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Liquid–solid fluidized beds (LSFB) modeling validation is crucial for establishing design rules and monitoring tools. However, it generally relies on comparing global variables, which overlook dynamic features that influence reaction outputs. This work aims to implement time series analysis tools to compare Radioactive Particle Tracking data with a simulation consisting of Computational Fluid Dynamics coupled with Discrete-Element Method. Experiments have been performed in a pilot-scale LSFB of calcium alginate spheres fluidized with a calcium chloride solution. The Diks’ test indicates that the simulation can capture the LSFB behavior. It also allows diagnosing flow regime transitions from the simulation. Trends of solid dispersion coefficients and mixing times predicted by the simulation are in good agreement with the experiments.

Electromagnetic wave absorption (EWA) materials for use in extreme environments are of great interest. Herein, SiC nanowires / SiC whiskers (SiCnw/SiCw) foam with unique “wire-on-sphere” hierarchical structure was developed for efficient high-temperature EWA. SiCw were assembled to porous SiCw spheres via spray drying and then SiCw spheres were 3D printed to SiCw foam. The catalyst-free precursor infiltration pyrolysis process was first developed to ensure that SiCnw can intentionally grow in situ on the surface of SiCw spheres, thereby achieving “wire-on-sphere” hierarchical structure foam. At room-temperature, the maximum electromagnetic wave effective absorption bandwidth (EABmax) and minimum electromagnetic wave reflection coefficient (RCmin) of SiCnw/SiCw foam can reach 4 GHz and -57 dB, respectively. At 600 °C, the EABmax and RCmin were 3 GHz and -15 dB, respectively. Furthermore, even oxidized at 1000–1500 °C, SiCnw/SiCw foam can still retain EABmax ranging from 2.7 to 3.9 GHz and RCmin ranging from -16 dB to -64 dB, because the formation of SiO2 layer with appropriate thickness can boost interfacial polarization and regulate impedance matching. The SiCnw/SiCw foam also shows the flexural strength as high as 17.05 MPa. All results demonstrate that the SiCnw/SiCw foam is a promising EWA material for applications of harsh environments. And the material-independent “wire-on-sphere” hierarchical structure and its novel preparation process should find the widespread use in the design and fabrication of high-efficiency EWA micro-nano materials.

In the present paper, the three dimensional (3D) settlement process of two side-by-side free-falling spheres in a water tank was numerically investigated using coupled Smoothed Particle Hydrodynamics (SPH) - Discrete Element Method (DEM) method. The maximum particle Reynolds number, calculated based on the terminal velocity and sphere diameter, is R e m = 2 . 4 × 1 0 4 . The accuracy of the model was firstly validated by simulating the single sphere water-entry, settlement of two circular cylinders arranged in series and two identical spheres settlement side by side problems, respectively. The simulation results exhibited a satisfactory agreement with the available numerical and experimental data in the literatures. Then, the settlement process of two spheres with different sizes and transverse distances were simulated. In particular, the motion patterns of two interacting spheres with different initial gaps and diameter ratios, including motion trajectory, vertical falling distance and flow field, were systematically investigated. The results demonstrate that when initial gap S 0 ∗ S 0 ∗ > 0.75, the interaction between the two spheres are negligible. In addition, the interaction between particles would slow down the settling velocity and affect the terminal settling distance.

The flow driven by electromagnetic forcing of an electrolytic fluid in a concentric sphere system with differential rotation is studied experimentally and theoretically in the laminar regime. The electromagnetic force is generated by the interaction of a direct current injected radially through electrodes located at the equatorial zone of the spheres and a dipolar magnetic field produced by a permanent magnet inside the inner sphere. Even though the flows are fully three-dimensional, under some assumptions, they can be mathematically modeled with a general one-dimensional solution from the incompressible Navier–Stokes equations. Additionally, in order to deepen the flow dynamics, a full three-dimensional numerical simulation is also obtained. Experimentally, velocity profiles in the equatorial plane between spheres were obtained with particle image velocimetry. The analytical solution reproduces qualitatively the experimental profiles, whereas the numerical solution reproduces quantitatively the experimental measurements.

