Numerical Simulations Of Particle Trajectories Research Articles

Numerical Simulation and Experimental Observation of Charged Particles Trajectories in Roll-Type Electrostatic Separators

Accurate prediction of the effects of the various factors that might influence the outcome of novel electrostatic separation process requires reliable physical and mathematical models for the numerical simulation of particle trajectories. The major objective of this article was to demonstrate that the use of a high-speed camera for recording particle trajectories could be instrumental in refining the understanding of the complex physical phenomena that occur in these electrostatic devices and in improving their operating conditions, based on valid numerical simulation results. The experiments were carried out with spherical conductive particles, using a roll-type corona-electrostatic separator. The particles trajectories were recorded using a high-speed camera at acquisition frame rate of 200 fps. The electrical field computation and the resolution of the differential equation of motion of the particles under the action of electrical and mechanical forces exerted on them enabled the prediction of the outcome of the separation process. The study was carried out for particles of different sizes, for different high voltages applied to the electrodes and for different electrode positions. The simulation results were in good agreement with the experimental data.

Numerical Simulation of Particle Trajectories in the Charge-injection Type of Electrostatic Oil Filter

Numerical Simulation of Particle Trajectories in the Charge-injection Type of Electrostatic Oil Filter

Understanding the dynamics of superparamagnetic particles under the influence of high field gradient arrays

The aim of this study was to characterize the behaviour of superparamagnetic particles in magnetic drug targeting (MDT) schemes. A 3-dimensional mathematical model was developed, based on the analytical derivation of the trajectory of a magnetized particle suspended inside a fluid channel carrying laminar flow and in the vicinity of an external source of magnetic force. Semi-analytical expressions to quantify the proportion of captured particles, and their relative accumulation (concentration) as a function of distance along the wall of the channel were also derived. These were expressed in terms of a non-dimensional ratio of the relevant physical and physiological parameters corresponding to a given MDT protocol.The ability of the analytical model to assess magnetic targeting schemes was tested against numerical simulations of particle trajectories. The semi-analytical expressions were found to provide good first-order approximations for the performance of MDT systems in which the magnetic force is relatively constant over a large spatial range.The numerical model was then used to test the suitability of a range of different designs of permanent magnet assemblies for MDT. The results indicated that magnetic arrays that emit a strong magnetic force that varies rapidly over a confined spatial range are the most suitable for concentrating magnetic particles in a localized region. By comparison, commonly used magnet geometries such as button magnets and linear Halbach arrays result in distributions of accumulated particles that are less efficient for delivery.The trajectories predicted by the numerical model were verified experimentally by acoustically focusing magnetic microbeads flowing in a glass capillary channel, and optically tracking their path past a high field gradient Halbach array.

Numerical Simulation of Particle Trajectories in the Charge-injection Type of Electrostatic Oil Filter

Numerical Simulation of Particle Trajectories in the Charge-injection Type of Electrostatic Oil Filter

Zeeman deceleration of metastable nitrogen atoms

In a proof-of-principle experiment, we show that the longitudinal velocity of a supersonic beam of nitrogen atoms in the metastable 2D state can be decreased from 460 to 410 m s−1 using a 12-stage Zeeman decelerator. The experimental results are in good agreement with three-dimensional numerical particle trajectory simulations. The generation of velocity-tunable supersonic beams of metastable nitrogen atoms opens new avenues for the study of chemical reactions at millikelvin temperatures.

Solutions to mitigate heat loads due to electrons on sensitive components of ITER HNB beamlines

The operation of neutral beam injectors for plasma heating and current drive in a fusion device provides challenges in the thermal management of beamline components. Sensitive components such as the cryogenic pumps at beamline periphery shall be protected from the heat flux due to stray electrons. These are emitted by the negative ion accelerator or generated along the beamline by interaction of fast electrons, ions or atoms with background gas and surfaces. In this article the case of the ITER Heating Neutral Beam (HNB) and its test facility MITICA is discussed, for which the beam parameters and the required pulse length of one hour is a major leap forward with respect to the present experience with neutral beam systems. The engineering solutions adopted for effective cryopump protection against the heat load from electrons are described. The use of three-dimensional numerical simulations of particle trajectories in the complex geometry of the beamline was needed for the quantitative estimations of the heat loads. The presented solutions were optimized to minimize the impact on gas pumping and on the functionality of other components.

