Motion Trajectories Of Particles Research Articles

Equivalent continuous and discrete realizations of Lévy flights: A model of one-dimensional motion of an inertial particle

The paper is devoted to the relationship between the continuous Markovian description of Lévy flights developed previously (see, e.g., I.A. Lubashevsky, Truncated Lévy flights and generalized Cauchy processes, Eur. Phys. J. B 82 (2011) 189–195 and references therein) and their equivalent representation in terms of discrete steps of a wandering particle, a certain generalization of continuous time random walks. To simplify understanding the key points of the technique to be created, our consideration is confined to the one-dimensional model for continuous random motion of a particle with inertia. Its dynamics governed by stochastic self-acceleration is described as motion on the phase plane {x,v} comprising the position x and velocity v=dx/dt of the given particle. A notion of random walks inside a certain neighborhood L of the line v=0 (the x-axis) and outside it is developed. It enables us to represent a continuous trajectory of particle motion on the plane {x,v} as a collection of the corresponding discrete steps. Each of these steps matches one complete fragment of the velocity fluctuations originating and terminating at the “boundary” of L. As demonstrated, the characteristic length of particle spatial displacement is mainly determined by velocity fluctuations with large amplitude, which endows the derived random walks along the x-axis with the characteristic properties of Lévy flights. Using the developed classification of random trajectories a certain parameter-free core stochastic process is constructed. Its peculiarity is that all the characteristics of Lévy flights similar to the exponent of the Lévy scaling law are no more than the parameters of the corresponding transformation from the particle velocity v to the related variable of the core process. In this way the previously found validity of the continuous Markovian model for all the regimes of Lévy flights is explained. Based on the obtained results an efficient “single-peak” approximation is constructed. In particular, it enables us to calculate the basic characteristics of Lévy flights using the probabilistic properties of extreme velocity fluctuations and the shape of the most probable trajectory of particle motion within such extreme fluctuations.

High speed imaging of particle flow fields in CFB risers

Particle flows of high particle concentration are important in many fields, including chemical processing, pharmaceutical processing, energy conversion and powder transport. Circulating fluidized beds (CFB) are widely employed in industry because they enhance reaction rates and heat transfer through rapid mixing of particles at high particle concentrations and high particle flow rates. However, despite decades of research and industrial application, the real time behavior of particle flow fields in CFB's is still not well understood. One of the reasons is that experimental data is difficult to acquire in such harsh, opaque environments. In this study, a new high speed particle imaging velocimetry (high speed PIV) technology, developed by the USDOE National Energy Technology Laboratory (NETL), is applied to observe and measure the real time behavior of individual particle motion inside the risers of CFB's. High speed PIV data acquired in three pilot scale CFB units at two laboratories: two CFB's with 0.305 m diameter risers and one CFB with a 0.2 m diameter riser. The high speed PIV system records high speed videos of particle motion with excellent spatial and temporal clarity. The high speed videos are analyzed to measure the concentration and the two-dimensional motion (velocity and trajectory) of individual particles. Data sample rates for velocity vectors are in the range of 0.1 to 3 million vectors per second thereby providing full resolution of the temporal domain of particle velocity. To see and measure particle motion inside the CFB risers at high particle concentrations, a custom borescope was inserted into the risers. The CFB risers were operated over a wide range of industrially relevant conditions: superficial gas velocities from 6.5 to 18.3 m/s with solid fluxes from 20 to 400 kg/m2/s. The particles used in the CFBs included fluid cracking catalyst (FCC) with a mean diameter of 70 μm, high density polyethylene (HDPE) with a mean diameter of 750 μm, and glass beads with mean diameters of 170 and 650 μm. High speed videos and high speed PIV data enabled careful study of the real time behavior of gas-particle flow fields in CFB risers. In all of the CFBs of this study, one or more “jets” of high speed gas were observed at any time in the CFB risers. The jets move around the riser and appear to wander from one location against the riser wall to another. The jets have width range of 1/10 to 1/2 of the riser diameter. When a jet moves away from an area, the void is immediately filled with large clusters of particles. The clusters have sizes up to several riser diameters and contain significant percentages of the total particle flow. Clusters reduce mixing and interaction of particles with the transport gas, and therefore may inhibit reaction rates. Shearing of the clusters by high speed jets gives rise to cluster shapes that are either undulating or in the form of long, thin vertical strands which are often called streamers. The well known core-annulus concentration profile does not exist in real time, but rather is a long time averaged phenomenon. The data and insight from this work should be valuable for design and operation of risers, and for development of computational fluid dynamic (CFD) models of riser flow fields.

