Particle Orientation Angle Research Articles

Eulerian multi-fluid simulations of local liquid distribution in a bed packed with cylindrical particles

Packed bed reactors (PBRs) are extensively used in chemical process industries to perform solid-catalyzed gas–liquid reactions. Their performance is significantly influenced by liquid distribution which is a strong function of particle shape and size. In the present work, we simulated the steady-state local liquid distribution, pressure drop (ΔP/L), and overall liquid holdup (〈εL〉) for the beds packed with spherical and cylindrical particles using a three-dimensional (3D) Eulerian multifluid model and validated the predictions using corresponding high-speed imaging measurements performed in pseudo-2D packed beds. We showed that the Eulerian model with existing closures significantly underpredicts the liquid distribution for the bed randomly packed with cylindrical particles. To address this, we proposed a modification in existing mechanical dispersion force (F→D) model as a function of average particle orientation angle (θ). The modification significantly improved agreement between the predictions and the corresponding measurements. Using the modified model, we showed that the increased magnitude of F→D in the lateral direction leads to higher lateral liquid spreading for cylindrical particles as compared to that for the spherical particles. Importantly, the modified model also predicted the local liquid distribution and ΔP/L for beds packed manually with cylindrical particles oriented at different θ in a satisfactory agreement with the corresponding measurements. On increasing θ, the F→D in lateral direction (i.e., perpendicular to flow) as well as liquid–solid interaction force (F→LS) in axial direction (i.e., parallel to flow) found to increase significantly. As a result, the lateral liquid spreading as well as ΔP/L decrease substantially on increasing θ.

Three-dimensional simulation on phase change heat transfer of moving spherical particle

Investigating the motion process of paraffin particle under a mesoscopic scale is very helpful to master the heat transfer mechanism of the mushy zone in solid–liquid phase change. Prior researches predominantly focused on either particle motion or phase change, without accounting for their coupling. In this study, the three-dimensional finite element method is used to solve the motion and heat transfer of the particle, taking into account the coupling of motion and phase change. The moving grid is employed to trace the interface of moving particles and liquid using the Arbitrary Lagrangian-Euler method, which is able to calculate flow and heat transfer in fluid region and allow grid deformation in solid region. The results indicate that uneven fluid velocity around the particles results in non-uniform temperature gradients on particle’s surface. In areas with larger temperature gradient, it melts more quickly and its deformation is obvious. The maximum is located at particle orientation angle 30°. Changing the size and direction of fluid velocity will reinforce or inhibit the movement of particle. The changing time of motion direction when fluid velocity is −0.03 m/s shorten 2.7 times than when fluid velocity is −0.01 m/s. The initial temperature of the surrounding fluid has a positive relationship with the particle melting rate. The channel width affects significantly the motion and melting of particle. The initial position of particle has an important effect on it’s falling movement, and the closer is close to the wall of channel, the greater the displacement of left and right movement.

The impact of initial fabric anisotropy on cyclic liquefaction behavior with polygonal particles using the discrete element method (DEM)

Liquefaction is one of the most significant phenomena that can occur in soil during an earthquake. The destructive effects of this phenomenon on earth structures have captured the attention of many geotechnical engineers. Additionally, the gradual increase in pore water pressure during the cyclic loading induced by the propagation of earthquake waves, known as cyclic liquefaction, is a crucial factor that might lead to the complete loss of shear strength in soils. A better understanding of cyclic liquefaction is essential for improving earthquake hazard analysis and mitigating structural damage. Factors influencing liquefaction behavior include particle size, particle grading, and soil fabric. By “soil fabric,” we refer to the arrangement and positioning of particles with each other, particle shape, and the shape of voids among particles. This research aims to focus on the effects of fabric anisotropy on cyclic liquefaction of granular soils with angular particles. To carry out this investigation, the discrete element method has been employed. In the discrete element method, the geometry of particles and, generally, the soil fabric can be considered. In this research, specimens with varying particle orientation angles were produced and subjected to cyclic loading tests under undrained conditions. By examining the stress paths of specimens during cyclic loading, it is observed that the initial fabric and inherent anisotropy significantly influence the behavior of the specimens. Inherent anisotropy leads to varying numbers of cycles required for the initial liquefaction of each specimen. Furthermore, it is observed that as the particle orientation angle increases, the localization of axial strains shifts from tensile to compressive directions. The effect of inherent anisotropy plays a substantial role in the initial liquefaction (ru = 1). If the liquefaction of specimens is of interest at lower values of ru, the effect of inherent anisotropy can be disregarded.

