of biochemical-hematological tests including the evaluation of the activated partial thromboplastin time and pro-thrombin time. Biodegradable materials based on cellulose nonwoven fabrics with the addition of copper offer a promising alternative to conventional materials. Their innovative properties, coupled with environmental friendliness and minimal impact on biological processes, offer vast application possibilities in healthcare and the production of hygiene products.

Controlling volume fluctuations for studies of critical phenomena in nuclear collisions

We generalize and extend the recently proposed method [1] to account for contributions of system size (or volume/participant) fluctuations to the experimentally measured moments of particle multiplicity distributions. We find that in the general case there are additional biases which are not directly accessible to experiment. These biases are, however, parametrically suppressed if the multiplicity of the particles of interest is small compared to the total charged-particle multiplicity, e.g., in the case of proton number fluctuations at top RHIC and LHC energies. They are also small if the multiplicity distribution of charged particles per wounded nucleon is close to the Poissonian limit, which is the case at low energy nuclear collisions, e.g., at GSI/SIS18. We further find that mixed events are not necessarily needed to extract the correction for volume fluctuations. We provide the formulas to correct pure and mixed cumulants of particle multiplicity distributions up to any order together with their associated biases.

Quantifying the effects of inlet gas and collision models in direct metal deposition using a CFD-DEM approach

Simulations of the powder jet in direct metal deposition (DMD) are often made with significant simplifications such as being incompressible, steady-state, or single-component, and do not provide explanation for the choice of parameters in the collision model. This work presents a coupled Computational Fluid Dynamics–Discrete Element Method model for the powder jet in DMD that considers all of the following features: compressibility effects, particle–wall and particle–particle collisions, turbulence, gas mixing, and melt pool boundaries. The goal of the simulation is to optimize the operating conditions and to predict the outcomes of experiments. After effective validation against experimental results, the effects of inlet gas, collision models and different boundary conditions in DMD have been comprehensively studied. It is demonstrated that gases with higher diffusivities, such as helium, are less effective shielding gases than those with lower diffusivities, such as argon. The increased wall temperature arising from the melt pool and track has little influence on the particle distribution.

Characterizing Chemical, Environmental, and Stimulated Subcellular Physical Characteristics of Size-Fractionated PMs Down to PM0.1.

Air pollution, especially particulate matter (PM), is a significant environmental pollution worldwide. Studying the chemical, environmental, and life-related cellular physical characteristics of size-fractionated PMs is important because of their different degrees of harmful effects on human respiratory tracts and organ systems, causing severe diseases. This study evaluates the chemical components of size-fractionated PMs down to PM0.1 collected during a biomass-burning episode, including elemental/organic carbon and trace elements. Single particle sizes and distributions of PM0.1, PM0.5-0.1, PM1.0-0.5, and PM2.5-1.0 were analyzed by scanning electron microscopy and Zeta sizer. Two commonly used cell lines, e.g., HeLa and Cos7 cells, and two respiratory-related cell lines including lung cancer/normal cells were utilized for cell cytotoxicity experiments, revealing the key effects of particle sizes and concentrations. A high-speed scanning ion conductance microscope explored particle-stimulated subcellular physical characteristics for all cell lines in dynamics, including surface roughness (SR) and elastic modulus (E). The statistical results of SR showed distinct features among different particle sizes and cell types while a E reduction was universally found. This work provides a comprehensive understanding of the chemical, environmental, and cellular physical characteristics of size-fractionated PMs and sheds light on the necessity of controlling small-sized PM exposures.

Tribological and mechanical properties of FSW joints of untainted stainless steel and titanium: novel characterization of similar and dissimilar joints

Friction Stir Welding (FSW) is an emerging solid-state welding process that joins dissimilar or similar metals based on requirements. The additional material to make the joint is also a weight reduction factor deemed vital in weight-sensitive industries like aerospace and orthopedic applications. The similar and dissimilar Ti-6Al-3Nb-2Zr-1Mo (Ti6321) and stainless steel (SS 310) joints are performed through friction stir welding. This investigation aims to identify the effect of process parameters on the mechanical behavior and microstructural characteristics of the FSW joints. Five plates are chosen; three are FSW joints, and two are kept in the original base material. In all five plates, tensile, microhardness, and wear tests are performed, including an analysis of grain size. It is observed that the similar Ti6321 joint with a 6 mm pin diameter, 60 mm transverse speed, 900 mm rotational speed, and a constant axial force of 1 KN exhibits a maximum microhardness of 362 HV and a tensile strength of 927 MPa when compared to other joints. The tribological properties are identified as varying load (10–50 N), sliding speed (1–5 m s−1), and a constant sliding distance (1000 m) on pin-on-disc apparatus. It reveals that welding parameters and tool diameter influence tribological characteristics. The surface morphology carried out by FE-SEM revealed that the HAZ is composed of acicular α. The increase in microhardness is higher in WC than in BM due to the uniform distribution of particles. The chemical composition and phases are analyzed using XRD.

