Aspherical Particles Research Articles

Numerical Modeling of Anisotropic Particle Diffusion through a Cylindrical Channel.

The transport of molecules and particles through single pores is the basis of biological processes, including DNA and protein sequencing. As individual objects pass through a pore, they cause a transient change in the current that can be correlated with the object size, surface charge, and even chemical properties. The majority of experiments and modeling have been performed with spherical objects, while much less is known about the transport characteristics of aspherical particles, which would act as a model system, for example, for proteins and bacteria. The transport kinetics of aspherical objects is an especially important, yet understudied, problem in nanopore analytics. Here, using the Wiener process, we present a simplified model of the diffusion of rod-shaped particles through a cylindrical pore, and apply it to understand the translation and rotation of the particles as they pass through the pore. Specifically, we analyze the influence of the particles' geometrical characteristics on the effective diffusion type, the first passage time distribution, and the particles' orientation in the pore. Our model shows that thicker particles pass through the channel slower than thinner ones, while their lengths do not affect the passage time. We also demonstrate that both spherical and rod-shaped particles undergo normal diffusion, and the first passage time distribution follows an exponential asymptotics. The model provides guidance on how the shape of the particle can be modified to achieve an optimal passage time.

High-Resolution Two-Phase Velocimetry Of Aspherical Particles Using Wavelet-Based Optical Flow Velocimetry (WOFV) Benchmarked With Fully Resolved Direct Numerical Simulations

Several techniques exist to measure the carrier and dispersed phases in multi-phase flows. Particle image velocimetry (PIV) analyzes the carrier phase by cross-correlating particle images, but its resolution is limited by the size of the interrogation window, making it difficult to resolve fine-scale turbulent structures. Particle tracking algorithms capture translational motion of dispersed particles well, but struggle with rotational motion, especially for irregular and aspherical particles. Currently, there is no method that universally measures both the carrier phase velocity field and the translational and rotational motions of dispersed particles. This study evaluates wavelet-based optical flow velocimetry (wOFV) for motion estimation in multi-phase flows, focusing on dispersed ellipsoidal particles and their surrounding turbulent carrier flow using synthetic image data. The research proceeds in two phases: first, the rigid motion of ellipses, including translational and rotational components, is analyzed using wOFV-generated dense motion fields. The results highlight the critical role of the regularization weighting parameter λ. Higher λ values improve translational motion estimation, while an optimal λ avoids under-regularization and non-physical structures in rotational motion. wOFV maintains accuracy in combined motion scenarios with optimal λ values. In the second phase, wOFV captures the turbulent carrier flow around an aspherical particle, benchmarked against DNS data and compared to PIV. wOFV outperforms PIV in resolving finer structures near the particle surface and in accurately representing the wake region. Error analyses confirm wOFV’s superior performance, with optimal results within a specific λ range. In conclusion, wOFV is a highly effective tool for the analysis of multi-phase flow dynamics, providing greater resolution and accuracy than PIV, especially in complex scenarios involving aspherical particles.

Flow and clogging behavior of a mixture of particles in a silo

We investigated the clogging behavior observed during the flow of aspherical particles from a silo in the presence of spherical particles of different sizes and proportions using flow visualization experiments and discrete element method simulations. The size of the avalanche, essentially the tendency of clogging, exhibits non-monotonic dependence on the spherical particle volume fraction. For small enough content of spherical particles, the clogging tendency intensifies, whereas it reduces rapidly for high enough spherical particle fractions, with a minimum in between. The non-monotonic behavior is observed to persist over for different spherical particle sizes. The overall behavior is shown to arise due to competing effects between the localized total particle fraction influencing avalanche strength and mean size of the particles exiting the silo, influencing the probability of arch formation.

Volume-interacting level set discrete element method: The porosity and angle of repose of aspherical, angular, and concave particles

Despite the many advances in the numerical modelling of granular materials using the discrete element method (DEM), the description of realistic particle shapes, especially concave shapes, remains challenging. Little is known about the effect of concavity on properties such as the porosity and angle of repose. In this work, volume-interacting level set DEM (VLS-DEM) was used to study the effect of asphericity, angularity, and concavity on the porosity and angle of repose. By taking the Platonic solids and applying a hyperbolisation procedure, a continuous spectrum of shapes, ranging from rounded to highly angular, was generated and investigated. Results show that, when combined, angularity and concavity have a disproportionately large effect on the porosity and angle of repose. They also demonstrate the importance of particle shape and that even convex polyhedra may be insufficient to accurately capture the effect of shape on fundamental powder properties.