Vibrating separation is a significant method for liquid–solid separation. A typical example is the vibrating screen to dewater wet granular matter. The properties of granular matter and the vibrating parameters significantly affect the separation efficiency. This study investigates the effect of vibration parameters in separation based on the breakage of large-scale liquid bridge numerically by using a calibrated simulation model. Through analysing the simulation results, the liquid bridge shape and the volume between two sphere particles for various particle sizes and particle distances were studied in the static condition under the effect of gravity. The results show a general reducing trend of liquid bridge volume when the radius ratio of two particles increases, particularly when the ratio increases to 5. Additionally, a set of vibrating motion was applied to the liquid bridge in the simulation model. A group of experiments were also performed to validate the simulation model with vibration. Then, the effect of vibrating peak acceleration, distance between spheres and radius on the separation efficiency which was reflected by the residual water were investigated. It is found that separation efficiency increased obviously with the peak acceleration and the increase slowed down after the peak acceleration over 1 m/s2.

Experimental investigations of two interacting spheres were carried out in a Mach 4 flow with a static pressure of 2.666 Pa. This study was performed in the MARHy wind tunnel, an adjustable supersonic or hypersonic low-density facility. The main purpose is to estimate how the interactions between spherical debris modify the aerodynamic forces during their atmospheric entry. Indeed, around 80 km, altitude experimentally reproduced thanks to MARHy flow conditions, most debris fragment. The multiple debris, resulting from fragmentation, interact with each other’s, which may impact their trajectory. The purpose of this work is to analyze the behavior of a moving sphere placed in the wake of another one. The moving sphere is suspended with two thin wires, so it can almost freely move in the flow direction and physically respond to the acting flow forces of the wake of the first one. Aerodynamic forces are then calculated from the sphere angle deflection. The qualitative analysis of the experimental results will be discriminated first with respect to the trajectory of the second sphere, and secondly with respect to the evolution of the aerodynamic forces according to the sphere.

Targeting the potential application of morphological carbon in electrode materials, a space-sacrificed pyrolysis strategy was applied for the preparation of boron-doped carbon spheres (B-CSs), using commercial triphenyl borate (TPB) as carbon and boron co-source. The unique structure of TPB play an important role in the sacrificed space, and has notable effect on the surface area of B-CSs. The as prepared B-CSs possess a high surface area and boron content with uniform boron atoms distribution and high surface polarity, which contributes to the improvement of pseudo-capacitance. The sizes, specific surface areas, and boron contents of B-CSs can be easily regulated by varying the experimental parameters. The optimal sample has a boron content of 1.38 at%, surface area of 560 m2 g−1 and specific capacitance of 235F g−1. We can believe that this work would provide a flexible and extensible preparation technique of B-CSs for electrochemical applications.

Sodium-Se (Na–Se) and potassium-Se (K–Se) batteries are prospective candidates for energy storage systems with high theoretical specific capacity and low cost. However, some intractable problems need to be overcome, such as the shuttle effect of polyselenide and the low Se loading, which lead to poor cyclic performance and low capacity. Herein, dual-wall hollow carbon spheres (DWHCSs) modified with cetyltrimethylammonium bromide (CTAB) were designed to be served as a host material (C-DWHCSs) for the load of Se to construct the Se electrode material (C-DWHCSs/Se). Dual-wall hollow structure with satisfactory specific surface area greatly increased the load capacity of Se, which effectively improved the battery capacity. In terms of physical confinement, the gap between two carbon walls provided a buffer space for the volume expansion of Se and prevented the escape behavior of electrode material after expansion pulverization. Based on the chemisorption strategy, the polyselenides were immobilized by CTAB functionalized graphite carbon through the Lewis acid-base interaction, which was demonstrated by theoretical calculation. As a consequence, C-DWHCSs/Se in Na–Se batteries delivered an outstanding cycling performance (∼331 mAh g−1 at 2 C after 1000 cycles). For K–Se batteries, they also exhibited a splendid cycling stability (∼292 mAh g− 1 at 0.5 C after 500 cycles).

Rational design of advanced polar hosts with high sulfur loading, facilitated ionic/electronic transport and effectively suppressed shuttling effect has great potential for high performance lithium-sulfur batteries, yet it remains challenging. Here we propose a novel templated spherical coassembly strategy to fabricate the MoS2/C hollow spheres as an efficient sulfur host material. The unique hollow structure provides enough interior space for accommodating a substantial amount of sulfur, and effectively suppresses the diffusion of dissolved polysulfides by both physical confinement and chemical adsorption. Moreover, the ionic transport as well as the ability to mitigate volume variation upon cycling is also improved, thereby maximizing the utilization of sulfur. Owing to these merits, when evaluated as a sulfur host for lithium-sulfur batteries, the MoS2/C hollow spheres exhibit appealing electrochemical performance with an impressive specific capacity of 1082 mA h g−1 at 0.1 C, excellent rate capability and superior cycling stability with a low fading rate of 0.04% per cycle.