Dark fluxes from electromagnetic cascades

We study dark sector production in electromagnetic (EM) cascades. This problem requires accurate simulations of Standard Model (SM) and dark sector processes, both of which impact angular and energy distributions of emitted particles that ultimately determine flux predictions in a downstream detector. We describe the minimal set of QED processes which must be included to faithfully reproduce a SM cascade, and identify a universal algorithm to generate a dark sector flux given a Monte-Carlo simulation of a SM shower. We provide a new tool, , which simulates EM cascades with associated dark vector production, and compare it against existing literature and “off the shelf” tools. The signal predictions at downstream detectors can strongly depend on the nontrivial interplay (and modelling) of SM and dark sector processes, in particular multiple Coulomb scattering and positron annihilation. We comment on potential impacts of these effects for realistic experimental setups.

Ultrasound wavelet spectra enable direct tissue recognition and full-color visualization

Traditional brightness-mode ultrasound imaging is primarily constrained by the low specificity among tissues and the inconsistency among sonographers. The major cause is the imaging method that represents the amplitude of echoes as brightness and ignores other detailed information, leaving sonographers to interpret based on organ contours that depend highly on specific imaging planes. Other ultrasound imaging modalities, color Doppler imaging or shear wave elastography, overlay motion or stiffness information to brightness-mode images. However, tissue-specific scattering properties and spectral patterns remain unknown in ultrasound imaging. Here we demonstrate that the distribution (size and average distance) of scattering particles leads to characteristic wavelet spectral patterns, which enables tissue recognition and high-contrast ultrasound imaging. Ultrasonic wavelet spectra from similar particle distributions tend to cluster in the eigenspace according to principal component analysis, whereas those with different distributions tend to be distinguishable from one another. For each distribution, a few wavelet spectra are unique and act as a fingerprint to recognize the corresponding tissue. Illumination of specific tissues and organs with designated colors according to the recognition results yields high-contrast ultrasound imaging. The fully-colorized tissue-specific ultrasound imaging potentially simplifies the interpretation and promotes consistency among sonographers, or even enables the applicability for non-professionals.

Microstructural and tribological properties of cold sprayed high content SiCp/Al coating by SiCp mild-oxidation treatment

This paper presents the results of the influence of irregular SiC particles, treated by mild-oxidation at 1100 °C, on deposition behavior (deposit rate, surface finish roughness), and deposition body (microstructure, friction, and wear). Coatings are obtained using the cold-sprayed method, employing a powder mixture comprising 36 vol% irregular SiC powder treated by mild-oxidation and 64 vol% aluminum powder as feedstock. Results show that the silicon carbide particles are treated by mild-oxidation, the external surface of silicon carbide particles is predominantly composed of soft ceramic silica, and the particle edges are passivated. The results indicate that, under identical cold-sprayed process conditions, both the deposition amount of the coating and the retention amount of SiC particles increased. The particle fragmentation and particle distribution of SiC are obviously improved. The coating did not exhibit any harmful phases. Local weak metallurgical bonding is found at the interface of SiCp and Al matrix. Furthermore, the coating's porosity decreased, after SiCp mild-oxidation, the friction coefficient (0.5716) is decreased by 12.9 %, and the wear amount (0.159 mm3/N·m) is decreased by 64.7 %. A dense and uniformly distributed aluminum matrix composite coating with a high SiC particles content is achieved.

Selected challenges in solidification processing of graphene nanoplatelets (GNPs) reinforced aluminum alloys composites

Solidification processing of aluminum graphene composite is an attractive option for synthesis of metal matrix composites. Graphene reinforced aluminum metal matrix composites (GAMMCs) are of interest due to the low density and ultrahigh physical and mechanical properties of Graphene which can improve the properties of Al-Graphene composites. However, solidification processing of aluminum graphene composites has served challenges, including agglomeration of reinforcement and porosity resulting in decrease in properties above 0.five to three wt% graphene. Also, the graphene surface can react with molten aluminum alloys to form aluminum carbide. Challenges with particle distribution and porosity are frequently caused by the poor wetting of reinforcement by melt, requiring additions of selected wetting agents. The other problems include movement of reinforcement within the melt due to density differences and convection leading to nonuniform distribution of reinforcements. The graphene reinforcements can be pushed by solidifying interfaces under certain conditions during solidification leading to segregation of reinforcements in the interdendritic regions. The paper critically analyzes the above problems related to solidification processing of Aluminum- Graphene composites which has not been done in previous publications aluminum-graphene composites. The objective of this paper is to examine the challenges, and suggest possible solutions including addition of elements like silicon and magnesium to aluminum melt, coating graphene with metals like nickel and copper, controlling rate of advancement and nature of advancing solid liquid interface in a manner that they engulf graphene with dendrites or grains.