Anomalous tumbling of colloidal ellipsoids in Poiseuille flows.

Shear flows cause aspherical colloidal particles to tumble so that their orientations trace out complex trajectories known as Jeffery orbits. The Jeffery orbit of a prolate ellipsoid is predicted to align the particle's principal axis preferentially in the plane transverse to the axis of shear. Holographic microscopy measurements reveal instead that colloidal ellipsoids' trajectories in Poiseuille flows strongly favor an orientation inclined by roughly π/8 relative to this plane. This anomalous observation is consistent with at least two previous reports of colloidal rods and dimers of colloidal spheres in Poiseuille flow and therefore appears to be a generic, yet unexplained feature of colloidal transport at low Reynolds numbers.

DNA origami traps for large viruses

Virus-enveloping macromolecular shells or tilings can prevent viruses from entering cells. Here, we describe the design and assembly of a cone-shaped DNA origami higher-order assembly that can engulf and tile the surface of pleomorphic virus samples larger than 100 nm. We determine the structures of subunits and of complete cone assemblies using cryoelectron microscopy (cryo-EM) and establish stabilization treatments to enable usage in in vivo conditions. We use the cones exemplarily to engulf influenza A virus particles and severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), chikungunya, and Zika virus-like particles. Depending on the relative dimensions of cone to virus particles, multiple virus particles may be trapped per single cone, and multiple cones can also tile and adapt to the surface of aspherical virus particles. The cone assemblies form with high yields, require little purification, and are amenable for mass production, which is a key requirement for future real-world uses including as a potential antiviral agent.

PEPT validated CFD-DEM model of aspherical particle motion in a spouted bed

Computational Fluid Dynamics coupled with Discrete Element Method (CFD-DEM) has been used to model the dynamics of aspherical particles in a spouted bed. CFD-DEM results were rigorously validated against high-resolution, three-dimensional experimental data acquired using Positron Emission Particle Tracking (PEPT). A workflow facilitating the direct, detailed, quantitative comparison of experimental and numerical data, and thus validation of CFD-DEM simulations, was developed. Sensitivity analysis considering a wide range of particle properties and drag correlations was carried out. It was observed that the Young’s modulus, Poisson’s ratio, and restitution coefficient do not have a significant effect on the system’s dynamics across the range of parameters explored, and that Gidaspow’s correlation using equivalent intrinsic particle density is an appropriate choice for modelling drag forces. Analysis shows PEPT-validated CFD-DEM models quantitatively capture key features including particle circulation time, particle velocity and occupancy distributions, and the proportion of residence time in the bulk-bed and freeboard regions, all of which are crucial to understanding mass and heat transfer within the system. Our results also demonstrated that models using simple, spherical particles were – with suitably modified friction and drag models – capable of quantitatively reproducing the dynamics of a range of highly aspherical materials.

Experimental and numerical investigation into the effect of surface roughness on particle rebound

