Ellipsoidal Particles Research Articles

Observation of the omega phase particles in Ti15Mo alloy by electron microscopy

High resolution scanning electron microscopy (SEM) is capable of imaging ω phase particles. The SEM observation of Ti15Mo metastable β titanium alloy after ageing at 500 °C for 16 h revealed that the material contains coarse β grains surrounded by grain boundary α phase. Thin lamellae associated with α phase were observed in grains interior. Most importantly, small ellipsoidal particles with the size of ∼100 nm were observed due to chemical contrast. Sample for TEM observation was extracted using focused ion beam to prove that these particles belong to isothermal ω phase that evolves during annealing. In the addition, presence of different families of the ω phase in the material was observed by the combination of bright and dark field imaging. Finally, thin lamellae of the α phase in the vicinity of grain boundary were observed using TEM.

Calibration of wet sand and gravel particles based on JKR contact model

The parameters of wet sand and gravel particles with different shapes are calibrated based on JKR contact model. The results reveal that surface energy and rolling friction coefficient are the significant factors affecting the tangent of repose angle, indicating the great influence on the simulation accuracy of wet sand and gravel particles during vibration screening. In addition, the tangent of repose angle and error between simulation and experiment both increase with the filling ball radius increasing, and the corresponding simulation accuracy decreases. Then the screening efficiency is further investigated to verify the accuracy of the calibration parameters. The parameters calibrated can well simulate the screening process. And it is found that non-spherical model instead of spherical model can better simulate the screening process of sand and gravel particles. Meanwhile, JKR model is also verified to better simulate the screening process than Hertz-Mindlin model. Moreover, as the filling ball radius increases, the screening efficiency increases while the simulation time and file size are greatly reduced. However, the corresponding error between simulation and experiment increases. Considering the error and screening time, the optimum filling ball radii for flat, triangular cone and ellipsoid particles are 2 mm, 1.5 mm and 1 mm, respectively.

Microscale magnetoelectricity: Effect of particles geometry, distribution, and volume fraction

Achieving efficient magnetoelectric coupling of core-shell and particulate multiferroic composites has been a challenging hurdle; however, research has shown unwavering interest to overcome this barrier in pursuit of their implementation into promising potential applications. Herein, a fully coupled computational model of core-shell and particulate composites is developed and verified to investigate the magnetoelectric interactions of the particle and matrix on the microscale. The effects of particle geometry, settling, and agglomeration were exhaustively studied by investigating seven different shapes and a wide range of vertical and lateral particle spacing. Overall, it was found that utilizing particle geometries and positioning that closely resemble a laminate configuration, such as a prolate ellipsoid and horizontal particle alignment, enhances the magnetoelectric coupling of the composite structure. The results coincided with the experimental results concerning settling and agglomeration.

Reynolds number effect on the concentration and preferential orientation of inertial ellipsoids

Direct numerical simulations are performed to study the influence of the flow Reynolds number (Re) on the dynamics of inertial, ellipsoidal particles in a turbulent wall-bounded flow. In wall units, the time required for the particle distribution to reach a statistically steady state increases with Re. Once the distribution reached a statistically steady-state, a more uniform concentration profile is observed for higher values of Re, regardless of particle shape, but with a noticeable influence of particle inertia. Finally, in the near-wall region, preferential orientation of all ellipsoids is modified when Re increases, with a strong dependence on the ellipsoids characteristics.

A complete analytical solution to the integro‐differential model describing the nucleation and evolution of ellipsoidal particles

In this paper, a complete analytical solution to the integro‐differential model describing the nucleation and growth of ellipsoidal crystals in a supersaturated solution is obtained. The asymptotic solution of the model equations is constructed using the saddle‐point method to evaluate the Laplace‐type integral. Numerical simulations carried out for physical parameters of real solutions show that the first four terms of the asymptotic series give a convergent solution. The developed theory was compared with the experimental data on desupersaturation kinetics in proteins. It is shown that the theory and experiments are in good agreement.

