Erosion Profile Research Articles

Insights into the relationship between particulate flow characteristics and local erosion behaviour under waterjet: The role of particle-fluid-surface interaction

In this study, the erosion characteristics of eutectic high entropy alloy under the liquid–solid two-phase flow is investigated by a coupled numerical-experimental method, in order to reveal the intrinsic relationship between microscopic erosion mechanism (experimental test) and the related particle-fluid-surface interaction (CFD modelling). Furthermore, instead of the common relation between average erosion rate and mainstream flow velocity, the relationship between local erosion distribution and local particulate flow characteristics is clarified. The erosion rate and erosion pattern match well between the experiment and simulation. The results demonstrate that NiCoCrFeNb0.45 exhibits superior anti-erosion performance when compared to other widely used equipment metals. The erosion profile agrees well with the shape of surface velocity distribution, indicating a close relationship between surface erosion behaviour and flow characteristics. In particular, the erosion pattern at a normal angle appears as a symmetric ring due to the flow stagnation phenomenon, with slight erosion damage in the centre area and severe erosion in the surrounding, whereas the erosion profile at an oblique angle displays an elliptic shape, with severe erosion damage in centre. Notably, the primary erosion mechanism varies dramatically in different surface regions, induced by the various impact velocities and angles associated with the corresponding changes in the flow field. This study provides a deeper understanding of erosion behaviour in terms of the interrelationship among the material mechanical properties, particulate flow field and particle-surface impingement behaviour.

On erosion wear of flat specimens incorporating roughness angle correction

Particle erosion-induced damage to structural walls constitutes a critical concern in aerospace and petrochemical engineering. Over time, this phenomenon leads to surface roughening, thereby altering particle impingement dynamics, a facet often overlooked in current simulation methodologies. This study proposes a novel numerical approach for investigating erosion characteristics of flat specimens, integrating a corrective model for roughness angle to enhance accuracy in predicting erosion profiles. Experimental validation confirms the superior performance of the proposed correction method, achieving a remarkable enhancement of approximately 60.27% in accurately predicting maximum erosion depth compared to conventional techniques. Notably, the corrected erosion depth exhibits a nonlinear relationship with erosion duration, closely mirroring experimental observations. In regions characterized by intensified erosion rates, the present method discloses a notable decrease of approximately 1.8° in forecasted particle impact angles with advancing erosion stages, thereby achieving closer adherence to empirical trends. The refined simulation method effectively rectifies historical overestimations, offering a robust framework for future studies in erosion prediction and mitigation strategies.

Phase composition of sputter deposited tungsten thin films

Sputter deposited tungsten thin films are studied by X-ray diffraction. Two phases can be identified: α-W and β-W based on the observed (110), and (200) and (210) Bragg reflections, respectively. With increasing film thickness (50 to 200 nm), the phase composition shifts from β-W towards α-W. No influence of the base pressure (3 × 10−3 – 3 × 10−5 Pa) on the phase composition is observed. Also the influence of the argon pressure (0.3 to 0.7 Pa) is rather weak. The strongest shift towards α-W composed thin films is obtained by increasing the discharge power (50 to 250 W). This trend is further studied by energy flux measurements using a calorimetric probe. These measurements rule out a strong change of the substrate temperature, and an impact of the energy flux scaled by the deposition rate (total energy per deposited atom). Test particle Monte Carlo simulations reveal the importance of the momentum of the reflected argon neutrals on the phase composition. The maximum energy of these species is mainly defined by the discharge voltage, and is higher than the directional dependent displacement energy of W. Despite the significant correlation between phase composition and the number of displacement per deposited atom, there is a strong scatter of the phase composition. As the deposition conditions were varied in random way, changes of the target erosion profile, and the changing discharge voltage over each series are probably partially responsible for the observed scatter. This scatter is also enhanced by the long term changes in the phase composition towards the more thermodynamic stable α-W phase.