Erosion damage and particle deposition are crucial wear phenomena in gas turbine engines. As a result, compressor efficiency decreases, stability margin reduces, and maintenance cost increases. Hence, predicting these phenomena in an accurate manner is of paramount importance for a cost-efficient, safe, and sustainable operation. Erosion and particle deposition in the annulus are affected by particle transportation in the fluid and particle-wall interaction. The latter involves the particle impact, the potential damage of the surface and/or the particle, and the particle rebound. Particle rebounds are statistical in nature due to the target surface roughness, the variability in particle sizes, and superimposed effects caused by particle shapes as well as particle rotation and particle break-up during contact. Multiple studies investigated the statistics of particle rebound, providing empirical-based models for median and spread. However, modeling the particle-wall interaction and its data spread on a transparent physical basis allows separating the effect of target roughness from superimposed effects. The presented article pursues this objective by assessing the statistical spread of particle rebound data through multiple techniques and utilizing their interdependencies. It combines experimental, numerical, and analytical considerations. For the first time, coherent boundary conditions for the experimental, numerical and analytical setup allow the distinction of the effect of roughness from the integral effect of the superimposed phenomena. A sandblast test rig equipped with laser measurement equipment was used to measure particle rebound from flat titanium and stainless steel plates at different angles. The numerical setup is developed under OpenFOAM 6 using a RANS solver for transient simulations with compressible media in combination with one-way coupled particle flows. The numerical model includes the rebound spread model proposed by Altmeppen et al. combined with the quasi-analytical rebound model proposed by Bons et al. The statistical spread of particle rebound is investigated for roughness levels that are similar to the ones of deteriorated high-pressure compressor blades as discussed by Gilge et al. The measured surface roughness of the experimentally investigated targets is used as input parameters to the numerical framework. The rebound statistics obtained in the numerical simulation are compared to the rebound data measured in the experiment. Based on this study, conclusions are drawn about which part of the rebound spread is attributable to surface roughness and which is caused by superimposed effects. It was found that the effect of surface roughness as characterized by Altmeppen et al. contributes in the order of 46 % to the rebound spread for small impact angles. However, the share in spread due to roughness gradually decreases with increasing global impact angles to a level of 13 % for angles close to 90°. The remaining percentage of rebound spread is attributed to superimposing phenomena. In addition to the rolling and sliding of aspherical particles, further phenomena such as plastic deformation and erosion of the roughness peaks during contact and the associated dissipation of energy gain in importance for steeper impact angles. Therefore, the effect of surface roughness should not be neglected in numerical simulations of particle-laden flows. Modeling the superimposed phenomena which are observed to be dominating at high impact angles opens up a further field of research.

Multi-angle holographic characterization of individual fractal aggregates.

Holographic particle characterization uses quantitative analysis of holographic microscopy data to precisely and rapidly measure the diameter and refractive index of individual colloidal spheres in their native media. When this technique is applied to inhomogeneous or aspherical particles, the measured diameter and refractive index represent properties of an effective sphere enclosing each particle. Effective-sphere analysis has been applied successfully to populations of fractal aggregates, yielding an overall fractal dimension for the population as a whole. Here, we demonstrate that holographic characterization also can measure the fractal dimensions of an individual fractal cluster by probing how its effective diameter and refractive index change as it undergoes rotational diffusion. This procedure probes the structure of a cluster from multiple angles and thus constitutes a form of tomography. Here we demonstrate and validate this effective-sphere interpretation of aspherical particles' holograms through experimental studies on aggregates of silica nanoparticles grown under a range of conditions.

Sensitivity of modeled snow grain size retrievals to solar geometry, snow particle asphericity, and snowpack impurities

Abstract. Snow grain size is an important metric to determine snow age and metamorphism, but it is difficult to measure. The effective grain size can be derived from spaceborne and airborne radiance measurements due to strong attenuation of near-infrared energy by ice. Consequently, a snow grain size inversion technique that uses hyperspectral radiances and exploits variations in the 1.03 µm ice absorption feature was previously developed for use with airborne imaging spectroscopy. Previous studies have since demonstrated the effectiveness of the technique, though there has yet to be a quantitative assessment of the retrieval sensitivity to snowpack impurities, ice particle shape, or solar geometry. In this study, we use the Snow, Ice, and Aerosol Radiative (SNICAR) model and a Monte Carlo photon tracking model to examine the sensitivity of snow grain size retrievals to changes in dust and black carbon content, anisotropic reflectance, changes in solar illumination angle (θ0), and scattering asymmetry parameter (g) associated with different particle shapes. Our results show that changes in these variables can produce large grain size errors, especially when the effective grain size exceeds 500 µm. Dust content of 1000 ppm induces errors exceeding 800 µm, with the highest biases associated with small particles. Aspherical ice particles and perturbed solar zenith angles produce maximum biases of ∼540 µm and ∼400 µm, respectively, when spherical snow grains and θ0=60∘ are assumed in the generation of the retrieval calibration curve. Retrievals become highly sensitive to viewing angle when reflectance is anisotropic, with biases exceeding 1000 µm in extreme cases. Overall, we show that a more detailed understanding of snowpack state and solar geometry improves the precision when determining snow grain size through hyperspectral remote sensing.