Surface discretization considerations for the boundary-element method applied to three-dimensional ellipsoidal particles in Stokes flow

The boundary-element method has often been used for simulating particle motion in Stokes flow, yet there is a scarcity of quantitative studies examining local errors induced by meshing highly elongated particles. In this paper, we study the eigenvalues and eigenfunctions of the double layer operator for an ellipsoid in an external linear or quadratic flow. We examine the local and global errors induced by changing the interpolation order of the geometry (flat or curved triangular elements) and the interpolation order of the double layer density (piecewise-constant or piecewise-linear over each element). Our results show that local errors can be quite large even when the global errors are small, prompting us to examine the distribution of local errors for each parameterization. Interestingly, we find that increasing the interpolation orders for the geometry and the double layer density does not always guarantee smaller errors. Depending on the nature of the meshing near high curvature regions, the number of high aspect ratio elements, and the flatness of the particle geometry, a piecewise-constant density can exhibit lower errors than piecewise-linear density, and there can be little benefit from using curved triangular elements. Overall, this study provides practical insights on how to appropriately discretize and parameterize three-dimensional boundary-element simulations for elongated particles with prolate-like and oblate-like geometries.

Particle size distributions following chewing: Transformation of two-dimensional outcome from optical scanning to volume outcome from sieving

Following chewing, the particle size distribution (PSD) by cumulative volume is characterized by X 50 , and b . Volume data are lacking when using less time-consuming optical scanning instead of sieving for characterizing PSDs. The aim was to transform 2D scanning data to 3D ones. Optosil® and almond were used as artificial and real solid foods, and minimal Feret-diameter (min-FD) as a measure of particle size. Border min-FDs were calibrated as a function of sieve aperture to determine size classes. Flakes produced by chewing were considered as ellipsoids. The ratio between the largest and the intermediate ellipsoid's radius was known by scanning. The ratio between the smallest and the intermediate radius was adjusted with Solver of Excel® to minimize the difference between the estimated total volume of the particles, and the known total volume. Estimated values of X 50 and b from scanning closely approached those from sieving, the ‘gold standard’. • Analysis of particle size distributions (PSDs) of a chewed solid artificial food. • PSDs by weight (volume) are usually obtained by labour and time consuming sieving. • Transformation of 2D optical scanning data to 3D volumes can replace sieving data. • Mathematical basis of 2D-3D transformation, assuming an ellipsoid particle shape. • The solution for 2D-3D transformation is also effective for real solid food (almond).

An immersed boundary-lattice Boltzmann framework for fully resolved simulations of non-spherical particle settling in unbounded domain

Particle settling at moderate to high Reynolds number takes a considerable distance to reach a periodical or statistically steady regime. Hence, hardware memory limitations in fully resolved simulations constrain the maximum domain size for this flow class. Due to the locality in most of its algorithms, the Lattice Boltzmann Method (LBM) is increasingly popular for CFD studies. In the present paper, a domain transferring scheme is implemented in LBM, enabling simulations of particle motion in a virtually infinite domain, and it is combined with a high-quality Lagrangian mesh algorithm to be solved with the Immersed Boundary Method (IBM). A thorough mesh generation procedure for ellipsoidal particles is disclosed, as well as an extension of the internal mass compensation strategy of Suzuki and Inamuro (2011). Comparison with analytical results shows that the numerical model appropriately describes the particle rotation and can predict a terminal velocity close to Stokes solution. The numerical results of a buoyant sphere moving diagonally presented remarkable concordance with experimental data. Also, an excellent agreement with a numerical study of oblate spheroids settling in a vast domain was found. The domain transferring scheme reduced the memory demand in one order of magnitude.