Study of flow resistance coefficients acting on regular non-spherical particles in simple shear flow at moderate Reynolds numbers

This contribution is devoted to the study of the aerodynamic characteristics of non-spherical particles of definite regular shape, such as prolate and oblate ellipsoids as well as cylinders, immersed in a locally linear shear flow. The flow resistance coefficients of drag, lift and pitching torque are computed by means of the Particle Resolved Direct Numerical Simulation (PR-DNS) technique for such shapes as function of the Reynolds number Re. The parameter space comprises particle aspect ratio, AR, fluid spin ratio, ζ, and particle orientation angle, α. The Reynolds numbers of interest are in the intermediate range 1≤Re≤100, common in industrial and environmental processes. To properly understand and explain the obtained results, the role of the friction and pressure contributions to total flow coefficients is analyzed in detail for the different cases, allowing the differences between the considered shapes to be pointed out. On the other hand, the behavior of the pressure and skin friction coefficients in the particle plane of symmetry parallel to the flow is investigated as a function of the previous parameters (shape, AR, ζ, α), which provides further insights into the features of the shear flow around the non-spherical particles at finite Re. Finally, the influence of the shear flow magnitude and incidence angle on the location of the center of aerodynamic force is devised for the three shapes considered as function of Reynolds number and particle aspect ratio. It is expected that the information generated in this work will be useful for researchers to enhance the modeling of non-spherical particles immersed in non-uniform flows.

Analysis of multiple successive collisions between a prolate spheroidal particle and a plane wall

This study investigates multiple successive collisions between elastic prolate spheroid particles and a rigid planar wall in vacuum. The influence of various factors on multiple particle–wall collisions, including the particle aspect ratio, orientation angle, impact velocity, material properties, size, impact angular velocity, and wall friction coefficient, is analyzed. The results show that secondary and tertiary collisions are primarily determined by the particle aspect ratio and orientation angle. Four particle aspect ratios (λ=1.5, 2, 3, and 5) are investigated. A secondary collision occurs for λ=2 to 5. For λ=5, the particle can collide with the wall three times in a row. The corresponding ranges of the particle orientation angles for the secondary and tertiary collisions are provided for different particle aspect ratios. The maximum elastic force acting on the particles during each collision was also analyzed. The proposed model is verified to be applicable to gas-driven particles, and an example of its implementation within a Lagrangian particle-tracking algorithm is provided.

Orientation dynamics of anisotropic and polydisperse colloidal suspensions

Small-angle light scattering (SALS) is employed to determine in situ microstructural changes of polydisperse colloidal suspensions under capillary flow. Titanium dioxide (rod-like) bundles and kaolinite nanoclay (platelet) flake-like stacks of particles are suspended in a Newtonian fluid to explore the effects of shape anisotropy. Subjecting the systems to a startup test in a flow cell in Stokes's regime, the evolution of the anisotropy factor (AF), and the average orientation angle (χ) of particles vs strain is probed at different averaged Péclet (Pe¯) numbers. Dilute and semi-dilute concentration regimes are explored in a capillary flow. Moving in the vorticity direction, we show significant changes in χ due to the gradient in shear rate in the capillary flow, while no cross-sectional flow migration was exhibited. In these polydisperse colloidal suspensions, two characteristic stages are observed: initial particle alignment and subsequent orientational demixing. Probing the velocity–vorticity (xy) plane, an initial particle alignment in the flow direction at high Pe¯ (> 1) occurs, is demonstrated by an elliptical SALS pattern, and then, an increase in AF is observed due to particles' phase mixing. This behavior is then followed by a breakdown in structure and loss of particle alignment due to orientational demixing. The evolution of the average orientation angle of particles in the xy plane can be clearly observed through these two stages by the help of high-resolution SALS contours. These experimental findings provide novel insights into the flow–microstructure relationship of polydisperse colloidal suspensions for the optimization of many industrial processing schemes.

Automatic acquisition of particle orientation by interferometric out-of-focus image

In this paper, the automatic acquisition of particle orientation is enabled by interferometric out-of-focus image. Based on optical transfer matrix theory, the slope expression of the speckle orientation and autocorrelation result of an out-of-focus image are acquired. The calculation formula of the particle orientation angle is derived. The processing algorithm which can automatically obtain the particle orientation from the out-of-focus image is proposed. Hough transform is utilized to improve the measurement accuracy. The out-of- focus images with different speckle orientations are acquired and the algorithm is applied to process the simulative and experimental out-of-focus images. The results show that the absolute measurement error of the algorithm is 2.7°. The algorithm has potential applications in particle measurements.