Characterization of tandem aerosol classifiers for selecting particles: implication for eliminating the multiple charging effect

Abstract. Accurate particle classification plays a vital role in aerosol studies. Differential mobility analyzers (DMAs), centrifugal particle mass analyzers (CPMAs) and aerodynamic aerosol classifiers (AACs) are commonly used to select particles with a specific mobility diameter, aerodynamic diameter or mass, respectively. However, multiple charging effects cannot be entirely avoided when using either individual techniques or tandem systems such as DMA–CPMA, especially when selecting soot particles with fractal structures. In this study, we calculate the transfer functions of the DMA–CPMA and DMA–AAC in static configurations for flame-generated soot particles. We propose an equation that constrains the resolutions of the DMA and CPMA to eliminate the multiple charging effect when selecting particles with a certain mass–mobility relationship using the DMA–CPMA system. The equation for the DMA–AAC system is also derived. For DMA–CPMA in a static configuration, our results show that the ability to remove multiply charged particles mainly depends on the particle morphology and resolution settings of the DMA and CPMA. Using measurements from soot experiments and literature data, a general trend in the appearance of the multiple charging effect with decreasing size when selecting aspherical particles is observed. As for DMA–AAC in a static configuration, the ability to eliminate particles with multiple charges is mainly related to the resolutions of the classifiers. In most cases, the DMA–AAC in a static configuration can eliminate the multiple charging effect regardless of the particle morphology, but multiply charged particles will be selected when decreasing the resolution of the DMA or AAC. We propose that the potential influence of the multiple charging effect should be considered when using the DMA–CPMA or DMA–AAC systems in estimating size- and mass-resolved optical properties in field and lab experiments.

Asphericity Can Cause Nonuniform Lithium Intercalation in Battery Active Particles

Uniform intercalation is desired to enable next-generation Li-ion batteries. While we expect nonuniformity in materials undergoing a phase change, single-phase intercalation materials such as nickel manganese cobalt oxide are believed to lithiate uniformly at the particle/electrolyte interface. However, recent imaging reveals nonuniform lithiation. Motivated by this discrepancy, we examine if aspherical particle shape can cause such nonuniformity since the conventional belief is based on spherical particle theory. We obtain real particle geometries using rapid lab-based X-ray computed tomography and subsequently perform physics-based calculations accounting for electrochemical reactions at the particle/electrolyte interface and lithium transport inside the particle bulk. The aspherical geometry breaks the symmetry and causes nonuniform reaction distribution. Such nonuniformity is exacerbated as the particle becomes more aspherical. The proposed mechanism represents a fundamental limit on achievable lithiation uniformity in aspherical particles in the absence of other mechanisms causing inhomogeneity, such as grain structure, nonuniform carbon-binder coating, etc.

Theoretical Foundation of the Relationship between Three Definitions of Effective Density and Particle Size

Effective density (ρe) is universally used in atmospheric science as an alternative measure of the density (ρ) of aerosol particles, and its definitions can be expressed in terms of the particle mass (mp), ρ, mobility diameter (Dm), vacuum aerodynamic diameter (Dva), and dynamic shape factor (χ), as ρeI = 6mp/(π∙Dm3), ρeII = ρ/χ, and ρeIII = Dva/Dm. However, the theoretical foundation of these three definitions of ρe is still poorly understood before their application. Here, we explore the relationship between ρe and aerosol size through theoretical calculation. This study finds, for the first time, that ρeI and ρeIII inherently decrease with increasing size for aspherical particles with a fixed ρ and χ. We further elucidate that these inherent decreasing tendencies are governed by χ, and the ratio of the Cunningham Slip Correction Factor of the volume-equivalent diameter to that of the mobility diameter (Cc(Dve)/Cc(Dm)), but not by ρ. Taking the variable χ into consideration, the relationships of ρeI and ρeIII to particle size become more complicated, which suggests that the values of ρeI and ρeIII have little indication of the size-resolved physicochemical properties of particles. On the contrary, ρeII is independent on size for fixed χ and ρ, which indicates that the change in ρeII with size can better indicate the change in morphology and the transformation of the chemical compositions of particles. Our new insights into the essence of three ρes provide an accurate and crucial theoretical foundation for their application.