Mineral dust cycle in the Multiscale Online Nonhydrostatic AtmospheRe CHemistry model (MONARCH) Version 2.0

Abstract. We present the dust module in the Multiscale Online Non-hydrostatic AtmospheRe CHemistry model (MONARCH) version 2.0, a chemical weather prediction system that can be used for regional and global modeling at a range of resolutions. The representations of dust processes in MONARCH were upgraded with a focus on dust emission (emission parameterizations, entrainment thresholds, considerations of soil moisture and surface cover), lower boundary conditions (roughness, potential dust sources), and dust–radiation interactions. MONARCH now allows modeling of global and regional mineral dust cycles using fundamentally different paradigms, ranging from strongly simplified to physics-based parameterizations. We present a detailed description of these updates along with four global benchmark simulations, which use conceptually different dust emission parameterizations, and we evaluate the simulations against observations of dust optical depth. We determine key dust parameters, such as global annual emission/deposition flux, dust loading, dust optical depth, mass-extinction efficiency, single-scattering albedo, and direct radiative effects. For dust-particle diameters up to 20 µm, the total annual dust emission and deposition fluxes obtained with our four experiments range between about 3500 and 6000 Tg, which largely depend upon differences in the emitted size distribution. Considering ellipsoidal particle shapes and dust refractive indices that account for size-resolved mineralogy, we estimate the global total (longwave and shortwave) dust direct radiative effect (DRE) at the surface to range between about −0.90 and −0.63 W m−2 and at the top of the atmosphere between −0.20 and −0.28 W m−2. Our evaluation demonstrates that MONARCH is able to reproduce key features of the spatiotemporal variability of the global dust cycle with important and insightful differences between the different configurations.

Mixing and dispersion behaviours of ellipsoid particles in a bubbling fluidized bed

Fluidization of non-spherical particles is widely practised in chemical engineering processes. In this work, the mixing and dispersion behaviours of non-spherical particles in a bubbling fluidized bed (BFB) are explored by a computational fluid dynamics-discrete element method (CFD-DEM) featuring a super-quadric model to describe particle morphology. After model validation, the general flow patterns, solid mixing, and solid dispersion of ellipsoid particles are studied, together with the discussion of the effect of aspect ratio (AR) on fluidization behaviours. The results show that minimum fluidization velocity increases with the aspect ratio. Bed permeability depends on bed porosity and particle shape. Bubbles place a significant role in determining flow patterns, which induce a double-recirculation pattern where particles mainly move from the wall region to the central region in the lower bed and oppositely in the upper bed. Ellipsoid particles with higher sphericity (e.g., AR = 0.75 and 1.5) show a smaller mixing index in the bed. The magnitudes of solid dispersion coefficients in x, y, and z directions are about ~10−3 m2/s, ~10−5 m2/s, and ~ 10−2 m2/s, respectively. Ellipsoid particles with higher sphericity show larger solid dispersion intensity. These findings shed light on the fundamental understanding of the particle shape on fluidization dynamics.

Mass transfer from small spheroids suspended in a turbulent fluid

By coupling direct numerical simulation of homogeneous isotropic turbulence with a localised solution of the convection–diffusion equation, we model the rate of transfer of a solute (mass transfer) from the surface of small, neutrally buoyant, axisymmetric, ellipsoidal particles (spheroids) in dilute suspension within a turbulent fluid at large Péclet number, $\textit {Pe}$ . We observe that, at $\textit {Pe} = O(10)$ , the average transfer rate for prolate spheroids is larger than that of spheres with equivalent surface area, whereas oblate spheroids experience a lower average transfer rate. However, as the Péclet number is increased, oblate spheroids can experience an enhancement in mass transfer relative to spheres near an optimal aspect ratio $\lambda \approx 1/4$ . Furthermore, we observe that, for spherical particles, the Sherwood number $\textit {Sh}$ scales approximately as $\textit {Pe}^{0.26}$ over $\textit {Pe} = 1.4\times 10^{1}$ to $1.4\times 10^{4}$ , which is below the $\textit {Pe}^{1/3}$ scaling observed for inertial particles but consistent with available experimental data for tracer-like particles. The discrepancy is attributed to the diffusion-limited temporal response of the concentration boundary layer to turbulent strain fluctuations. A simple model, the quasi-steady flux model, captures both of these phenomena and shows good quantitative agreement with our numerical simulations.

