Particle Diffusion Coefficient Research Articles

Impact of spatially varying transport coefficients in EMC3-Eirene simulations of W7-X and assessment of drifts

Abstract Modelling the scrape-off layer of a stellarator is challenging due to the complex magnetic 3D geometry. The here presented study analyses simulations of the scrape-off layer (SOL) of the stellarator Wendelstein 7-X (W7-X) using spatially varying diffusion coefficients for the magnetic standard configuration, extending our previous study (Bold et al 2022 Nucl. Fusion 62 106011). Comparing the EMC3-Eirene simulations with experimental observations, an inconsistency between the strike-line width (SLW) and the upstream parameters was observed. While to match the experimental SLW a particle diffusion coefficient D ≈ 0.2 m2 s−1 is needed, D ≈ 1 m2 s−1 is needed to get experimental separatrix temperatures of 50 eV at the given experimental heating power. We asses the impact of physically motivated spatially varying transport coeffients. Agreement with experimental data can be improved, but various differences remain. We show that drifts are expected to help overcome the discrepancies and, thus, the development of SOL transport models including drifts is a necessary next step to study the SOL transport of the W7-X stellarator.

Reduction of neoclassical bulk-ion transport to avoid helium-ash retention in stellarator reactors

Abstract The reduction of neoclassical energy transport in stellarators has traditionally focussed on optimizing magnetic fields for small values of ‘effective helical ripple’ — ϵ eff , the geometric factor associated with electron 1 / ν transport—and relying on the radial electric field, E r , needed to maintain ambipolarity in the plasma, to simultaneously diminish ion energy losses to a tolerable level. As one must generally expect E r < 0 , such a strategy has a drawback for reactor operation, however, as negative values of E r tend to hinder the exhaust of helium ash, and this will become intolerable if it results in excessive fuel dilution. Theoretically, one can show that the neoclassical transport of low-Z impurities depends critically on the ratio L 11 e / L 11 i , where the L 11 σ are the neoclassical particle diffusion coefficients of the bulk-plasma electrons ( σ = e ) and ions ( σ = i ). Increasing the value of this ratio is shown here to counteract impurity retention, but maintaining good confinement of the bulk species requires this to be achieved by decreasing L 11 i rather than increasing L 11 e , implying the need for more than just minimization of ϵ eff in reactor design. To assess the prospects of such an endeavor, a predictive 1-D transport code is used here to determine the range of L 11 e / L 11 i values which arises in simulations of conventionally optimized reactor candidates. This range is found to be considerable, and includes examples with L 11 e / L 11 i values large enough to provide neoclassical temperature screening of the helium ash and even to flip the sign of the neoclassical convective velocity from inward- to outward-directed. More intriguingly, the strong reduction of L 11 i in such cases can also lead to the appearance of E r > 0 (a so-called ‘electron root’) within the core of plasmas having central densities as large as 2 × 10 20 m−3. Having E r > 0 in the plasma core produces the ideal situation in which all thermodynamic forces aid in the exhaust of helium ash, although this benefit is tempered by the small values of L 11 z which accompany an electron root (where σ = z denotes helium ash). Means are discussed for improving the results presented here, so that avoiding helium-ash retention can be explicitly targeted in future reactor optimizations.

Compression Acceleration of Protons and Heavier Ions at the Heliospheric Current Sheet

Recent observations by the Parker Solar Probe (PSP) suggest that protons and heavier ions are accelerated to high energies by magnetic reconnection at the heliospheric current sheet (HCS). By solving the energetic particle transport equation in large-scale MHD simulations, we study the compression acceleration of protons and heavier ions in the reconnecting HCS. We find that the acceleration of multispecies ions results in nonthermal power-law distributions with a spectral index consistent with the PSP observations. Our study shows that the high-energy cutoff of protons can reach Emax∼0.1 –1 MeV depending on the particle diffusion coefficients. We also study how the high-energy cutoff of different ion species scales with the charge-to-mass ratio Emax∝(Q/M)α . When determining the diffusion coefficients from the quasi-linear theory with a Kolmogorov magnetic power spectrum, we find that α ∼ 0.4, which is somewhat smaller than α ∼ 0.7 observed by PSP.