Eulerian approach for erosion induced by particle-laden impinging jets

Particle dispersion and erosion play an important role in various engineering applications, particularly in impinging jet flows. This study presents a new Eulerian method for characterizing these phenomena in axisymmetric, laminar, and turbulent jets, impinging and transiently eroding a flat wall. The Eulerian mass and momentum conservation equations are solved assuming a one-way coupling between the flow and the particles. The carrier flow boundary layer velocity profiles in the laminar case are validated with analytical solutions. The particle calculation involves two stages, incident and reflected particles, connected via a restitution model. The reflected particles’ results offer insights into secondary erosion areas but are not used for the main erosion calculations. Subsequently, erosion at the eroded surface is computed using an empirical erosion model, followed by the displacement of computational nodes using the linear-elastic, small-strain deformation equations, all of which are solved transiently. The solutions reveal the spatial particle concentrations and momentum for different Stokes numbers: smaller Stokes particles follow the carrier flow streamlines, medium Stokes particles deviate, forming a W-shaped erosion profile, while the largest Stokes particles create a U-shaped profile. This numerical model offers a computationally efficient framework for CFD-based transient erosion calculation due to its Eulerian implementation.

Antimicrobial adhesive self-healing hydrogels for efficient dental biofilm removal from periodontal tissue

ObjectivesOral biofilms, including pathogens such as Porphyromonas gingivalis, are involved in the initiation and progression of various periodontal diseases. However, the treatment of these diseases is hindered by the limited efficacy of many antimicrobial materials in removing biofilms under the harsh conditions of the oral cavity. Our objective is to develop a gel-type antimicrobial agent with optimal physicochemical properties, strong tissue adhesion, prolonged antimicrobial activity, and biocompatibility to serve as an adjunctive treatment for periodontal diseases. MethodsPhenylboronic acid-conjugated alginate (Alg–PBA) was synthesized using a carbodiimide coupling agent. Alg–PBA was then combined with tannic acid (TA) to create an Alg–PBA/TA hydrogel. The composition of the hydrogel was optimized to enhance its mechanical strength and tissue adhesiveness. Additionally, the hydrogel’s self-healing ability, erosion and release profile, biocompatibility, and antimicrobial activity against P. gingivalis were thoroughly characterized. ResultsThe Alg–PBA/TA hydrogels, with a final concentration of 5 wt% TA, exhibited both mechanical properties comparable to conventional Minocycline gel and strong tissue adhesiveness. In contrast, the Minocycline gel demonstrated negligible tissue adhesion. The Alg–PBA/TA hydrogel also retained its rheological properties under repeated 5 kPa stress owing to its self-healing capability, whereas the Minocycline gel showed irreversible changes in rheology after just one stress cycle. Additionally, Alg–PBA/TA hydrogels displayed a sustained erosion and TA release profile with minimal impact on the surrounding pH. Additionally, the hydrogels exhibited potent antimicrobial activity against P. gingivalis, effectively eliminating its biofilm without compromising the viability of MG-63 cells. SignificanceThe Alg–PBA/TA hydrogel demonstrates an optimal combination of mechanical strength, self-healing ability, tissue adhesiveness, excellent biocompatibility, and sustained antimicrobial activity against P. gingivalis. These attributes make it superior to conventional Minocycline gel. Thus, the Alg–PBA/TA hydrogel is a promising antiseptic candidate for adjunctive treatment of various periodontal diseases.

Dynamical integrity of the safe basins in a problem of forced escape.

This paper explores the use of the approximation of isolated resonance method for determining the safe basins (SBs) in the problem of escape from a potential well. This study introduces a novel approach to capture the location and shape of the SBs and establish their erosion profiles. This research highlights the concept of "true" safe basins, which remain invariant with phase shifts, a critical factor often faced in real-world applications. A cubic polynomial potential serves as the benchmark to illustrate the proposed method.

Hydrogel-forming viscous liquid in response to ROS restores the gut mucosal barrier of colitis mice via regulating oxidative redox homeostasis