Magnetophoretic trajectory tracking magnetometry: A new technique for assessing magnetic properties of submagnetic microparticles and cells

We develop a new approach for assessing magnetic properties of submagnetic microparticles and cells, magnetophoretic trajectory tracking magnetometry (MTTM), that employs recording of long 2D trajectories of particle motion in a slot fluid channel caused by the action of crossed gravitational and magnetic forces. The studies are focused on the development of theoretical backgrounds of the method and evaluation of its uncertainty caused by the mutual hydrodynamic entrainment of moving particles. Computerized equipment implementing MTTM technique is described and its performance is illustrated. According to our studies, the new technique can serve a reliable experimental method with analytical qualities.

Study on the Wave Deformation of a Traveling Wave Piezoelectric Stator Using Composite Transducer

In a previous study, the authors have presented and developed a cylindrical traveling wave piezoelectric motor using a composite transducer. This study focuses the research on the wave deformation problems in the proposed stator. Firstly, the standing wave excited by the longitudinal vibration of the transducer is analyzed, and the vibration amplitudes of particles on the driving teeth are extracted to present the objective wave shape. Then, the wave deformation of the standing wave excited by the bending vibration of the transducer is analyzed. Finally, the longitudinal and bending PZT are excited together to gain a flexural traveling wave in the stator, and the vibration amplitude distributions in radial and circumferential directions are gained. Study result indicates that there are obvious deformations on the two standing waves, which cause the motion trajectories of the surface particles are inconsistent.

Theoretical study of photoelectron transfer process in the nano supramolecular [Vitamins B].Cn complexes

The flocculation processes for differential settling of cohesive sediment were simulated via the Lattice Boltzmann method (LBM) in which the hydrodynamics and attractive van der Waals forces were considered. The simulations were performed with different initial sediment concentrations, and hydrodynamic properties of flocs formed by differential settling, such as size spectra, settling velocities, flow fields around flocs and particle motion trajectories, are discussed in detail. Results indicate that flocs containing the same primary particles formed by different sediment concentrations have similar settling velocities, which means that sediment concentrations exert few effects on flocs settling velocities themselves. Otherwise, sediment concentrations influence the bulk mean settling velocity of suspended sediment. The higher the sediment concentration, the larger the bulk mean settling velocity, which is attributed to the higher-concentration particles colliding easily and quickly forming larger flocs. Statistical analysis shows that numerical results clearly reproduce collision properties because of the differential settling at the mesoscale. These results suggest that LBM may be a promising approach to study the flocculation mechanisms of cohesive sediments.

Motion and collisions of two small spherical particles in a shear flow

The relative motion of small particles in a shear flow is considered. On the basis of the expressions for the velocity of relative motion, the motion trajectories of particles were calculated using the published data for the coefficients that enter into these equations. The critical trajectories determining the collision cross sections are obtained. The coagulation rate in the shear flow is estimated using the method of matching moments.

Measurement of Lamb wave polarization using a one-dimensional scanning laser vibrometer (L)

A single head scanning laser Doppler vibrometer is used for the estimation of the polarization of the first symmetric (S(0)) and antisymmetric (A(0)) Lamb wave modes. The measurements at two known incidence angles are performed in order to resolve the two components of motion. Filtering in the frequency/wavenumber domain of the response recorded along a scan line separates the contributions from each mode and allows the evaluation of the corresponding elliptical trajectories of particle motion. Comparison between measured and analytically estimated trajectories validates the measurement technique and suggests its application for the development of material characterization and diagnostics tools.

Lattice Boltzmann simulation of the flocculation process of cohesive sediment due to differential settling

The flocculation processes for differential settling of cohesive sediment were simulated via the Lattice Boltzmann method (LBM) in which the hydrodynamics and attractive van der Waals forces were considered. The simulations were performed with different initial sediment concentrations, and hydrodynamic properties of flocs formed by differential settling, such as size spectra, settling velocities, flow fields around flocs and particle motion trajectories, are discussed in detail. Results indicate that flocs containing the same primary particles formed by different sediment concentrations have similar settling velocities, which means that sediment concentrations exert few effects on flocs settling velocities themselves. Otherwise, sediment concentrations influence the bulk mean settling velocity of suspended sediment. The higher the sediment concentration, the larger the bulk mean settling velocity, which is attributed to the higher-concentration particles colliding easily and quickly forming larger flocs. Statistical analysis shows that numerical results clearly reproduce collision properties because of the differential settling at the mesoscale. These results suggest that LBM may be a promising approach to study the flocculation mechanisms of cohesive sediments.