The Mean Free Path of 13–64 MeV Protons Derived from Statistical Results of Solar Energetic Particle Events

A recent study by Wang et al. investigated gradual solar proton events with energies >10 MeV, as observed by STEREO-A, STEREO-B, and the Solar and Heliospheric Observatory spacecraft. For each event, the spacecraft with the best magnetic connection to the source region among the three spacecraft was identified, and energetic proton intensities observed by the spacecraft were analyzed through fitting. The fitting process produced two parameters, b and c, for four energy channels (13–16 MeV, 20–25 MeV, 32–40 MeV, and 40–64 MeV) in each event. Parameters b and c govern the rise and decay of particle intensities, respectively. Statistical analysis revealed a power-law correlation between b and c, expressed as c ∼ b −γ . In this study, in order to explain the relation between the two parameters, we investigate the model of particle diffusion coefficients in the interplanetary space. In our simulations, the radial mean free path is modeled as a power function of radial distance, successfully reproducing the b–c relation. Consequently, the observations demonstrate that the radial mean free path varies with radial distance in a power law. In future research, the model of diffusion coefficients holds promise in determining the mean free path of energetic protons.

Exploring the graphitization transformation mechanism of deposited carbon in molten salt electrolysis: A novel insight from molecular structure models

Molten salt electrolysis graphitization is a novel method for the electrochemical graphitization, offering significant technological advantages. Researchers have shown keen interest in preparing graphite materials through molten salt strategies. However, there is still a lack of comprehensive research methodologies at the molecular scale for the removal of heteroatoms and rearrangement of carbon atoms in different amorphous carbon conversion systems. To address the above issue, the deposited carbon (DC, a coking byproduct) was converted into graphitized material (electrolysis products, EP) through the electrochemical method in this study. By processing Transmission Electron Microscope images with Python programming, aromatic skeleton structure information was quantitatively extracted. The evolution of the structure of DC was studied using Fourier transform infrared spectroscopy and X-ray photoelectron spectroscopy. Based on information about elemental content, aromatic skeletal structure, and heteroatom functional groups, average chemical structure models were constructed for DC and EP, and relevant chemical bond parameters were statistically analyzed. Then, the influence of the electric field on the structural transformation of amorphous carbon in molten salts was investigated. The research results show that the electric field significantly affects the graphitization transformation process of amorphous carbon in molten salts, enhancing the interaction between calcium ions and DC molecules, increasing the diffusion coefficient of particles in the system, and promoting the formation of more sp2-hybridized carbon atoms, thus forming a more compact aromatic ring network. This study provides a new research method and molecular/atomic-level insights for a deeper understanding of the mechanism of graphitization transformation of amorphous carbon.

Short-time self-diffusion in binary colloidal suspensions

The Brownian dynamics of a colloidal particle is consistently modified by the presence in the solvent of other particles of comparable size, whose effects on the particle diffusion coefficient cannot be attributed to a change of the effective solvent viscosity. So far, despite their impact on subjects ranging from microrheology to phoretic transport in crowded environments, a detailed experimental survey of these effects is still lacking. By exploiting the peculiar properties of fluorinated colloidal particle, we have performed an extensive dynamic light scattering (DLS) investigation of short-time self-diffusion in binary colloidal mixtures, focusing on systems where one of the two species (the “tracer” particles) is very diluted compared to the other one (the “host” particles). From the dependence on the host concentration of the DLS correlation function, we have obtained the first-order correction hs1s to the tracer single-particle diffusion coefficient, varying the tracer-to-host size ratio q in the range 0.2 ≤ q ≤ 2. Our results support the functional relation of hs1s on q proposed to account for the theoretical and numerical results for hard-sphere mixtures. However, hs1s seems to have a weaker dependence on the size ratio than theoretically predicted, possibly because of an imperfect matching of the suspensions we used for an ideal hard-sphere mixture. This may be due to the presence of a stabilizing surfactant layer on the particle surface that, although very thin, has significant effects on hydrodynamic lubrication forces.