Effects of particle contact characteristics on the performance of fast-response heat storage tank of ellipsoidal metal particle

Energy Internet can guarantee the efficient and stable use of renewable energy, and the energy storage device bears an important linking task. In order to achieve a fast response to Energy Internet, energy storage devices often use metal particle heat storage tanks. The contact between particles is complicated, which directly affects the heat storage performance of the particle tank. Therefore, it is very important to study the effects of the contact between the particles on the performance of the fast-response heat storage tank. In this paper, a 2D steady-state heat storage and release model of the elliptical particles tank was established. The influence of particle contact coefficient on the performance of the heat storage tank was studied. The results showed that with increases of the particle contact coefficient, the average heat flux increases, and the apparent thermal resistance decreases. The work performance and dynamic response performance of the heat storage tank increase. The effect of vacancy on the performance of the heat storage tank is basically not affected by the change of particle contact coefficient.

Transient dispersion process of active particles

Active particles often swim in confined environments. The transport mechanisms, especially the global one as reflected by the Taylor dispersion model, are of great practical interest to various applications. For the active dispersion process in confined flows, previous analytical studies focused on the long-time asymptotic values of dispersion characteristics. Only several numerical studies preliminarily investigated the temporal evolution. Extending recent studies of Jiang & Chen (J. Fluid Mech., vol. 877, 2019, pp. 1–34; vol. 899, 2020, A18), this work makes a semi-analytical attempt to investigate the transient process. The temporal evolution of the local distribution in the confined-section–orientation space, drift, dispersivity and skewness, is explored based on moments of distributions. We introduce the biorthogonal expansion method for solutions because the classic integral transform method for passive transport problems is not applicable due to the self-propulsion effect. Two types of boundary condition, the reflective condition and the Robin condition for wall accumulation, are imposed respectively. A detailed study on spherical and ellipsoidal swimmers dispersing in a plane Poiseuille flow demonstrates the influences of the swimming, shear flow, initial condition, wall accumulation and particle shape on the transient dispersion process. The swimming-induced diffusion makes the local distribution reach its equilibrium state faster than that of passive particles. Although the wall accumulation significantly affects the evolution of the local distribution and the drift, the time scale to reach the Taylor regime is not obviously changed. The shear-induced alignment of ellipsoidal particles can enlarge the dispersivity but impacts slightly on the drift and the skewness.

DISTRIBUTION AND EVOLUTION OF FREE VOLUME OF ELLIPSOIDAL PARTICLE SYSTEMS DURING SHEARING

Granular material is a complex multi-body interaction system which is composed of a large number of discrete particles and their surrounding free volume. Although the correlation between free volume and the mechanical properties as well as the deformation characteristics of granular materials has been proved, the local free volume of non-spherical particles is not fully understood at present due to the difficulties in characterizing. In this paper, the combined finite and discrete element method (FDEM) is used to simulate the triaxial tests of ellipsoidal particles with different principal axis lengths, and the Set Voronoi tessellation method is applied to construct the Voronoi cells of the particles during shearing. The statistical distribution and evolution of the local free volume of the granular systems during shearing are analyzed, and the influence of particle shape on the evolution of free volume is studied. Our results show the anisotropy of Voronoi cells gradually increases during shearing, and the degree of anisotropy increase will be intensified with the increase of particle shape asphericity, which means the granular assembly with a larger asphericity will experience more intense rearrangement during shearing. The local void ratio of ellipsoidal particle systems with different asphericity statistically complies with a k-gamma distribution, which is controlled by the global void ratio of granular assembly and not affected by particle shape and shear state. The local void ratio fluctuations follow an Asymmetric Laplace Distribution (ALD), and its asymmetric parameter which has a linear relationship with the global void ratio of granular assembly describes the competition between contraction and dilatation of local free volume.