The Numerical Simulation of the Single Abrasive Motion Law in the Environment of Structural Surface

As far as the controllability of turbulence flow field surface effect of the soft abrasive flow was concerned, to begin with the analysis of the motion of the particle in the flow field, the paper studied the motion law of particle in the flow field, especially in the boundary layer. Based on the fluid-solid two-phase flow coupling style, it established the single particle dynamics model. Then it established the realizable k-ε model, in the light of the numerical simulation of turbulent flow. With the adoption of the computational method of SIMPLEC, it asked for the velocity and the pressure of fluid in the U-shaped flow passage, the velocity and the motion law of particles with different granularities and velocity, in the boundary layer. Experimentation results tell us that the original velocity plays a leading role in the motion trajectory of particles. The diameter influenced the particles motion trajectory in some degree.

Nanoparticle motion trajectories and deposition in an inlet channel of wall-flow diesel particulate filter

A two-dimensional gas–particle two-phase flow model in an inlet channel of diesel particulate filter (DPF) has been developed. The interaction between the gas and the particle is treated as one-way coupling due to the extremely dilute particle concentration. The drag force, the Brownian excitation, and the partial slip are included in the particle motion equation. The particle motion trajectories for various particle source locations and various particle sizes are presented. The dependences of the velocity field of the channel on wall permeability and upstream velocity are evaluated. The effects of particle size, upstream velocity, wall permeability, Brownian motion, and partial slip on the particle deposition are investigated. The three dominant mechanisms, which are drag force, Brownian motion, and particle inertia, are analyzed deeply. These results demonstrate that the drag force always plays the most primary role in determining the particle motion and deposition. On the other hand, the effects of Brownian motion and particle inertia vary with Pe number and Re p * number, respectively. As Pe number and Re p * number increase, the effect of particle inertia enhances, while the effect of Brownian motion lowers. The predicted velocity field is compared with the results obtained from the classical one-dimensional model, and the computational pressure loss of DPF is compared with the experimental values. The reasonable agreements of the two cases are both observed.

Thermophoresis of particles in aqueous solution in micro-channel

A theoretical analysis of micro motion of particles under the action of thermophoresis in aqueous electrolyte solution is presented in this paper. A two-dimensional, incompressible and laminar fluid flow model is proposed to simulate the fluid flow and particle motion trajectory in micro-channel. The effects of thermophoretic force and viscous force on the particle are calculated. The particle trajectories considering the effects of particle size, inlet flow velocity and temperature difference between bottom side and top side in micro-channel with a length of 2000 μm and a height of 500 μm are simulated. The effect of thermophoresis on separation motion of particles in micro-channel is analyzed. The results show that thermophoretic force increases with the increase of temperature gradient in micro-channel and particles with smaller diameter, smaller density and smaller gravity acceleration can pass the micro-channel more easily.

Experimental investigation of the motion trajectory of solid particles inside the hydrocyclone by a Lagrange method

Experimental investigations on the motion trajectory of solid particles inside the hydrocyclone have been successfully carried out by using a high-speed motion analyzer to track the particle movement. For each single particle, the motion trajectory is featured with stochastic characteristic; however, for the overall samples of particles, their motions hold the statistical property. The initial position of particles at the entrance of hydrocyclone heavily affects the motion trajectory of particles inside hydrocyclone and consequently the separation performance. An inlet with pre-sedimentation effect should be very helpful for the separation inside hydrocyclones. The results in this study are valuable for understanding the stochastic and statistical behaviors of particle motion in the separation process inside hydrocyclones, and provide some valuable information for finding some effective way to improve the separation performance in the hydrocyclone.