Detection of diffusion anisotropy from an individual short particle trajectory

In parallel with advances in microscale imaging techniques, the fields of biology and materials science have focused on precisely extracting particle properties based on their diffusion behavior. Although the majority of real-world particles exhibit anisotropy, their behavior has been studied less than that of isotropic particles. In this study, we introduce a method for estimating the diffusion coefficients of individual anisotropic particles using short-trajectory data on the basis of a maximum likelihood framework. Traditional estimation techniques often use mean-squared displacement (MSD) values or other statistical measures that inherently remove angular information. Instead, we treated the angle as a latent variable and used belief propagation to estimate it while maximizing the likelihood using the expectation-maximization algorithm. Compared to conventional methods, this approach facilitates better estimation of shorter trajectories and faster rotations, as confirmed by numerical simulations and experimental data involving bacteria and quantum rods. Additionally, we performed an analytical investigation of the limits of detectability of anisotropy and provided guidelines for the experimental design. In addition to serving as a powerful tool for analyzing complex systems, the proposed method will pave the way for applying maximum likelihood methods to more complex diffusion phenomena. Published by the American Physical Society 2024

Preparation of modified Jordanian bentonite with cetyltrimethylammonium bromide as novel adsorbent for phosphate ion removal from synthetic and real wastewater

Jordanian bentonite was examined for its capacity to remove phosphate ions from aqueous solutions, both synthetic and natural. by converting Jordanian bentonite to organo-bentonite (CTAB-bentonite). Investigation on the ability of organo-bentonite to remove phosphate ions under different conditions including initial concentration, temperature, particle size, pH levels, adsorbent dosage, and contact time. Kinetic experiments results were analyzed employing first and second pseudo order models. The results of R2 for both kinetic models confirmed that fill in the pseudo- second-order and was preferred for the transport of phosphates other than pseudo-first order. For both synthetic and actual wastewater, the activation energy for removal was computed and determined to be 22.88 kJ/mol and 58.73 kJ/mol, respectively. The rate of phosphate ion absorbing was investigated at different temperatures, particle sizes, agitation levels, and pH values. The study predicted both particle diffusion (Dp) and film diffusion (Df) coefficients, concluding that film diffusion (Df) determines rate.

Flotation Coefficient Distributions of Lipid Nanoparticles by Sedimentation Velocity Analytical Ultracentrifugation.

The robust characterization of lipid nanoparticles (LNPs) encapsulating therapeutics or vaccines is an important and multifaceted translational problem. Sedimentation velocity analytical ultracentrifugation (SV-AUC) has proven to be a powerful approach in the characterization of size-distribution, interactions, and composition of various types of nanoparticles across a large size range, including metal nanoparticles (NPs), polymeric NPs, and also nucleic acid loaded viral capsids. Similar potential of SV-AUC can be expected for the characterization of LNPs, but is hindered by the flotation of LNPs being incompatible with common sedimentation analysis models. To address this gap, we developed a high-resolution, diffusion-deconvoluted sedimentation/flotation distribution analysis approach analogous to the most widely used sedimentation analysis model c(s). The approach takes advantage of independent measurements of the average particle size or diffusion coefficient, which can be conveniently determined, for example, by dynamic light scattering (DLS). We demonstrate the application to an experimental model of extruded liposomes as well as a commercial LNP product and discuss experimental potential and limitations of SV-AUC. The method is implemented analogously to the sedimentation models in the free, widely used SEDFIT software.

On Calculating Diffusion Coefficients Numerically in Synthetic Turbulence Using Particle Pushers

Numerical simulations of test particle transport in the presence of synthetic turbulence with known properties still provide the most reliable estimations of the diffusion coefficients of charged particles in turbulent space plasmas available. The development and implementation of such simulations, however, are far from straightforward. The present study provides a comprehensive treatment of the development and testing of such a simulation code, detailing the simulation of synthetic turbulence and diffusion coefficients, as well as various numerical tests to validate code output. Furthermore, a novel test for such codes is proposed, namely, the transport of charged particles in pure slab turbulence, which proves sensitive to numerical factors prior tests remain insensitive to.