Transport of ellipsoidal microplastic particles in a 3D lid-driven cavity under size and aspect ratio variation

The primary goal of this paper is to model and study the behavior of ellipsoidal microplastic particles in a 3D lid-driven cavity. An Eulerian equation for the hydrodynamics is solved toward stationarity under the Reynolds number 1000 and coupled with a Lagrangian system governing the particle dynamics. The key points of departure in the modeling are laminar flow and small particle Reynolds number under which the drag force has extensively been studied. We then address the question, what would be the behavior of prolate and oblate particles under extreme conditions, where the aspect ratio tends to either ∞ (thin needle) or 0 (thin disk). The corresponding tool, Singular Perturbation Theory, not only settles the analysis of the critical manifold but also underlies a quasi-steady state approximation (QSSA) of the particle velocity around the manifold. We show that in a certain range of particle aspect ratio, the QSSA gives quite good approximations of the particle positions yet more computational efficiency. Sedimentation is shown to highly be dependent on the particle’s initial position, aspect ratio, and size. Meanwhile initial position determines to which direction the fluid stream drifts the particles, larger size and aspect ratio closer to 1 increase the likelihood of sedimenting. We also show that neutrally buoyant particles prefer to deposit on the cavity base as well as on vorticity-dominating regions. Generally, buoyant particles with aspect ratios between 1/20 and 20 spin faster than tumble, and they spin even faster as the aspect ratio gets smaller.

Advanced DEM simulation on powder mixing for ellipsoidal particles in an industrial mixer

Tons of products are facilitated through powder mixing processes. The quality of the final products is highly influenced by the mixing state. Hence, detailed information about the mixing state is necessary to improve the quality. Recent remarkable advancements in computer hardware enable the evaluation of the mixing state via numerical simulation. The Discrete Element Method (DEM) is frequently used in numerical simulations, where computational particle shapes are typically modeled by a spherical body. On the other hand, not all particle shapes in industries are spherical, and the structure of industrial mixers is generally complex. Thus, when the DEM is applied to an industrial mixer, modeling of particle shape and the complex structure of the mixers may be taken into consideration. In the present study, an innovative model is newly developed to simulate the powder mixing of non-spherical particles in an industrial mixer. Here, a non-spherical particle is modeled by the ellipsoidal equation, and an industrial mixer is modeled using the Signed Distance Function (SDF), where the wall boundary shape is flexibly modeled by a scalar field. This approach is referred to as the ellipsoidal DEM/SDF. In the current study, the adequacy and applicability of the ellipsoidal DEM/SDF are demonstrated by the following steps. First, the compatibility of the ellipsoidal DEM with the SDF wall boundary model and the applicability of a soft linear spring in the ellipsoidal DEM/SDF are demonstrated through validation tests. Subsequently, the effect of particle shape on mixing progress in a ribbon mixer is examined. Through computations, the effect of the non-spherical shape is shown to be insignificant on powder mixing progress in the ribbon mixer. Consequently, the ellipsoidal DEM/SDF is shown to be applicable to the industrial powder mixing, and therefore, will contribute to optimization of the mixer design and the operational conditions in chemical, food, and pharmaceutical engineering fields.