Efficient high-fidelity TRISO statistical failure analysis using Bison: Applications to AGR-2 irradiation testing

The ability of tri-structural isotropic (TRISO) fuel to contain fission products is largely dictated by the quality of the manufacturing process, since most of the fission product release is expected to occur due to coating layer failure in a small number of particles containing defects. The Bison fuel performance code has capabilities to predict failure in individual particles, accounting for the presence of defects, and to apply statistical analysis methods to compute the probability of failure in a set of fuel particles. Bison has recently undergone significant development both to improve its physical representations of fuel particle behavior and to improve the efficiency of its statistical failure calculations. Physical model improvements include new capabilities to account for the pressure generated by fission gases on inner pyrolytic carbon (IPyC) crack surfaces and to use local material coordinate orientation to accurately incorporate the anisotropy in the material properties in aspherical particles. To improve statistical modeling efficency, a direct integration approach which involves directly integrating the failure probability function associated with statistically varying parameters has been developed. The direct integration approach is much more efficient than the Monte Carlo (MC) schemes commenly employed, and allows Bison to directly run high-dimensional fuel performance models, which improves the accuracy of failure probability calculations. A set of benchmark problems is considered here to compare the MC and direct integration approaches, and a statistical failure analysis of compacts in the Advanced Gas Reactor (AGR)-2 experiments is performed using the direct integration approach.

Industrial scale mesofluidic particle separation

Here we explore the potential of a mesofluidic separator that fits within industrial piping to remove large aspherical particles out of an abrasive slurry at fast flowrates. Mesofluidic separators have demonstrated separation of spherical particles at flowrates of ∼1 gpm (6.10−5 m3/s). Yet, the performance of these separators at flowrates achievable within industrial piping has not been explored. Here we evaluate the exiting flowrate split, large particle mass fraction, and pressure drop observed in a mesofluidic separator operating in a three-inch (0.076 m) tube carrying an abrasive and modestly non-spherical slurry at flows ranging from 35 to 100 gpm (0.0022–0.0063 m3/s). We find the flow through the separator and pressure drop both increase with flowrate, though the pressure drop remains modest. Only two feet (0.6 m) of inserts removed 97.6 ± 2.1% of large particles for conditions tested. Separation was demonstrated in both vertical and horizontal orientations with the horizontal orientation benefiting marginally from gravitational settling.

Mutiparametric Characterization of Atmospheric Particulate in a Heavy-Polluted Area of South Italy

To obtain a real-time image of atmospheric particulate matter (PM) in highly polluted areas and to understand how the anthropogenic component linked to urban activities (industrial activities, domestic heating, road traffic, waste disposal) can locally affect near-surface measurement of PM, several measurement campaigns were achieved in the Campania region (Southern Italy) using both Lidar and in-situ instruments. A comparison between the obtained results highlights a good correlation between the data and the potential of remote sensing instruments for air quality monitoring. Data analysis was performed in terms of particle backscattering coefficient profile at 355 nm, PM mass concentration, and size distribution. Wind profiles, which covered a range of altitudes from 40 m to 290 m, were also used to study sources and physical processes involved. Measurement carried out in a rural area with a landfill site highlighted the presence of a homogeneous particulate layer throughout the sounded area due to winds driving aerosol from the landfill to the surrounding areas. The size distribution in mass concentration, highlighted a modal diameter moving towards 0.9 and 2 μm with a larger mass concentration of particles in the morning, before noon and in the afternoon when a large number of trucks delivered solid wastes. Moreover, large concentrations of particulate matter were measured in a small urban town with few industrial activities which peak (211 ± 33 μg·m-3) was measured in the direction of the most urbanized area, probably due to the lighting of the domestic heating systems. Bimodal size distribution in number concentration was measured, indicative of two types of atmospheric particles sources: gas and liquid combustion (particles with sizes below 80 nm), including vehicular traffic and domestic gas-heating, and biomass combustion (particles with sizes of the order of 200 - 500 nm). Finally, data collected in a highly populated and industrialized area highlights the presence of particles having a high level of spherical geometry (aerosol depolarization below 5%) pointing towards the industrial area. Conversely, the measurements performed pointing toward other directions highlighted a diffused source of aspherical particles (depolarization values of about 3%) spreading throughout all city territory. The work showed as the co-location of remote sensing and near surface instruments is a promising approach to studying aerosol properties in the atmospheric layers and has more accurate information on atmospheric dynamics. Moreover, the correlation between the obtained results highlighted the potential of remote sensing instruments for air quality monitoring.