The disrupted oxidative redox homeostasis plays a critical role in the progress of ulcerative colitis (UC). Herein, hydrogel-forming viscous liquid (HSD) composed of cysteamine-grafted hyaluronic acid (HS) and superoxide dismutase (SOD) has been designed for UC. When the viscous HSD liquid was infused into colitis colon, SOD would convert the pathological superoxide (O2·−) to hydrogen peroxides (H2O2), which was subsequently scavenged by HS. Accordingly, the sol-gel transition of HSD was initiated by scavenging H2O2, enhancing its adhesion toward colitis colon. H2O2-treated HSD presented the higher storage modulus and stronger adhesion force toward porcine colon than the untreated HSD. Besides, H2O2-treated HSD presented the slower erosion profile in the colitis-mimicking medium (pH 3-5), while its rapid degradation was displayed in physiologic condition (pH7.4). The combination of pH-resistant erosion and ROS-responsive adhesion for HSD rendered it with the specifical retention on the inflamed colonic mucosa of DSS-induced colitis mice. Rectally administrating HSD could effectively hinder the body weight loss, reduce the disease activity index and improve the colonic shorting of DSS-induced colitis mice. Moreover, the pro-inflammatory cytokines (IL-1β, IL-6 and TNF-α) were substantially decreased, the colonic epitheliums were well rearranged and the tight junction proteins were greatly recovered after HSD treatment. Besides, HSD also modulated the gut flora, markedly augmenting the abundance of Firmicutes, Barnesiella and Lachnospiraceae. Moreover, HSD treatment could regulate oxidative redox homeostasis via activating Nrf2-HO-1 pathway to reduce ROS and malondialdehyde and upregulate antioxidant enzymes (SOD, GPx and GSH). Collectively, HSD might be a promising therapy for UC treatments. Statement of significanceHerein, a hydrogel-forming viscous liquid (HSD) was designed by cysteamine-grafted hyaluronic acid (HS) and superoxide dismutase (SOD) for UC treatments. When the viscous HSD liquid was infused into a colitis colon, SOD would convert the pathological superoxide to hydrogen peroxides (H2O2), which was subsequently scavenged by HS. Accordingly, the sol-gel transition of HSD was initiated by scavenging H2O2, enhancing its adhesion to the colitis colon. The colonic epitheliums of DSS-induced colitis mice were well rearranged and the tight junction proteins (Zonula-1 and Claudin-5) were greatly recovered after the HSD treatment. Moreover, the HSD treatment could regulate oxidative redox homeostasis via activating the Nrf2-HO-1 pathway to reduce ROS and malondialdehyde and upregulate antioxidant enzymes (SOD, GPx and GSH).

Multiphase flow and nozzle wear with CFD-DEM in high-pressure abrasive water jet

The issue of wear failure in High-Pressure Abrasive Water Jet (HP-AWJ) nozzles is an unavoidable challenge, and studying methods to enhance and predict the effective lifetime of nozzles is worth deep exploration. This paper employs a CFD-DEM coupling numerical approach to investigate wear phenomena inside the HP-AWJ nozzle, aiming to capture the realistic particle wear and erosion failure issues at the focusing tube region, which is a high-wear area of the HP-AWJ nozzle. Furthermore, the study considers realistic particles and nozzle wall constitutive models, incorporating material properties into the physical model, and employs computer-aided design methods to reflect wear failure conditions at different time intervals in the inner wall of the focusing tube at the nozzle. The results demonstrate that the number of realistic particles and initial inlet velocity has no impact on the particle exit kinetic energy. However, the particle-wall restitution coefficient affects the average particle kinetic energy at the outlet in the AWJ nozzle. The equivalent model of the realistic particles reflects the influence of the particle roundness on particle kinetic energy, acceleration, and stress concentration variations in the nozzle. These variations further affect the particle erosion rate on the nozzle wall and the actual wear failure problems on the wall surface. Finally, by combining the proposed erosion and wear model, a representative erosion profile at the AWJ focusing tube location comparable to experimental results is obtained, and the wear depth of the focusing tube changing with time is also studied. The results and methodologies presented in this paper provide valuable guidance for controlling the effective service lifetime of the AWJ nozzle, improving machining efficiency, and extending the lifespan of the AWJ nozzle.

Failure analysis and numerical simulation of the regulating valve with particle erosion and cavitation erosion in the black-water treatment system

The black-water regulating valve is very easy to be damaged due to the erosion of the key components, such as valve spool and valve seat. This work presents the failure analysis of the spool and seat of regulating valve in the black-water treatment system. Scanning electron microscopy and X-ray energy-dispersive spectrometer were used to detect the morphology and chemical compositions of failure valve samples. The computational fluid dynamics method was also adopted to simulate the medium flow characteristics in black-water regulating valve. The results show that most erosion areas of the valve occur at the spool-seat throttle zone. The erosion profile is mainly manifested in plastic deformation pits, cutting abrasions, furrows, pinhole pits and impact pits. The particles and cavitation bubbles move toward the throttle zone driven by black-water medium, causing particles impact and bubbles collapse. The particle flow velocity in the throttle zone of the valve is between 50 and 175 m/s, while the maximum velocity can reach 175 m/s. The valve suffered severe particle erosion and cavitation erosion under the particle impact and bubble collapse, finally resulting in its failure.