Discrete element analysis of the dynamic behavior of ballast track-subgrade system under train dynamic load

To study the dynamic response law of the ballast track-subgrade coupling system under the action of train dynamic load, considering the real shape of ballast particles, a refined discrete element model of the rail-sleeper-ballast bed-subgrade coupling system was established. The established model can realistically simulate the coupling mechanism between irregular ballast particles, between track panel and ballast bed, and between ballast bed and subgrade under train dynamic load. The validity of the established model is verified using on-site measurement results. This study, from a microscopic perspective, focuses on particle contact forces, vibrations, and frictional energy consumption in the rail-sleeper-ballast bed-subgrade coupling system under train dynamic load and investigates the influence of train speed and axle weight. Results show that an increase in train speed and axle weight enhances the number and probability distribution of strong force chains between ballast particles, increasing the risk of particle breakage and deterioration. The influence range and depth in the ballast bed-subgrade system increase with the train's speed and axle weight. Due to the granular nature of the ballast bed, the vibration acceleration distribution of ballast particles under train dynamic loads is relatively random. Overall, the vibration level of the ballast bed increases with train speed and axle weight. The frictional energy consumption of ballast particles rapidly grows as the train's bogie load passes, and the effect of train axle weight on the frictional energy consumption of ballast particles is more significant than the train's speed.

Study on the Occurrence Characteristics of the Remaining Oil in Sandstone Reservoirs with Different Permeability after Polymer Flooding.

After polymer flooding, the heterogeneity between different layers intensifies, forming intricate seepage channels and fluid diversions, which results in decreased circulation efficiency and lower recovery rates, leaving a significant amount of residual oil trapped within the reservoir. Understanding the characteristics of residual oil occurrence is crucial for enhancing oil recovery post-polymer flooding. This study focused on sandstone reservoirs with varying permeability in the Saertu block of the Daqing oilfield. Using cryosectioning and laser scanning confocal microscopy, the occurrence characteristics of the residual oil in these sandstone reservoirs post-polymer flooding were investigated. Additionally, micro-CT and scanning electron microscopy were employed to analyze the impact of the pore structure on the distribution characteristics of the residual oil. The results indicate that laser scanning confocal images reveal that post-polymer flooding, the residual oil in high- and low-permeability sandstone reservoirs predominantly exists in a bound state (average > 47%), mostly as particle-adsorbed oil. In contrast, the residual oil in medium-permeability reservoirs is primarily in a free state (average > 49%), mostly as intergranular-adsorbed oil. In high-permeability sandstone reservoirs, heavy oil components are mainly in a particle-adsorbed form; in medium-permeability sandstone reservoirs, residual oil predominantly consists of heavy components, with most light components occurring in a clustered form; in low-permeability sandstone reservoirs, clustered residual oil exists in a balanced coexistence of light and heavy components, while the heavy components primarily exist in a particle-adsorbed form. Post-polymer flooding, the large pore-throat structure in high-permeability sandstone reservoirs results in effective displacement and less free residual oil; medium-permeability sandstone reservoirs, with medium-large pores and throats, have preferential channels and fine particles blocking the throats, leading to some unswept pores and more free residual oil; low-permeability sandstone reservoirs, with small pores and throats, exhibit weak displacement forces and poor mobility, resulting in more bound residual oil. The distribution and content of clay particles and clay minerals, along with the complex microscopic pore structure, are the main factors causing the differences in the residual oil occurrence states in sandstones with varying permeability.

Design and optimization of gradient fibrous media using the method of moments

The goal of this work is to optimize the deposition mass distribution of polydisperse particles inside the fibrous media by modifying the distribution of the fiber packing density across filter depth. Two types of gradient fibrous media with linear and exponential fiber packing density distribution along the flow direction were derived. The method of moments was employed to study the transport and deposition characteristics of polydisperse aerosol particles inside the fibrous media. The reliability of the calculated results by the method of moments was confirmed by the numerical simulations based on the discrete phase model (DPM). Results indicate that the gradient fibrous media allows more particles to transport and deposit into the interior of the fibrous media, which improves the uniformity of particle deposition distribution across filter depth. There exists an optimal fiber packing density distribution ratio for the gradient fibrous media where the non-uniformity of deposition mass distribution of polydisperse particles across filter depth is minimized. In this way, uniform deposition distribution along the flow direction can be generally achieved by optimizing the fiber packing density distribution, which will contribute to the optimal design of microstructures for the fibrous filter.