Crystallization-Induced Fluid Flow in Polymer Melts Undergoing Solidification

The influence of processing conditions on the morphology of solidified semicrystalline polymer materials formed under dynamic melt processing conditions has been of concern for decades.1 Although there has been much recent progress in modeling the kinetics and origin of polymer spherulitic crystallization,2,3 the influence of fluid flow and the viscous properties of the undercooled polymer melt on the crystallization morphology have received relatively little attention due to the great computational problems involved in modeling and the experimental difficulties in observing this phenomenon. It is often argued that the macromolecules of the undercooled melt can diffuse to the crystal growth front during crystallization,4 and fluid flow processes are simply ignored. While this assumption may be a reasonable approximation under low undercooling conditions, one may well wonder whether this situation remains true under the conditions of rapid solidification that normally arise during polymer material processing. Flow in the undercooled polymer melts has not been studied much experimentally previously because of the lack of methods of sufficient temporal and spatial resolution to discriminate between the crystalline and amorphous phases during the course of the crystallization process. It is well-known, however, that the formation of commercial semicrystalline polymeric products by injection moldings, film extrusions, film blowing, etc, can be accompanied by the formation of unwanted defects (voids, pores, and other imperfections) and that the ultimate properties of these materials can be appreciably affected by processing conditions.5 The present study indicates that rapid fluid flow can occur in a model undercooled polymer melt (a common commercial polymer, isotactic polypropylene) during the course of crystallization under confinement conditions (simply crystallizing polymer film between cover glasses). We have also observed a similar behavior (not yet published) in crystallizing poly(ethylene oxide) (PEO) melts, indicating some degree of generality for the phenomenon. The isotactic polypropylene (iPP) polymer employed in this work was a commercial grade polymer obtained from the Αldrich Chemical Co., and we show typical results for an isothermal crystallization temperature of 138 °C. The “weight” and “number” molecular masses Mw and Mn were about 340 000 and 97 000, respectively, so this polymer was rather polydisperse, typical of commercial material. The carbon black (CB) relative mass of the probe particles to the polymer matrix was relatively low, 0.5%. The iPP and CB were mixed by meltpressing repeatedly (five times) on a hot plate at 200 °C. Samples for the crystallization and flow measurements were prepared by pressing the melt mixtures between two cover glasses into thin films having a thickness of about 30 μm, thus providing a model confinement environment for the polymer melt crystallization process. Our optical microscope (Carl Zeiss JENA, made in Germany), equipped with a CCD camera (HV1301UC, made by the Da Heng Co. in Beijing), was used to image flows in the undercooled melts by following the motion of CB particles during isothermal crystallization. The resolution of the CCD camera in the x and y directions was about 0.2 μm. A homemade dual-temperature microscope hot stage provided a temperature control, with a temperature uncertainty of ( 0.1 °C. The iPP samples were first melted at 200 °C for 10 min to melt the crystallized structures formed in the course of the previous sample history and then were rapidly transferred to a crystallization temperature below the melting temperature (160 °C). Figure 1 shows a serial of micrographs of the iPP sample during isothermal crystallization at 138 °C. The present work not only considers the standard problem of characterizing the spherulite growth, but also considers how spherulite growth induces flow in the surrounding polymer melt by observing the motion trajectories of CB particles in the undercooled iPP “melt”. The basic concept of our measurement can be understood from the following nautical analogy: The undercooled melt can be viewed as a sea and the growing spherulites as islands that grow up out of this sea. The CB particles are convected by the fluids, providing information about the prevailing local “currents” in the undercooled polymer melt.

DIELECTROPHORETIC ASSEMBLY OF DRUG-LOADING NANOPARTICLES WITH DRUG-ELUTING STENTS

A novel drug-loading method using dielectrophoretic self-organization is proposed to solve the local drug-loading of intravascular stents studded with microprobes. Based on dielectrophoretic assembly mechanism, the dimensionless dielectrophoretic force and the governing equation of motion for a particle, the drug-loading model of intravascular stents by dielec-trophoresis is built for finite element analysis of the dielectrophoretic force distribution and the motion trajectories of particles in the problem space. The influence of the relative particle/electrode position and Brownian motion on the assembly efficiency is also discussed. It is proved that the assembly scheme using dielectrophoresis is feasible in theory. Finally, upon the results of the simulation, theoretical predictions of the particle response under the electric fields are experimentally confirmed by the drug-loading testing platform. Results show that for 4.4μm latex beads suspended in de-ionized (DI) water, when the value (peak-to-peak) of the applied voltage is 10 V and the AC frequency is in the range of 0.1 ~ 1.0 MHz, the particles begin to move towards the electrodes drived by positive dielectrophoretic force, and when the AC frequency is 500 kHz, the motion rate of particle reaches the highest level.

NUMERICAL SIMULATION OF PARTICALE MOTION TRAJECTORY IN A HYDROCYCLONE USING A STOCHASTIC TRAJECTORY MODEL

Based on the consideration of the dispersed phase interaction with continuous phase, applying the Reynolds stress model and the stochastic trajectory model to the continuous and dispersed phase, the particle motion trajectory is simulated successfully, which can visually show the separation process in a hydrocyclone. According to the analysis of the particle motion trajectory, the effect factors of the separation performance, such as particle diameter and particle injection region ,as well as particle flow characteristic within circulation stream are known. Besides, using the ratios of the particles quantities in underflow and overflow, the grade efficiency curve can be plotted. The results of the simulation calculation are verified by a comparison of the experimental data with simulation values. Based on these results another plotting method of the grade efficiency curve for engineering handle is provided.