Impacts of anthropogenic structures in long- and short-term shoreline evolution of Santa Marta Bay (Colombian Caribbean)

Interaction of Anthropic interventions (rigid structures) with coasts is an essential aspect for understanding their geomorphic evolution and incorporating these data into adequate coastal management. This study analyses the short and long-term behavior (1985 to 2019) of shoreline at Santa Marta Bay (Caribbean - Colombia) and their relationship with coastal protection structures. The shoreline variations were analyzed through aerial photographs and satellite images using DSAS tools. The short-term assessment showed initial intense 1985–1991 erosion, with an average retreat speed rate of − 1.6 m·y− 1. It changed gradually since 2003, due to the construction of rigid structures and beach nourishment, decreasing shoreline retreat and even a progradation rate of 0.2 m·y− 1 was observed. The 2009–2019 period, despite recording a positive average value, exhibited a high percentage of erosion profiles. Therefore, in a decadal or long-term analysis (1985–2019), despite engineering works present positive results in the short term, new interventions are required. The coastal erosion is not uniform along the shoreline, because the area is a closed bay with small sediment inputs, the variations in erosion and accretion rates change with human intervention and the installation of new structures. Therefore, quantifying the scale and rate of shoreline changes and correlating them with anthropogenic structures is an essential step in assessing shoreline vulnerability.

Quantitative estimation of dust transport in the desert region of northwest China by plutonium isotopes

Dust is an important source of atmospheric pollution, and quantitative estimation of desert dust transport is crucial for air pollution control. In this study, five typical sandy soil profiles in the Tengger Desert were collected and analyzed for 239,240Pu concentration and 240Pu/239Pu atomic ratios in order to identify the source of 239,240Pu in this area and explore the sedimentary characteristics of dust in different profiles. The results revealed that the concentrations of 239,240Pu in the soil profiles were between 0.002 and 0.443 mBq/g with an exception of the deep layer soil at one site. The measured atomic ratios of 240Pu/239Pu are at the global atmospheric fallout level with a mean of 0.184 ± 0.020, indicating that global fallout is the dominant source of plutonium in this region. The total inventories of 239,240Pu in the reference sites in this area were estimated to be 39.2–44.6 Bq/m2, this is in agreement with the value from the global fallout of atmospheric nuclear weapon tests at the similar latitude (30–40 °N: 42 Bq/m2). The estimated erosion rate in the erosion profile utilizing soil erosion intensity mode is 2491 t/km2/yr and the soil erosion depth is 9.86 cm, While, the stacking rate of the accumulation profile is 1383 t/km2/yr, and the depth of accumulation is estimated to be 5.48 cm. The difference between the erosion and accumulation profiles indicated that approximately 1107 t/km2/yr of dust was exported from the Gobi landform area of the Tengger Desert, which might be transported long distance in the downwind direction.

Advancing Sea Turtle Monitoring at Nesting and Near Shore Habitats with UAVs, Data Loggers, and State of the Art Technologies

In the face of environmental change, high-quality and fine-scale information is essential in order to monitor the highly dynamic environments on land and sea. While traditional approaches to data collection face a number of practical limitations, advanced technologies could supplement and further improve our efforts. Taking sea turtles as a modeling organism, we present a novel methodological framework for monitoring species by means of advanced technologies, including Unmanned Aerial Vehicles coupled with image and temperature sensors. Diverse monitoring protocols were refined through pilot studies conducted in both terrestrial and nearshore sea turtle habitats. Our approach focuses on the collection of information for critical biological parameters concerning species reproduction and habitat use, following the complex life cycle of the species. Apart from biological information, our framework encompasses also the collection of information on crucial environmental factors that might be changing due to current and future human-derived pressures, such as beach erosion and temperature profile, as well as highly important human activities such as recreational use within nesting beaches that could undermine habitat quality for the species. This holistic and standardized approach to monitoring using advanced technologies could foster our capacity for conservation, resolving difficulties previously addressed and improving the collection of biological and environmental data in the frame of an adaptive management scheme.