Clustering and turbophoresis in a shear flow without walls

We investigate the spatial distribution of inertial particles suspended in the bulk of a turbulent inhomogeneous flow. By means of direct numerical simulations of particle trajectories transported by the turbulent Kolmogorov flow, we study large and small scale mechanisms inducing inhomogeneities in the distribution of heavy particles. We discuss turbophoresis both for large and weak inertia, providing heuristic arguments for the functional form of the particle density profile. In particular, we argue and numerically confirm that the turbophoretic effect is maximal for particles of intermediate inertia. Our results indicate that small-scale fractal clustering and turbophoresis peak in different ranges in the particles’ Stokes number and the separation of the two peaks increases with the flow’s Reynolds number.

Zeeman deceleration of electron-impact-excited metastable helium atoms

We present experimental results that demonstrate—for the first time—the Zeeman deceleration of helium atoms in the metastable 23S1 state. A more than 40% decrease of the kinetic energy of the beam is achieved for deceleration from 490 m s−1 to a final velocity of 370 m s−1. Metastable atom generation is achieved with an electron-impact-excitation source whose performance is enhanced through an additional discharge-type process which we characterize in detail. Metastable helium is efficiently generated even in a mixture of other noble gases that have much lower excitation energies. Comparison of deceleration data at different electron beam pulse durations confirms that a matching between the initial particle distribution and the phase-space acceptance of the decelerator is crucial for the production of a decelerated packet with a well-defined velocity distribution. The experimental findings are in good agreement with three-dimensional numerical particle trajectory simulations.

High-field-seeking Rydberg atoms orbiting a charged wire

Pulsed supersonic beams of helium atoms in the high-field-seeking $52p$ Rydberg state have been guided while following helical trajectories in the electrostatic field of a charged wire suspended along the axis of a grounded cylindrical metallic tube. The operation of this electrostatic wire guide for samples in high-field-seeking Rydberg-Stark states has been investigated with dc and pulsed electric potentials applied to the wire while the guided atoms were detected by pulsed electric-field ionization. The acceptance of the guide has been determined through numerical particle trajectory simulations.

Getting a grip on the transverse motion in a Zeeman decelerator

Zeeman deceleration is an experimental technique in which inhomogeneous, time-dependent magnetic fields generated inside an array of solenoid coils are used to manipulate the velocity of a supersonic beam. A 12-stage Zeeman decelerator has been built and characterized using hydrogen atoms as a test system. The instrument has several original features including the possibility to replace each deceleration coil individually. In this article, we give a detailed description of the experimental setup, and illustrate its performance. We demonstrate that the overall acceptance in a Zeeman decelerator can be significantly increased with only minor changes to the setup itself. This is achieved by applying a rather low, anti-parallel magnetic field in one of the solenoid coils that forms a temporally varying quadrupole field, and improves particle confinement in the transverse direction. The results are reproduced by three-dimensional numerical particle trajectory simulations thus allowing for a rigorous analysis of the experimental data. The findings suggest the use of a modified coil configuration to improve transverse focusing during the deceleration process.

A boundary integral formulation for particle trajectories in Stokes waves

Recently important theorems have been established presenting qualitative results for particle trajectories below a Stokes wave. A diversity of orbit patterns were described, including the case of a closed orbit when a Stokes wave propagates in the presence of an adverse current. In this work these results are revisited in a quantitative fashion through a boundary integral formulation which leads to very accurate numerical simulations of particle trajectories. The boundary integral formulation allows the accurate evaluation of the vector field of the (particle's) dynamical system, without resorting to a series expansion and a small parameter. Accurate trajectories are benchmarked against well known expansions for weakly nonlinear waves. Simulations are then performed beyond this regime. Closed orbits are found in the presence of an adverse current, as well as non-smooth trajectories that have not been reported. These occur for both adverse and favorable currents.

Approximate relationship between voltage and mobility for Brownian particles in cylindrical DMAs

This work presents the results of a theoretical investigation aimed at the determination of the relationship between applied voltage V and mobility Z for highly diffusive particles classified in a concentric cylindrical differential mobility analyzer (DMA). Based on knowledge of the mean of the first passage time probability distribution, the expression V/Vnd=1−2πkTLZ/peQsh has been obtained (Vnd=classification voltage for non-diffusing particles; k=Boltzmann's constant; T=absolute temperature; L=DMA length; p=number of elementary charges on the particle; e=electron's charge; Qsh=sheath air flow rate). Numerical simulations of particle trajectories have shown that the above expression is only approximate and that the last term, accounting for the effect of diffusion, has to be multiplied by a geometrical factor which is approximately given by the fitting expression 2.49ln−0.66(R2/R1), where R1 and R2 are the inner and outer electrode radii, respectively. The V/Vnd ratio departs from one only in extreme cases, namely, classification of particles with very high mobility in a quite long DMA operated at relatively low flow rates. For other situations the difference between V and Vnd is negligible.