Dynamics of Suspended Nanoparticles in a Time-varyingGradient Magnetic Field: Analytical Results

We study theoretically the deterministic dynamics of single-domain ferromagnetic nanoparticles in dilute ferrofluids, which is induced by a time-varying gradient magnetic field. Using the force and torque balance equations, we derive a set of the first-order differential equations describing the translational and rotational motions of such particles characterized by small Reynolds numbers. Since the gradient magnetic field generates both the translations and rotations of particles, these motions are coupled. Based on the derived set of equations, we demonstrate this fact explicitly by expressing the particle position through the particle orientation angle, and vice versa. The obtained expressions are used to show that the solution of the basic set of equations is periodic in time and to determine the intervals, where the particle coordinate and orientation angle oscillate. In addition, this set of equations is solved approximately for the case of small characteristic frequency of the particle oscillations. With this condition, we find that all particles perform small translational oscillations near their initial positions. In contrast, the orientation angle oscillates near the initial angle only if particles are located in the vicinity of zero point of the gradient magnetic field. The possible applications of the obtained results in biomedicine and separation processes are also discussed.

Drag, lift and torque acting on a two-dimensional non-spherical particle near a wall

Gas-solid granular flows with non-spherical particles occur in many engineering applications such as fluidized beds. Such flows are usually contained by solid walls and always some particles move close to a wall. The proximity of a wall considerably affects the flow fields and changes the hydrodynamic forces and torque acting on particles moving near the wall. In this paper, we numerically investigate the drag, lift and torque acting on a non-spherical particle in the vicinity of a planar wall by means of lattice Boltzmann simulations. To gain an exhaustive understanding of the complex hydrodynamics and study the influence of various geometrical and flow parameters, a single 2D elliptical particle is selected as our case study. In the simulations, the effect of particle Reynolds number, distance to the wall, orientation angle and aspect ratio on drag, lift and torque is studied. Our study shows that the presence of a wall causes significant changes in hydrodynamic forces, with increasing or decreasing drag and lift forces, depending on the distance from the wall. Even the direction of lift and torque may change, depending on both the distance from the wall and particle orientation angle. Also, an ellipse with higher AR experiences larger hydrodynamic forces and torque whatever the gap size and orientation angle.

Effects of rotation speed and outlet opening on particle flow in a vertical rice mill

Rice mill is the key equipment to food processing used for milling unpolished rice to milled rice. However, there are few investigations about the flow process on rice particles inside the mill and the role of operation parameters. In addition, the detailed information about particle interaction and mechanisms of milling remains poorly understood. This paper presents a numerical study based on the discrete element method (DEM) to investigate the flow of rice particles in a vertical rice mill. The effects of operation parameters on the hidden flow properties, including particle orientation angle, particle fill level, collision energy and energy efficiency, were analyzed. The results showed that the particle orientations prefer pointing to 0° and 180° and orientation angles fluctuate at U-shaped distributions on a vertical plane. The wear process of particles can be described by the spatial distribution of collision energy. Wear of particles occurs mainly in the upper half of milling chamber, in which is defined as milling area. The effects of outlet opening on flow structure and particle fill level in milling area are more obvious, compared with that of the rotation speed. However, the increase of rotation speed results in higher collision energy, collision number and energy efficiency, which accelerates wear of rice particles. The findings are useful to understand particle flow, wear and milling behavior of the vertical rice mill.

Study of orientation and morphology of elliptical particles in drum granulation by dynamic simulation

Sphericity is an important indicator of particle flow properties in rotary granulation. Here, a dynamic simulation approach is proposed to study the formation of particle sphericity during agglomeration by investigating both the orbit and attitude of non-spherical particles in a rotary drum. First, geometric criteria are presented to substitute a dual-sphere particle model for the commonly encountered ellipsoidal particle model assuming the long radius of the dual-sphere particle is equal to that of the ellipsoidal particle. Next, a discrete element method is applied to calculate the positions and orientations of dual-sphere particles during granulation. The relationship between shape and attitude in the dual-sphere model is then analyzed by comparing the obtained orientation angle–oblateness curves. A conclusion can be drawn that the particle orientation angle decreases with increasing particle oblateness within a certain range.