Polyaniline (PANI)-based networks combined with Fe3O4 hollow spheres and carbon balls (FCP) for improved electromagnetic wave (EMW) absorption were investigated using an easy-to-industrialize solvothermal and physical method. Hollow structure Fe3O4 spheres with a lower density than that of the common solid sphere were prepared. As a thin and light magnetic material, Fe3O4 hollow spheres generate magnetic loss, carbon balls and PANI networks generate dielectric loss. The magnetic and conductive parts play appropriate roles in achieving complementarity in the EMW absorption. The relatively high specific surface area introduced by PANI networks promotes interfacial polarization and further supports dielectric loss. In conclusion, the above reasons provide multiple attenuation mechanisms. Samples FCP1 (−65.109 dB, at 12.800 GHz, 1.966 mm, from 5.6 to 18.0 GHz) and FCP2 (−61.033 dB, at 8.480 GHz, 3.328 mm, from 4.3 to 18.0 GHz) demonstrated a wide bandwidth, a small thickness, a minimum reflection loss (RL), and a low loading ratio (25%) in paraffin-based composites. Specifically, their loading ration of 25% is much lower than the loading ratio of conventional materials (usually 50% and above). In addition, the bandwidth is excessively wide, above 12 GHz, possessing good absorption performance in continuous intervals with different thicknesses. Such excellent characteristics have rarely been reported in literature.

In this study, the macro-structure of quartz flocs was assessed from X-ray computed tomography images. An image segmentation workflow was established to identify the floc sub-units that comprised each macro-floc, which permitted the macro-structure to be defined in terms of the number, size, and connectivity of the sub-units. A simplified structural model of non-penetrating spheres was used to understand the scaling relationships of the macro-floc properties. It was found that although sub-unit size varied widely, there was a limiting volume (2.8 × 106μm3), above which floc growth occurs only by sub-unit aggregation. This approach permits the quantification of macro-floc structure and composition in 3D on the scale of tens of μm to the mm scale. Knowledge of macro-floc structure allows a deeper understanding of the role of macro-floc breakage and re-arrangement in subsequent dewatering treatments such as thickening or filtration.

Empirical correlations and experimental works relating the drag coefficient (CD) of spheres to the Reynolds number (Re) and Re to the Archimedes number (Ar) were reviewed with a focus on the correlations applicable to the entire Re range. In addition, experiments with various spherical particles and fluids for the entire range of Re were conducted using high-speed video and added to the literature data. One of the correlations from the literature for Re-Ar and a modified correlation for CD–Re were found to best fit the experimental results. The analysis also established new correlations for Re–Ha (a non-dimensional number for velocity not including particle size) and CD–Ar. The latter is easier to use than the common CD–Re curve.

International audience; We have measured the three-dimensional coordinates of retroreflecting glass spheres using a multilateration technique. To this end, the distances between each target and our measurement heads have been determined by an in-house prototype of electro-optical absolute distance meter. The used targets are spheres of glass refractive index n=2 and of diameter 14.2 mm. They offer a much larger aperture than corner cubes and a lower cost, but they present a low reflectivity. However, this paper shows that with a proper collimation of the laser beams it is possible to reach a range of operation of 20 m. The standard uncertainty on such distances is better than 11 µm, including the mechanical errors of the gimbal mechanisms of our aiming systems. This uncertainty has been validated thanks to a comparison with an interferometric bench. In addition, the measurement of the coordinates of 16 glass spheres using a self-calibration multilateration algorithm has also confirmed the performances of the developed system: the standard deviation on the position errors has been estimated to about 10 µm.

Apple is one of the most widely consumed fresh fruit in the world. Simulation of kinetics and physical aspects of fruit could be considered as an emerging technology in most of harvest and postharvest phases. Impact damage of fruit is a common phenomenon during handling and transportation, therefore, in this work, experimental and computational analysis of the free fall of apples was conducted. Discrete element method (DEM) simulations of a free fall drop test were performed for four different apple-shaped models. DEM simulations can lead to promising new insights in phenomena involved in particulate processes and discontinuous systems, in which the shape model used plays a key role. This work demonstrated that shape modelling in DEM simulation could be a potentially helpful tool for analysing collisions, and the behaviour and dynamics of particle–particle (apple–apple) and particle-surface (apple-surface) contacts. The computational time of DEM simulation increases when the complexity of apple shape increased. It was found in this work that an increase in the number of spheres in model apple increased the accuracy of the numerical results until a threshold number of spheres was reached. Exceeding that threshold resulted in a decrease in the accuracy of the model. A model of an apple consisting of 50 spheres in 5 sets predicted the end up locations of apples after free-fall with the least errors. It was therefore considered as the most appropriate method for modelling apples in DEM simulations.