Solid–liquid–gas-like phase transition in electric field driven dense granular media

The polarization induced by an external electric field significantly influences the contact charge of particles. It can easily cause solid–liquid–gas-like phase transitions in dense granular media, which are the key factors leading to environmental and safety disasters such as sandstorms, volcanic eruptions, and spacecraft emergencies. In this letter, our investigation focused on a densely packed granular system with different thicknesses subjected to bottom excitation and an external electric field. Using the discrete element method (DEM), we proposed conditions for the first- and second-order phase transitions and revealed the mechanism of electrical signal transformation. We presented the physical characteristics of charge and polarization diffusion coefficients for charged particles, and introduced a theoretical Turing model to predict critical phase transitions. Additionally, this phase transition model was extended to the application of electrostatic dust removal, quantitatively predicting the relationship between dust removal efficiency, particle layer thickness, and electric field intensity.

Evolution of some flow-related properties of diffusive aerosols along a tube

This is the third of a series of papers dealing with the behavior of Brownian aerosol particles immersed in a laminar fluid flow. The evolution along the tube of the distributions of particle radial positions (RPD), particle residence time (RTD), and particle mean axial velocity (MAVD) were determined by Monte Carlo (MC) simulation of particles trajectories. The RPD and particle penetration was also determined by numerical solution of the advection-diffusion equation (ADE) with negligible particle axial diffusion. The fairly good agreement shown between the results obtained by these two methods justifies our confidence on the use of the MC technique to determine other particle properties, as MAVD and RTD, for which the corresponding differential equation is yet unknown. Flow-related properties of the aerosol, such as penetration and residence time, are mainly determined by its MAVD. The MAVD is intimately related to the RPD; the latter evolves in such a manner that the surviving particles tend to accumulate nearer the tube axis and farther from the wall. When the fluid local velocity depends on the spatial location, the mean particle axial velocity increases as the aerosol flows downstream the tube, and its value can be considerably larger than the mean fluid velocity, in spite that no external force is acting on the particle. A direct consequence of this counterintuitive fact is that the mean aerosol residence time in the tube can be much smaller, by a factor of ∼0.65, than that of the fluid for even moderate values of the particle diffusion coefficient. This asymptotic value of the aerosol mean residence time can be predicted using the ADE in conjunction with a simple estimation model proposed here. If the fluid velocity is constant within the tube (uniform or plug flow), the mean particle axial velocity is everywhere equal to the fluid velocity, and particles and fluid spend the same time to traverse the tube. The larger the departure of the fluid velocity profile from uniformity, the larger the difference of mean axial velocity and mean residence time between particles and fluid.

Molecular dynamic modeling and analysis of the sintering behaviors of GDC modified BSCF nanorods for rSOC oxygen electrode

Degradation including segregation and high stress related issues are significant challenges for reversible solid oxide cells (rSOCs), particularly concerning the oxygen electrode. Understanding the sintering preparation is crucial for enhancing the performance and reliability of the oxygen electrode under long-term dual-mode operation. In this study, the sintering process of Ba0.5Sr0.5Co0.8Fe0.2O3-δ nanorods anchored with Gd-doped CeO2 nanoparticles (GDC-BSCF-NR) was predicted by using molecular dynamics method. To optimize the sintering process, the stress distribution, A-site ion migration behavior and thermal properties of the composite electrode materials were analyzed at different sintering temperature, the effects of nanoparticle size were also investigated. Both thermal conductivity and thermal expansion increase with sintering temperature. The particle stress of the composites correlates positively with the diffusion coefficient of ions. The diffusion coefficients of surface and internal Ba/Sr ions increase by 6%–9% from 973 K to 1373 K, while stress increases by 19%–33 %. The diffusion coefficient of BSCF particles decrease by 15.1 % with an increase in GDC nanoparticle size, which is beneficial for suppressing Ba/Sr segregation.