Adhesion study between micron-scale graphite particles and rough walls using the finite element method

The characteristics of how graphite particles adhere to the walls of high-temperature gas-cooled reactors are very important for analyzing reactor source terms. In the present study, atomic force microscopy (AFM) is used to measure the particle adhesion force and the wall morphology, then Lennard-Jones potential theory and the finite element method (FEM) are coupled to calculate the adhesion force between different particles and rough walls. The obvious deviations between the AFM measurements and the theoretical models are due to the contact hypothesis of a sphere with a smooth flat plane in the latter. The FEM results reveal the formation of maximum adhesion at the pull-off point of the particle and the corresponding stress distribution. For aspherical particles, the local curvature of the particle contact interface is the main factor affecting the adhesion force. In addition, for rough walls, different contact regimes correspond to different adhesion trends. When discrete wall roughness with hemispheres and truncated cones is used, the FEM predictions are closer to the AFM measurements, indicating that roughness dominates the adhesion weakening.

PHIPS-HALO: the airborne Particle Habit Imaging and Polar Scattering probe – Part 3: Single-particle phase discrimination and particle size distribution based on the angular-scattering function

Abstract. A major challenge for in situ observations in mixed-phase clouds remains the phase discrimination and sizing of cloud hydrometeors. In this work, we present a new method for determining the phase of individual cloud hydrometeors based on their angular-light-scattering behavior employed by the PHIPS (Particle Habit Imaging and Polar Scattering) airborne cloud probe. The phase discrimination algorithm is based on the difference of distinct features in the angular-scattering function of spherical and aspherical particles. The algorithm is calibrated and evaluated using a large data set gathered during two in situ aircraft campaigns in the Arctic and Southern Ocean. Comparison of the algorithm with manually classified particles showed that we can confidently discriminate between spherical and aspherical particles with a 98 % accuracy. Furthermore, we present a method for deriving particle size distributions based on single-particle angular-scattering data for particles in a size range from 100 µm ≤ D ≤ 700 µm and 20 µm ≤ D ≤ 700 µm for droplets and ice particles, respectively. The functionality of these methods is demonstrated in three representative case studies.

Collisional dissipation rate for binary mixtures of aspherical particles

The homogeneous cooling process of binary mixtures of large aspherical particles and small spheres is modeled using DEM. The dissipation rate increases with the increasing total solid volume fraction of the mixture. For a specified total solid volume fraction of the mixture, the dissipation rate increases with the increasing fraction ratio of small spheres in the mixture. Energy equipartition analysis shows that the translational and rotational components of the granular temperature for the large aspherical particles are generally equivalent. Energy equipartition is also present between the translational granular temperature for the large and small particles. Both particle aspect ratio and shape irregularity affect the collisional dissipation rate. The collisional dissipation rate increases with the aspect ratio (AR) for the same particle shape. For the same AR, the collisional dissipation rate of more-irregular oval-like particles are larger than less-irregular rod-like particles. The collisional dissipation rate decreases with the increasing particle sphericity.

Holographic characterization and tracking of colloidal dimers in the effective-sphere approximation.

An in-line hologram of a colloidal sphere can be analyzed with the Lorenz-Mie theory of light scattering to measure the sphere's three-dimensional position with nanometer-scale precision while also measuring its diameter and refractive index with part-per-thousand precision. Applying the same technique to aspherical or inhomogeneous particles yields measurements of the position, diameter and refractive index of an effective sphere that represents an average over the particle's geometry and composition. This effective-sphere interpretation has been applied successfully to porous, dimpled and coated spheres, as well as to fractal clusters of nanoparticles, all of whose inhomogeneities appear on length scales smaller than the wavelength of light. Here, we combine numerical and experimental studies to investigate effective-sphere characterization of symmetric dimers of micrometer-scale spheres, a class of aspherical objects that appear commonly in real-world dispersions. Our studies demonstrate that the effective-sphere interpretation usefully distinguishes small colloidal clusters in holographic characterization studies of monodisperse colloidal spheres. The effective-sphere estimate for a dimer's axial position closely follows the ground truth for its center of mass. Trends in the effective-sphere diameter and refractive index, furthermore, can be used to measure a dimer's three-dimensional orientation. When applied to colloidal dimers transported in a Poiseuille flow, the estimated orientation distribution is consistent with expectations for Brownian particles undergoing Jeffery orbits.