Particle-processing industries, such as those for manufacturing pharmaceuticals, ceramics and polymers, require accurate and reliable monitoring and controlling techniques for particle-size distribution to stabilize product quality and maximize productivity. Imaging is a highly valuable monitoring technique because it can measure precise particle-size distributions by detecting particles individually and also can measure particle shape. However, detecting submicron particles or smaller is difficult due to the diffraction of light in the optics. We propose an imaging-based monitoring system that extends the detectable particle-size range towards the submicron level by combining particle-shade and scattered-light imaging. The system consists of newly developed optics and an analysis algorithm. We evaluated the accuracy of the proposed system using polystyrene standard spheres.

To study ellipsoidal and spherical particle flow, clogging behavior and unclogging dynamics, a series of numerical simulations were carried out using our validated 3-D coupled computational fluid dynamics–discrete element method (CFD–DEM) model. For the first time, the strength of clogging arches is assessed in terms of fluid pressure gradient, which can effectively break up the clog. The main findings are as follows. In a clogged assembly, only when the flushing fluid reaches the unclogging pressure gradient, the ellipsoidal and spherical particles can flow in a continuous state. For the ellipsoids and spheres with the same equivalent volume, the unclogging pressure gradient of an ellipsoidal assembly is 11.8 times higher than that of a spherical assembly. Clogging arches at the outlet show the highest strength when the longitudinal orientations of the ellipsoids are perpendicular to the outlet plane. In contrast, the formed arch has the lowest stability when the longitudinal orientations of the ellipsoids are in the same direction as the long side of the outlet, as shown in the graphical abstract. The unclogging pressure gradient of the former case is 1.9 times greater than that of the latter case. The granular arches observed in our 3-D model are categorized as complex 3-D backbone arches. In the flowing region, particles rotate nearly perpendicular to the outlet plane, especially those approaching the outlet. Moreover, triangular stagnant zones are formed on both sides of the bottom of the rectangular box. The model presented here offers a great promise for future investigation of various granular systems at the particle scale.

Discrete Element Method (DEM) simulations are carried out to investigate the packing structure of the vibrated mono-sized and polydisperse particle assemblies in slender prismatic containers. Quantities like void fraction distributions, coordination number distribution, Voronoi packing fraction distributions were analyzed. DEM simulations show excellent agreement with the experimental data. The transient response of the packing structure during the vibration of mono-sized spheres reveals that the crystallization starts at the walls. The packing structure's crystallinity enhances during vibration, increasing the packing density of the assembly. Vertical vibration is found to be more effective compared to lateral vibration. The packing structure is found to be independent of the container's orientation during the filling process. The influence of the ratio of the container dimensions to mean particle diameter (X/dm) and polydispersity (λ) on the packing structure is analyzed. The results showed that the increase of X/dm ratio or λ, increases the random arrangement of particles.

Breakage occurs in several particulate systems that are simulated using the discrete element method (DEM), namely crushing and grinding as well as inadvertently in several others that include transportation, handling, mixing, separation and geotechnical applications. Different approaches may be used to describe particle breakage using DEM, but in cases in which particle breakage influences significantly the flow behaviour of the material, imbedding the breakage description in DEM provides the only valid alternative. This study describes the implementation of a detailed breakage model based on particle replacement with spheres in the commercial software EDEM. It accounts for variability and size-dependency in particle fracture energies, weakening of particles by unsuccessful stressing events, as well as addressing several reported shortcomings in sphere replacement schemes. The model is verified in great detail on the basis of single-particle breakage information and validated using measurements in unconfined particle beds of mineral ores.

To actually describe the flow behaviors of particles in the liquid-solid fluidized bed, the effects of liquid film covered on the particles surface and the sphericity of particles need to be considered for quasi-spherical wet particles. Liquid-solid fluidization characteristics are predicted using a two-fluid model incorporating with the kinetic theory of rough spheres (KTRS) model. Simulation results show that the normal restitution coefficient for wet particles covered liquid film increases with an increase of the particles diameter. As for the sphericity of particles, a higher sphericity of particles gives rise to a lower granular temperature and higher solids pressure and viscosity. Also, the normal restitution coefficient of quasi-spherical particles is relatively small, compared with completely sphere. The simulation results obtained by the kinetic theory of rough spheres model for quasi-spherical wet particles are in satisfactory agreement with the experimental data from Lu et al.