Parabolic velocity profile causes shape-selective drift of inertial ellipsoids

Understanding particle drift in suspension flows is of the highest importance in numerous engineering applications where particles need to be separated and filtered out from the suspending fluid. Commonly known drift mechanisms such as the Magnus force, Saffman force and Segré–Silberberg effect all arise only due to inertia of the fluid, with similar effects on all non-spherical particle shapes. In this work, we present a new shape-selective lateral drift mechanism, arising from particle inertia rather than fluid inertia, for ellipsoidal particles in a parabolic velocity profile. We show that the new drift is caused by an intermittent tumbling rotational motion in the local shear flow together with translational inertia of the particle, while rotational inertia is negligible. We find that the drift is maximal when particle inertial forces are of approximately the same order of magnitude as viscous forces, and that both extremely light and extremely heavy particles have negligible drift. Furthermore, since tumbling motion is not a stable rotational state for inertial oblate spheroids (nor for spheres), this new drift only applies to prolate spheroids or tri-axial ellipsoids. Finally, the drift is compared with the effect of gravity acting in the directions parallel and normal to the flow. The new drift mechanism is stronger than gravitational effects as long as gravity is less than a critical value. The critical gravity is highest (i.e. the new drift mechanism dominates over gravitationally induced drift mechanisms) when gravity acts parallel to the flow and the particles are small.

Dynamic Analysis and Simulation of an Optically Levitated Rotating Ellipsoid Rotor in Liquid Medium

Optical trap, a circularly polarized laser beam can levitate and control the rotation of microspheres in liquid medium with high stiffness. Trapping force performs as confinement while the trapped particle can be analog to a liquid floated gyroscope with three degree-of-freedom. In this work, we analyzed the feasibility of applying optically levitated rotor in the system. We presented the dynamic analysis and simulation of an ellipsoid micron particle. The precession motion and nutation motion of a rotating ellipsoid probe particle in optical tweezers were performed. We also analyzed the attitude changes of an optically levitated ellipsoid when there was variation of the external torque caused by deviation of the incident light that was provided. Furthermore, the trail path of the rotational axis vertex and the stabilization process of a particle of different ellipticities were simulated. We compared the movement tendencies of particles of different shapes and analyzed the selection criteria of ellipsoid rotor. These analytical formulae and simulation results are applicable to the analysis of the rotational motion of particles in optical tweezers, especially to the future research of the gyroscope effect.

Effects of AP powder topology on microscale combustion properties of AP/HTPB propellant

A three-dimensional model has been developed to capture burning properties of ammonium perchlorate(AP)/hydroxyl–terminated polybutadiene(HTPB) composite propellant. Interfacial coupling between condensed domain and gas phase was conducted to obtain the surface temperature and burning rate. The condensed phase was governed by heat transfer equation, and reacting Navier-Stokes equations with pressure dependent 3-step and 12-species global kinetics were adopted. The current model was verified and validated by comparing with analytical and experimental results. Thereafter, the influences of ellipsoidal AP's orientation and aspect ratio on the burning rate were investigated. The flame structure of a typical propellant with ellipsoidal AP particle was examined, and the characteristic heights of multiple flames were determined. Besides, the flame properties of a typical propellant with spherical/ellipsoidal AP particle and different AP topologies were analyzed. Furthermore, the temperature sensitivity coefficients were calculated for composite propellant with different AP contents and sizes, matching reasonably with the experimental results.

Numerical investigation on effect of particle aspect ratio on the dynamical behaviour of ellipsoidal particle flow

Flow of ellipsoidal particles in a modal shear cell was investigated at the microdynamic level based on discrete element method simulations. In a stress-controlled double-shear condition, the flow was studied by varying the aspect ratio of ellipsoidal particles and comparing with the flow of spherical particle assembly in terms of some key properties, including particle alignment, linear velocity, angular velocity, porosity, contact force and contact energy. It was found that particle elongation impacts the rotational displacement around the axis perpendicular to the shear direction, which causes that the ellipsoidal particles with higher elongation are more aligned with the direction of the shear velocity, with more uniform force network. This then affects other particle properties. The fluctuation of linear velocity and the angular velocity decreases with an increase in particle aspect ratio, although the particle elongation does not significantly affect the flow velocity gradient. There is a reduction in both normal and tangential forces per contact with an increase of particle elongation. Due to the variation of the particle alignment with elongation, the standard deviation of the contact energies increases and then reduces when an increase in particle aspect ratio occurs, and on contrary, the porosity has an opposite variation trend.