Numerical and Experimental Study of Insulating Particles Behavior in Roll-Type Corona-Electrostatic Separators

The efficiency of the electrostatic separation process depends on the accurate control of particle trajectories. The aim of this article is to point out the role of the following factors that might affect the behavior of the insulating particles in roll-type corona-electrostatic separators: i) electrode system configuration, ii) applied high voltage, iii) roll speed, iv) particle size, and v) relative humidity of ambient air. The numerical simulation of particle trajectories, based on the balance equation of the electrical and mechanical forces that act on charged insulating particles, took into account both the charging and discharging phenomena. Pauthenier's equation for spheres in a uniform electric field served as the model for particle charging. The equation of particle discharging was established after the experimental study of the potential decay at the surface of a layer of millimeter size PVC granules in contact with an electrode. Samples of the same granular material were then processed in a laboratory roll-type corona-electrostatic separator. The analysis of the products collected after passage through the electric field of the separator validated the accuracy of the numerical simulations.

Symplectic integrators in the shearing sheet

The shearing sheet is a model dynamical system that is used to study the small-scale dynamics of astrophysical disks. Numerical simulations of particle trajectories in the shearing sheet usually employ the leapfrog integrator, but this integrator performs poorly because of velocity-dependent (Coriolis) forces. We describe two new integrators for this purpose; both are symplectic, time-reversible and second-order accurate, and can easily be generalized to higher orders. Moreover, both integrators are exact when there are no small-scale forces such as mutual gravitational forces between disk particles. In numerical experiments these integrators have errors that are often several orders of magnitude smaller than competing methods. The first of our new integrators (SEI) is well-suited for disks in which the typical inter-particle separation is large compared to the particles' Hill radii (e.g., planetary rings), and the second (SEKI) is designed for disks in which the particles are on bound orbits or the separation is smaller than the Hill radius (e.g., irregular satellites of the giant planets).

Phase stability in a multistage Zeeman decelerator

The phase stability of a multistage Zeeman decelerator is analyzed by numerical particle-trajectory simulations and experimental measurements. A one-dimensional model of the phase stability in multistage Stark deceleration [Bethlem et al., Phys. Rev. Lett. 84, 5744 (2000)] has been adapted to multistage Zeeman deceleration and compared with one- and three-dimensional particle-trajectory simulations, including the analysis of the effect of finite switch-on and -off times of the deceleration pulses. The comparison reveals that transverse effects in the decelerator lead to a considerable reduction of the phase-space acceptance at low values of the phase angle and an enhancement at high values. The optimal combinations of phase angles and currents with which a preset amount of kinetic energy can be removed from atoms and molecules in a pulsed supersonic beam using a multistage decelerator are determined by simulation. Quantitative analysis of the phase-space acceptance within a given volume reveals that for our decelerator (8 $\mathrm{\ensuremath{\mu}}\mathrm{s}$ switch-off time) optimal conditions are achieved for values of the phase angle between ${45}^{\ifmmode^\circ\else\textdegree\fi{}}$ and ${55}^{\ifmmode^\circ\else\textdegree\fi{}}$. This conclusion is examined and confirmed by experimental measurements using deuterium atoms. Alternative approaches to generate optimal deceleration pulse sequences, such as the implementation of evolutionary algorithms or the use of higher-order modes of the decelerator, are discussed.

Influence of substrate porosity and thickness on the collection efficiency of an impactor stage

Abstract This study investigates particle collection efficiency of porous foam within an impaction cup by experimental and numerical techniques to clarify why the cut-off aerodynamic diameter (Dpa 50 ) of porous substrates tends to decrease as thickness and porosity increase. Careful measurements confirm this tendency in the particle size ranging from 1 to 10 μm and with foams of varying porosity. The measurements serve as the basis for a numerical simulation of particle trajectories, which demonstrates that particles can penetrate into the foam to varying degrees, dependent also on the Reynolds number and their distance from the jet axis. The proposed numerical models are then used to investigate the influence of substrate thickness and porosity on particle collection efficiency of porous foam within an impaction cup. The simulations explain and quantify the ratio in Dpa 50 as a function of foam properties, compared to a solid impaction surface. They also show that the steepness of efficiency curves declines slightly with foam thickness and porosity, compared to a solid substrate and at the same Reynolds number.