Kinetic modeling of the plasma–wall interaction in the DTT divertor region

A precise estimate of the local energy fluxes and erosion profiles at the divertor monoblocks of a fusion reactor requires a kinetic modeling of the plasma–wall interaction. Here, a two-dimensional Particle-in-Cell code is used to quantify the particle and energy fluxes and ion impact distribution functions across the divertor monoblocks of the ‘Divertor Tokamak Test’ reactor, focusing on poloidal gaps with toroidal bevelling. The considered critical locations are close to the strike points at both Inner and Outer Vertical Targets. A worst-case scenario for particle fluxes corresponding to attached plasma conditions and featuring a single-null magnetic configuration is assumed. The separate and cumulative effects of including electron wall emission and ions/electrons collisions with a background neutral gas (recycled at the walls) are also assessed. It is found that a non-negligible energy flux affects the shadowed regions of the monoblocks, especially when accounting for collisions, and that the ion impact distribution functions are strongly influenced by the considered kinetic effects, with important implications on the induced sputtering yield.

Copper target erosion during unbalanced magnetron sputtering under different electromagnetic fields

Unbalanced magnetron sputtering (UBMS) is used to deposit mechanical and optical coatings due to the advantages of high deposition rate and low pollution level, but the low utilization rate of the target material limits its applications for industrial-scale production. To improve target utilization during UBMS, a magnetron system combining a coil magnet and a permanent magnet has been developed. The effects of the operating parameters of the magnetic flux density on the magnetic field were investigated, and the erosion profiles on the target surface were examined in terms of the plasma distribution. It was found that the erosion center was located where the lines of magnetic induction were parallel to the target surface. A strategy of changing the current of the central coil was finally proposed, which improved the target utilization to 52.9 %. These results provide theoretical guidance to improve the target utilization of UBMS by optimizing the design of the cathode target and magnetic field.

Моделирование эрозионного износа титанового сплава высокоскоростным потоком частиц

Introduction. Predicting solid particle erosion (SPE) in gaseous flow and managing its intensity is still a relevant problem in mechanical engineering. It requires the development of a general modeling methodology, which also depends upon many special cases studying various physical processes. Such studies should also include verification analysis, process parameters and model sensitivity studies. Mainly computational fluid dynamics and finite element analysis (and mesh-free methods such as smooth particle hydrodynamics or similar) are used to simulate the erosion process. Papers focused on CFD simulation of solid particle erosion of metal alloys are widely presented, but most of it is associated with relatively low or medium particle velocities (< 100–150 m/s) and is close to uniform diameter distribution. This paper presents a CFD study of Ti6Al4V titanium alloy SPE at relatively high particle velocities and sufficiently non-uniform unimodal particle diameter distribution. The paper also studies the turbulence model influence and particle shape effect which appears as a “shape factor” coefficient in the particle drag model. Methods. The heterogenous flow simulation was based on the Reynolds-averaged Navier-Stokes formulation, where the particles, according to Euler-Lagrange formulation, were simulated as mathematical points with corresponding properties. The influence of turbulence models, such as k-epsilon standard, RNG k-epsilon, and a relatively new Generalized equation k-omega (GEKO) model and its coefficients were also studied. Oka and DNV erosion models were also compared based on the general sample mass loss and more specific erosion intensity profile criterions. The simulation results were compared to the lab-scale experimental results. Results and discussion. It is shown that neither erosion intensity profile or sample mass loss do not depend upon the turbulence model choice or GEKO parameters variation. As expected, erosion is dependent on the erosion model and its coefficients. A notable influence of the shape factor is shown. As the drag coefficient increased due to the particle shape, the erosion intensity decreased and the erosive profile on the surface also changed due to the changing velocity and diameter distribution of the heterogenous flow. It is expected that such results would be useful not only for erosion prediction in all areas of mechanical engineering, but also for wear management in mechanical assemblies and shot peening / shot peen forming management and simulation.

Controlling lateral thickness distributions of magnetron sputtering deposited coatings using shadow masks

A lateral thickness distribution control model for magnetron sputter-deposited coatings was established using shadow masks. The sputtering yield distributions were investigated in detail, particularly the variation trend from straight to curved tracks, based on the erosion profiles of rectangular targets. On this basis, a mathematical model for a planetary rotation system was established to simulate the thickness distribution of coatings on different substrates, including flat, spherical, and aspherical shapes, accurately. A shadow mask with multi-Gaussian outlines was proposed, and the coating thickness was effectively controlled according to specific distribution requirements by optimizing the profile parameters of the masks using a genetic algorithm. Flat and ellipsoidal substrates were used to prepare Mo and Si monolayer coatings to verify the effectiveness of this model. Although the diameters of the substrates were close to the lengths of the rectangular targets, the results showed that uniform coatings were obtained on the flat substrate, whereas the ellipsoidal substrate exhibited high-precision gradient coatings, with maximum deviations below 0.5%, which proved the validity of this approach.