Measurements and modeling of instantaneous particle orientation within abrasive air jets and implications for particle embedding

Previous theoretical studies indicate that the material removal mechanism and the likelihood of particle embedding in solid particle erosion processes strongly depend on instantaneous particle orientation at impact. The present study utilized pulsed laser shadowgraphy to measure the size, shape, and instantaneous orientation distributions of particles within a micro-abrasive jet at various pressures, particle sizes, and nozzle standoff distances. A particle orientation angle was defined as the angle between the particle linear velocity vector (approximately parallel to the jet centerline axis) and the line connecting the center of mass to the furthest downstream particle vertex. Particles were considered to be ‘oriented’, i.e. in a configuration favorable to embedding, if this angle was between 0 and 10°. The measurements revealed that, at all pressures (i) between 24% and 29.5% of the particles were oriented at the nozzle exit; (ii) the percentage of oriented particles increased slowly with standoff distance; (iii) larger particles had a stronger tendency to orient than smaller ones; (iv) particles having larger aspect ratios had a stronger tendency to aerodynamically align with the jet, and (v) although not all particles that were oriented actually embedded, the measured percentage of embedded particles on Al 6061-T6 surfaces nevertheless correlated with the percentage of oriented particles. A model capable of predicting the instantaneous particle orientation and velocity within and downstream of the nozzle was presented and shown to agree well with measurements. To the knowledge of the authors, these are the first measurements of the instantaneous orientation of abrasive particles under conditions that are typical of abrasive air jets. The results may have important implications for optimizing solid particle erosion tests and in abrasive jet machining applications.

Effect of ultrasonic treatment on clay microfabric evaluation by atomic force microscopy

Researchers previously thought the only ways to investigate the microfabric of clayey soil were through a scanning electron microscope (SEM), a transmission electron microscope (TEM), an X-ray, and an optical microscope. However, in this research, ultrasonic equipment was used to disperse clayey soils (bentonite, illite, and kaolinite) for different lengths of time. After dispersion, an atomic force microscope (AFM) was employed to take three-dimensional (3D) photographs. While the samples were intact, AFM was able to take 3D photographs in different environments. The IA_P9_BUILD software was employed to analyze the data to obtain the angle of particle orientation and the particle size distribution. In this investigation, it was observed that with the use of an ultrasonic device with 30KHz of power, bentonite, illite, and kaolinite reached a dispersion state after 12, 8, and 6min, respectively.

Effects of hollow particle shape and distribution on the elastic properties of syntactic foams: 3D computational modeling

Syntactic foams, i.e., hollow particles filled composites, attract intense studies due to their lightweight and excellent mechanical properties. A 3D computational model is developed to study the elastic properties of syntactic foams. The Young’s modulus and Poisson’s ratio predicted by this model with spherical hollow particles agree well with the available experimental and analytical results. This model is further applied to investigate the effects of hollow particle shape and distribution on the elastic properties of syntactic foams. It is observed that particle shapes have strong influence on the elastic properties of syntactic foams when the particles are aligned unidirectionally. The relationship between the elastic constants and the hollow particle orientation angle θ depends on the hollow particle shape. This study is useful for optimizing the microstructure of syntactic foams.

Development of Intermediate Microfabric in Kaolin Clay and Its Consolidation Behaviour

The effect of microfabric on the mechanical behaviour of clays has been explored previously based on the response of dispersed and flocculated microfabrics only. However, the natural clays often have the geometric arrangement of particles between these two extreme cases which can be termed as intermediate microfabric. This paper explores the formation of intermediate microfabric of kaolin clay and its impact on soil’s consolidation behaviour by performing self-weight consolidation, slurry consolidation and 1-D consolidation tests. The effect of calgon content (dispersing agent) on geometric arrangement of the particles has been evaluated through cluster size distribution by performing double hydrometer tests. Then these clay slurries have been used to perform the AFM (Atomic Force Microscopy) test to obtain the variation in average angle of particle orientation with respect to the calgon content present in the slurry. AFM technique provides 3D image of the clay sample and 2D image with Z-information with the potential of measuring intermediate microfabric of clayey soil quantitatively including dispersed and flocculated microfabrics. Other traditional techniques such as SEM, TEM & XRD are limited to only qualitative analysis of soil’s microfabric, thus, having no capability to measure intermediate microfabric of clay. A methodology of preparing bulk specimens of clay with intermediate microfabric has been developed using slurry consolidation technique; and then these specimens have been consolidated under 1-D loading to evaluate the effect of intermediate microfabric on compressibility and permeability of clay. In this study, all the experiments reports that the dispersed type geometric arrangement increases with the increase in calgon content in soil up to 2 % and then the reverse behaviour is observed at 3 %; which may depend on the required amount of sodium cations to neutralize the negatively charged faces of the clay platelets present in the slurry.