An Almost-Poisson Structure for Autoparallels onRiemann-Cartan Spacetime

An almost-Poisson bracket is constructed for the regular Hamiltonianformulation of autoparallels on Riemann-Cartan spacetime, which isconsidered to be the motion trajectory of spinless particles in thespace. This bracket satisfies the usual properties of a Poisson bracketexcept for the Jacobi identity. There does not exist a usual Poissonstructure for the system although a special Lagrangian can be found forthe case that the contracted torsion tensor is a gradient of a scalarfield and the traceless part is zero. The almost-Poisson bracket isdecomposed into a sum of the usual Poisson bracket and a ``Lie-Poisson''bracket, which is applied to obtain a formula for the Jacobiizer and todecompose a non-Hamiltonian dynamical vector field for the system. Thealmost-Poisson structure is also globally formulated by means of apseudo-symplectic two-form on the cotangent bundle to the spacetimemanifold.

Polarization filter with singular value decomposition

We present a singular value decomposition (SVD) based algorithm for polarization filtering of triaxial seismic recordings based on the assumption that the particle motion trajectory is essentially 2-D (elliptical polarization). The filter is the sum of the first two eigenimages of the SVD on the signal matrix. Weighing functions, which are strictly dependent on the intensity (linearity and planarity) of the polarization, are applied. The efficiency of the filter is tested on synthetic traces and on real data, and found to be superior to solely covariance‐based filter algorithms. Although SVD and covariance‐based methods have similar theoretical approach to the solution of the eigenvalue problem, SVD does not require any further rotation along the polarization ellipsoid principal axes. The algorithm presented here is a robust and fast filter that properly reproduces polarization attributes, amplitude, and phase of the original signal. A major novelty is the enhancement of both elliptical and linear polarized signals. Moreover as SVD preserves the amplitude ratios across the triaxial recordings, the particle motion ellipse before and after filtering retains a correct orientation, overcoming a typical artifact of the covariance‐based methods.

Effects of subsidiary faults on the geometric construction of listric normal fault systems (Geologic Note)

Listric normal fault systems are one of the most important sites for petroleum exploration in extension basins. The geometry of these systems at depth is commonly uncertain because of poor seismic data. Thus several techniques have been developed to construct the shape and position of the master fault at depth using one or more shallower horizons. Antithetic and synthetic faults commonly disrupt the continuity of bedding in the deformed hanging wall and contribute to the overall extension. Current models either neglect or do not adequately account for the effect of these faults in estimating the geometry of the master fault. We suggest that the extension of individual subsidiary faults should be added to the amount of extension on the master fault during the bed-fault construction. The extension on subsidiary faults is supposed to be transferred into the main fault, along the inclination of shear, although the linking mechanism between the small and main faults is unclear. The inclined shear angle can be estimated by orientation of the antithetic faults. Occurrence of synthetic faults may slightly distort the particle motion trajectories (inclined shear) relative to a hanging-wall reference frame but does not change the overall relative motion pattern. Application of our modification of the inclined shear model to unpublished and published seismic data, as well as an analog experiment model, agrees well with observed fault geometry. Negating the amount of heave on subsidiary faults results in an overestimation of depth to detachment.

Exact solutions of the one-dimensional Russo-Smereka kinetic equation

We obtain new classes of invariant solutions of the integrodifferential equations describing the propagation of nonlinear concentration waves in a rarefied bubbly fluid. For all the solutions obtained, trajectories of particle motion in phase space are calculated. The stability of some flows is studied in a linear approximation. In several cases, the construction of solutions reduces to an integrodifferential equation of the second kind, which can be solved by the iteration method.

107 平板に衝突する微粒子の跳ね返り軌跡

A detailed experiment investigation of rebound trajectory of impinging particle on a flat plate was carried out using Ar+ laser and a camera. The jet velocity was 6.9 m/s and 15 m/s, and three kinds of glass beads of 30, 58 and 100 μm in diameter were used. The photographs of particle motion trajectory show that the impingement and the rebound depend on the momentum of particle: and the secondimpingement depends on the particle diameter and the entrainment velocity of environment air. The particle motion near the plate shows a rounded trajectory in radial direction by air flow along the wall.