Mixing via thermocapillary generation of flow patterns inside a microfluidic drop

The heating produced by a focused laser has been shown to provide a range of manipulation tools on droplets in microfluidic situations, through the generation of thermocapillary flows whose net result is to produce a force on the drop. In particular, droplets of water in oil that are produced in microchannels can be blocked in a special test section. Here, the manipulation of the flow within the droplet is explored through spatial and temporal modulation of the laser pattern used to block the drop. When a stationary pattern of two laser spots is used, the flow preserves the mirror symmetry inside the drop, as happens in the case of two alternating spots if the frequency of the switching is higher than the response rate of the fluid. Lower frequency switching produces a time periodic flow that breaks the mirror symmetry and which leads to efficient mixing inside the droplet. The mixing that is produced by this alternating flow is studied both experimentally and using numerical simulations of particle trajectories from measured velocity fields. This mixing can be optimized for certain parameter ranges, namely by varying the distance between the spots and the forcing frequency.

Aerosol deposition on an arbitrarily oriented single rectangular fiber in a uniform electric field

This paper deals with the numerical simulation of particle trajectories and deposition efficiency of a single rectangular-shaped fiber in an electric field. The air flow and electric field are perpendicular to the fiber axis, but the fiber can be rotated at an arbitrary angle. The potential air flow has been assumed, and it was analyzed using the boundary-element method. The same technique was used to determine the electric field distribution. Calculated deposition efficiencies are presented for different values of the Stokes number and the nondimensional electric number.

Mouvements des particules conductrices dans un séparateur à haute tension pour matériaux granulaires

Electric field computation by means of the finite element method was employed for the numerical simulation of particle trajectories in the electroseparators for granular materials. The experiments, carried out on a laboratory electroseparator, partially confirmed the computational hypothesis. At the same time, they pointed out the necessity of improving the mathematical model. In order to reveal the specific physical phenomena, the preliminary researches presented in this paper were done on several simplified electric field configurations. Particle movement equations were written for a uniform mono-ionised electri field. The “lift-off” field of spherical and cylindrical particles was experimentally evaluated for different conditions: harmonic field, corona discharge between point-plate electrodes, mono-ionised field between coaxial cylindrical electrodes. The theoretical analysis and the experimental data pointed out the multitude of factors which determine the movements of conductive particles in corona-electrostatic fields of the electroseparators for mixed granular materials.

Particle Dispersion in Turbulent Flow: The effect of particle size distribution

AbstractThe measured velocity fluctuation of particles in dispersed twophase flow systems is discussed and an interpretation of particle velocity statistics is given. Besides the turbulent velocity fluctuations resulting from the particle's response to the fluid turbulence, two additional apparent fluctuation components may be distinguished, caused by inertial effects of the particles and by a polydisperse particle phase.Especially for larger particles inertial effects may become important and therefore the particle motion in the flow field is strongly governed by the inlet conditions, namely the instantaneous particle velocity. Therefore, the measured axial particle velocity fluctuation at a given location may be considerably increased as particles from different starting locations with different initial velocities may cross the same measuring point. This dynamic particle behaviour is demonstrated by the numerical simulation of particle trajectories in a given flow field. The results show the importance of including appropriate inlet conditions for the numerical prediction of particulate two‐phase flows.Further, in experimental realizations of particulate two‐phase flows, the particles usually exhibit a certain size distribution. Owing to the different responses of the different sized particles to both the mean flow field and the turbulence characteristics of the flow, the measured particle velocity fluctuations are higher than in the comparable monodisperse case. Therefore, the particle size distribution was taken into account in the present numerical calculations in order to obtain results which are comparable to the corresponding experiments. In this numerical simulation the particle mean velocity and the rms value of the velocity fluctuation were obtained by averaging over the whole particle size distribution and then compared with the measured values. Calculations are presented for two different shaped particle size distributions with a different mean size and compared with calculations with a monosized particle material and experimental results.Further, the behaviour of the different sized particles in the particle size distribution is discussed by considering the changes in the particle size distribution and the particle velocity distribution throughout the flow field.