New formula for drag coefficient of cylindrical particles

The drag force on a cylindrical particle is calculated using lattice Boltzmann method. The results show that the drag coefficient of a particle with different orientation angles decreases with increasing Reynolds number. When the principal axis of the particle is parallel to flow, the drag coefficient is much larger than that of others and decreases fastest with increasing Reynolds number, which becomes more obvious with increasing particle aspect ratio. When the principal axis of the particle is inclined to flow, the drag coefficient is nearly the same for different particle aspect ratios. In the case of flow with small Reynolds number ( Re < 100), the drag coefficient decreases with increasing orientation angle at different aspect ratios and Reynolds numbers. The drag coefficient is more sensitive to particle orientation angle when the particle orientation angle is small and the aspect ratio is large. Finally, a new correlation formula for the drag coefficient of cylindrical particle is established, with which the drag force on a cylindrical particle can be directly calculated based on the Reynolds number, particle aspect ratio and orientation angle.

Effect of particle orientation and of flow velocity on the combustibility of Pinus pinaster and Eucalyptus globulus firebrand material

Spotting is a very important mechanism of forest fire spread. Its negative effect increases in extreme fire danger conditions. In order to predict the maximum spotting distance, the duration of the combustion reaction of potential firebrands should be evaluated. This paper reports the results of an experimental laboratory study of the combustibility of firebrand material (pine cones and scales and pieces of bark of eucalypt) of two representative species in Portugal, Pinus pinaster Ait. and Eucalyptus globulus Labill. The main purpose was to assess the role on the burning conditions of the firebrand particle orientation angle θ in relation to the airflow and of the flow velocity (U) around the particle. Tests were made varying the angle of orientation of the main axis of the particle in relation to incident flow in the range of ±90°; flow velocities were tested from 0 to 6.5 m s–1. After ignition, particle mass loss owing to flaming or glowing combustion of the particle was continuously measured. Residual mass, duration of the flaming phase and the burnout times are reported for each case. Empirical models to estimate the trends of variation of some of these parameters with θ and U are proposed to illustrate their importance for the range of test conditions.

Use of atomic force microscopy (AFM) for microfabric study of cohesive soils

Microfabric reflects the imprints of the geologic and stress history of the soil deposit, the depositional environment and weathering history. Many investigators have been concerned with the fundamental problem of how the engineering properties of clay depend on the microfabric, which can be defined as geometric arrangement of particles within the soil mass. It is believed that scanning electron microscopy (SEM) and transmission electron microscopy (TEM) are the only techniques that can reveal particle arrangements of clayey soils directly; however, current research introduces a novel and more advanced technique, atomic force microscopy, to evaluate the microfabric of cohesive materials. The atomic force microscopy has several advantages over SEM/TEM for characterizing cohesive particles at the sub-micrometre range by providing 3D images and 2D images with Z-information used in quantitative measurements of soil microfabric using SPIP software, and having the capability of obtaining images in all environments (ambient air, liquids and vacuums). This paper focuses on the use of atomic force microscopy technique to quantify the microfabric of clayey soils by developing the criteria for average and maximum values of angle of particle orientation within the soil mass using proposed empirical equations for intermediate and extreme microfabrics (dispersed, flocculated).

Conservative dichroism of a sheared suspension in the Rayleigh-Gans light scattering approximation

A polarization modulation linear dichroism technique has recently been developed and applied to studies of the particle microdynamics associated with subjecting dilute colloidal suspensions to time-dependent flows. In this paper, we compare the abilities of the Rayleigh and Rayleigh-Gans light scattering approximations to represent experimental dichroism data in terms of calculations based on known hydrodynamic models. In particular, the importance of considering finite particle size in the light scattering theory is investigated. Calculations of the conservative linear dichroism and of the average particle orientation angle are carried out for dilute suspensions subjected to transient simple shear flow in the absence of Brownian motion and in the presence of weak Brownian motion. For both situations, only small differences in the features associated with the particle orientation statistics of the simulation occur between the Rayleigh and the Rayleigh-Gans calculations over a wide range in particle geometry. In particular, the calculation of the average particle orientation angle is found to be insensitive to the choice of light scattering treatment. Generally, we infer from these simulations that the additional complexity of the Rayleigh-Gans treatment is usually not warranted for the analysis of typical rheo-optical data from dilute suspensions.