Coal particle size-dependent gas diffusion coefficient

The tests on gas (CH4 or CO2) desorption-diffusion in coal particles, together with the analytical unipore or bidisperse diffusion model, are widely used to study the gas diffusion behavior, but the fitted diffusion coefficient always increases with particle size, which makes it difficult to determine an identical diffusion coefficient for coal particles. In this work, five sets of anthracite particles with different sizes are prepared, and tests on CO2 desorption-diffusion in different coal particles are carried out. Four continuum models (including an analytical unipore diffusion model, an analytical bidisperse diffusion model, a numerical unipore diffusion model, and a dual-porosity model) and a discrete fracture model are established. The continuum models can all fit the experimental results well, while the fitted diffusion coefficients always increase with particle size. Based on the identical matrix’s side length, matrix diffusion coefficient, and fracture diffusion coefficient, the discrete fracture model fits the experimental results of different coal particles successfully, and the size effect of diffusion coefficient is resolved. The diffusion coefficient fitted by the continuum models is the equivalent diffusion coefficient of matrix diffusion and fracture diffusion, so the equivalent diffusion coefficient increases with fracture path (i.e., particle size), and the size effect of diffusion coefficient occurs. The results provide an insight into the size effect of diffusion coefficient and make it possible to determine an identical diffusion coefficient for coal particles of different sizes.

Effect of a high-gradient magnetic field on particle concentration distribution in a magnetic fluid seal: Rivalry of the diffusion and magnetophoresis

In this paper, the unsteady process of particle concentration distribution in a magnetic fluid is studied. Diffusion and the effect of a high-gradient magnetic field in a magnetic fluid seal (MFS) are taken into consideration. It is crucial to take into account how particle mobility and diffusion coefficient vary on particle concentration in order to determine the possibility and time of the formation of a close packing of particles. The Carnaghan-Starling approximation was employed. It is demonstrated numerically that the geometry of the MFS, namely its gap width and pole base width, as well as the magnitude of the magnetic field strength under the pole tooth of the MFS, both influence the time of the formation of a close packing of particles. This period can be regarded as the MFS's uptime. Depending on the design of the working gap, the uptime seal for magnetic fluid based on vacuum oil may require between two weeks and six months. The uptime seal also becomes shorter when the carrier fluid's viscosity decreases.

The motion of Brownian particles suspended in a non-uniform fluid flow

The effect of the type of fluid flow velocity profile on the motion of a Brownian particle in a circular tube has been studied using a Monte Carlo technique to simulate particle trajectories. Three types of fluid flow were studied: uniform (UF), parabolic (PF), and an initial uniform flow which evolves and may eventually attain the parabolic velocity profile, i.e. transient flow (TF). For UF and PF, radial and axial particle diffusion were simultaneously considered in some cases; for TF, where fluid dynamics equations had to be solved in addition to the Monte Carlo simulations, axial diffusion was neglected for fluid and particles, so that calculations had to be restricted to tube aspect ratios (radius/length) smaller than 0.1, a common scenario in most practical aerosol applications. A first series of simulations were performed to determine the overall particle penetration through the tube. For fixed tube geometry and particle diffusion coefficient, penetration in TF lied between those in PF (highest) and UF (lowest), in such a manner that, for a given value of the diffusion coefficient, the larger the degree of flow development (i.e., the smaller the values of the tube aspect ratio and the Reynolds number), the larger the penetration. These findings are coherent with those found in a former investigation dealing with the particle residence time in the tube. In a second series of simulation runs, calculations were done for selected initial locations of the particle within the tube entrance cross section, to examine the effect that the proximity of the particle starting position to the tube wall or to the tube axis has on variables such as penetration, mean first hitting time and length, mean first exit time, and mean axial velocity of lost and survived particles. When the fluid flow is not uniform but varies from place to place, the mean particle axial velocity is larger than that of the fluid. This counterintuitive fundamental result allows interpretation of the trends observed in penetration and residence time.