Two-dimensional analytical description of the plasma potential in a magnetron discharge

Simple analytical formulas are proposed to describe the plasma potential in a steady-state magnetron discharge, based on the results of various experiments and numerical simulations reported in the literature. The description is two-dimensional (2D), covering two main regions, the cathode sheath and the ionization region, both contributing to electron energization. A parabolic potential in the axial direction governs the cathode sheath. The thickness of the cathode sheath is obtained from the 1D collisionless Child–Langmuir law. A parabolic or linear potential in the axial direction characterizes the ionization region. The local ion current density to the cathode, estimated from the target erosion profile, sets the radial dependence of the potential. The proposed formulas use a set of input parameters that can be experimentally obtained. The analytical description captures all characteristics of the highly inhomogeneous plasma potential of a steady-state magnetron discharge operated in a reduced magnetic field BRT/p lower than 0.1 T/Pa, as revealed by the comparison to self-consistent 2D numerical simulations.

Plasma sputtering of biased electrodes in an oblique magnetic field

The surface erosion of biased electrodes immersed in a radio frequency (RF) plasma was investigated in oblique magnetic fields ranging from 0.1 T to 3.5 T. The plasma potential and density in the vicinity of the biased electrode have been measured using an RF-compensated cylindrical Langmuir probe moved by a three-dimensional motorised arm in the ALINE facility at 0.1 T. The erosion profiles were determined for different gases (argon and helium), magnetic field strength and plasma volume for the same electrode surface area at an angle of 5∘ with the magnetic field in three different experimental geometries. The radial electric field (perpendicular to the magnetic field) in the plasma column has been deduced from plasma potential measurements. This radial field makes the ions converge to the core of the plasma column at grazing angles (30∘) and is reversed at larger angles. The ion flux on the sample increases with the magnetic field magnitude leading to a strong erosion inhomogeneity. At lower plasma volume, the erosion rate is sensitively enhanced. Local redeposition was identified using x-ray photoelectron spectroscopy on the surfaces exhibiting preferential deposition directions. Finally, the asymmetric erosion patterns obtained from a molybdenum layer etching are explained by the similar asymmetric density maps obtained with the probe and by the drift and the local sheath acceleration.

Surface Eroding Methacrylic Anhydride Copolymers and Model Drug Release

AbstractMethacrylic anhydride (MAA)‐based copolymers are synthesized to probe how comonomer composition and type affect the erosion profiles. Anhydrides readily undergo hydrolysis, which when combined with high crosslink density and hydrophobicity tend to exhibit an ideal surface erosion mechanism for drug delivery, tissue adhesives, and biocement applications. The cylindrical (10 mm diameter × 5 mm height) polyanhydrides are degraded under pseudo‐physiological conditions and surface erosion is qualitatively observed via photographs. The non‐anhydride comonomer can be utilized to tune erosion profiles while retaining degradability and product solubility. The comonomer can accelerate or slow the degradation process to a greater extent at low MAA concentrations. Drug release is conducted using purpurin to model hydrophobic drugs. Purpurin concentration is quantified using UV–visible spectral analysis. Purpurin extends the degradation profile due to a combination of local pH changes, hydrophobicity, and molecular diffusion. Linear purpurin release is observed as a function of polymer erosion (0.9897 R2) thus confirming a surface erosion‐mediated drug release mechanism.

Particle-in-Cell Simulations for the Improvement of the Target Erosion Uniformity by the Permanent Magnet Configuration of DC Magnetron Sputtering Systems

Improving the target erosion uniformity in a commercial direct current (DC) magnetron sputtering system is a crucial issue in terms of process management as well as enhancing the properties of the deposited film. Especially, nonuniform target erosion was reported when the magnetic flux density gradient existed. A two-dimensional (2D) and a three-dimensional (3D) parallelized particle-in-cell (PIC) simulation were performed to investigate relationships between magnetic fields and the target erosion profile. The 2D PIC simulation presents the correlation between the heating mechanism and the spatial density profiles under various magnet conditions. In addition, the 3D PIC simulation shows the different plasma characteristics depending on the azimuthal asymmetry of the magnets and the mechanism of the mutual competition of the E × B drift and the grad-B drift for the change in the electron density uniformity.