Validation of SOLPS-ITER simulations against the TCV-X21 reference case

This paper presents a quantitative validation of Scrape-Off Layer Plasma Simulation-ITER (SOLPS-ITER) simulations against the TCV-X21 reference case and provides insights into the neutral dynamics and ionization source distribution in this scenario. TCV-X21 is a well-diagnosed diverted L-mode sheath-limited plasma scenario in both toroidal field directions, designed specifically for the validation of turbulence codes (Oliveira, Body et al 2022 Nucl. Fusion 62 096001). Five new, neutrals-related observables are added here to the extensive, publicly available TCV-X21 dataset. These are three deuterium Balmer lines in the divertor and neutral pressure measurements in the common and private flux regions. The quantitative agreement metric used in the validation is combined with the conjugate gradient method to approach the SOLPS-ITER input parameters that return the best overall agreement with the experiment. A proof-of-principle test of this method results in a modest improvement in the level-of-agreement; the shortcomings impacting the result and how to improve the methodology are discussed. Alternatively, a scan of the particle and heat diffusion coefficients shows an improvement of 10.4% in the level-of-agreement, approximately twice as high as that achieved by the gradient method. This result is found for an increased transport coefficient compared to what is usually used for TCV L-mode plasmas. The simulations further indicate that ∼65% of the total ionization occurs in the SOL, from which ∼70% in the divertor regions, despite being a sheath-limited regime, motivating the inclusion of self-consistent neutral models in future turbulence simulations on the path towards improved agreement with the experiment.

Computational fluid dynamics method for determining the rotational diffusion coefficient of cells

This work presents a straightforward computational method to estimate the rotational diffusion coefficient (Dr) of cells and particles of various sizes using the continuum fluid mechanics theory. We calculate the torque (Γ) for cells and particles immersed in fluids to find the mobility coefficient μ and then obtain the Dr by substituting Γ in the Einstein relation. Geometries are constructed using triangular mesh, and the model is solved with computational fluid dynamics techniques. This method is less intensive and more efficient than the widely used models. We simulate eight different particle geometries and compare the results with previous literature.

Parallel Diffusion Coefficient of Energetic Charged Particles in the Inner Heliosphere from the Turbulent Magnetic Fields Measured by Parker Solar Probe

Diffusion coefficients of energetic charged particles in turbulent magnetic fields are a fundamental aspect of diffusive transport theory but remain incompletely understood. In this work, we use quasi-linear theory to evaluate the spatial variation of the parallel diffusion coefficient κ ∥ from the measured magnetic turbulence power spectra in the inner heliosphere. We consider the magnetic field and plasma velocity measurements from Parker Solar Probe made during Orbits 5–13. The parallel diffusion coefficient is calculated as a function of radial distance from 0.062 to 0.8 au, and the particle energy from 100 keV to 1 GeV. We find that κ ∥ increases exponentially with both heliocentric distance and energy of particles. The fluctuations in κ ∥ are related to the episodes of large-scale magnetic structures in the solar wind. By fitting the results, we also provide an empirical formula of κ ∥ = (5.16 ± 1.22) × 1018 r 1.17±0.08 E 0.71±0.02 (cm2 s−1) in the inner heliosphere, which can be used as a reference in studying the transport and acceleration of solar energetic particles as well as the modulation of cosmic rays.

Mechanism insight of sorption of Er(III) and Nd(III) ions onto Aluminium barium tungstate synthesized via streamlined sol–gel technique: Time-transient study

Aluminium barium tungstate powder (ABT) was chemically synthesized via streamlined sol–gel technique and exploited as a sorbent material for sorption of erbium and neodymium ions from aqueous solutions under simulated conditions using batch technique. The pH influence, time and temperature factors have been studied. The sorption of neodymium ions was found to be marginally higher than that of erbium ions and the apparent sorption capacity has a progressive influence with temperature. Thermodynamic parameters such as Gibbs free energy change (ΔG◦), enthalpy change (ΔH◦) and entropy change (ΔS◦) were calculated. The negative ΔG◦ values declines with an increase in temperature value, demonstrating that the sorption reaction for both studied ions was spontaneous and more promising at greater temperature. The positive ΔH◦ values affirm that the nature of the sorption processes is endothermic. The comparison of different time transient models applied to the sorption data was assessed for the pseudo first-order (PFO), the pseudo second-order, (PSO) and homogeneous particle diffusion (HPD) models. The results revealed that both PSO and HPD models were found to best correlate the experimental sorption rate data and a monolayer model was adopted as the best suitable model to explore the sorption mechanism for both studied ions. The attained particle diffusion coefficients and rate constant values were acquired from the graphical illustration of the anticipated models. Activation energy change (Ea) and activation entropy change (ΔS±) were also calculated from the linearized Arrhenius model and indicated that the binding process between the sorbent and the studied ions occurred through chemisorption and the sorption of both ions onto synthetic sorbent took place through associative mechanism.