Rational design of the morphology and structure is important for the functional materials to improve their physicochemical properties. Herein, we design hierarchically three-dimensional (3D) structures assembled with yolk-shelled spheres-supported nitrogen-doped CNTs (NCNTs) using Ni(OH)2@SiO2 core-shelled spheres as precursors for electromagnetic wave absorption. In the 3D structures, the yolk materials are SiO2 spheres, while the shell materials are N-doped carbon layers containing Ni, Si and O elements. Importantly, The NCNT arrays with encapsulated Ni NPs are branched out from the yolk-shelled spheres. The hierarchical structures feature the merits of both yolk-shelled and 3D structures. Furthermore, the SiO2 sphere in the 3D structure can tune the electrical conductivity, affording our hierarchically 3D structure better impedance matching characteristic for electromagnetic wave absorption. As a result, the reflection loss and effective absorption bandwidth of our optimal 3D structure can reach −59.90 dB and 4.24 GHz, respectively, while the thickness of the absorbing film is only 1.4 mm, superior to most of reported carbon-based absorbers. The present method for the regulation of the structure and morphology provides an efficient way to construction of high-performance electromagnetic wave absorbers.

Hollow carbon spheres (HCSs) with flexible morphology configuration and pore structure have always been expected owing to their promising broad applications. In this work, chemical reaction kinetics guided strategy was proposed to tailor the size and pore structure of HCSs based on the modified stober method. By varying the reaction temperature and the moment of adding carbon precursors to the solution of tetrapropyl orthosilicate (TPOS), the particle size, cavity diameter, shell thickness and pore size could be tuned conveniently. By altering the reaction temperature from 6 to 45 °C or varying the time-lag of adding carbon precursors from 0 to 180 min, the size, shell thickness and pore size of HCSs could be successfully tailored in the range of 199–697 nm, 10–104 nm and 4.35–18.87 nm, respectively. Moreover, the resulting HCSs not only exhibited excellent adsorption for Vitamin B12 (VB12), methylene blue (MB) and Cr(Ⅵ), but also featured with selective adsorption for different-sized adsorbates. This demonstrates that the chemical reaction kinetics guided pore structure tuning strategy could be an effective way to develop adsorbents with specific pore structure.

Two special tetrahedra packing clusters were analytically calculated and discussed. Diamond and double-diamond, periodic superstructures emerge. Both structures exemplify an efficient, congruent tetrahedra space tiling strategy. The diamond superstructure exhibits a remarkable packing density of φ ∼ 0.76 exceeding maximal density for the packing of equal spheres. The presented architectures display long range order with specific, repetitive structural motifs. Due to their simple tetrahedral symmetry, the investigated clusters have the potential to become interesting, unique sub-units both in construction technology and in self-assembled systems design. The modified structure of presented cluster can entirely tile three-dimensional Euclidean space ℝ 3 through periodic tessellations. Moreover, detailed analysis of the cluster enables definition of a new plesiohedron.

We establish a method of scaling spheres for the integral system { u ( x ) = ∫ R n | y | a v p ( y ) | x − y | n − α d y , x ∈ R n , v ( x ) = ∫ R n | y | b u q ( y ) | x − y | n − β d y , x ∈ R n , where 0 α , β n , a > − α , b > − β and p , q > 0 . By using this method, we obtain a Liouville theorem for nonnegative solutions when 0 p ≤ n + α + 2 a n − β , 0 q ≤ n + β + 2 b n − α and ( p , q ) ≠ ( n + α + 2 a n − β , n + β + 2 b n − α ) . As an application, we derive a Liouville theorem for nonnegative solutions of the polyharmonic Henon-Hardy system { ( − Δ ) m u ( x ) = | x | a v p ( x ) in R n , ( − Δ ) l v ( x ) = | x | b u q ( x ) in R n , where m and l are integers in ( 0 , n 2 ) .

Discrete element method (DEM) is an effective approach to investigate non-spherical granular systems that are widely encountered in nature, industry, and our daily life. To describe the complex shapes of non-spherical particles, different particle shape representation approaches have been developed. In this paper, comparative study of modeling tablets using multi-sphere approach, multi-super-ellipsoid approach, and polyhedron approach is done to investigate the effect of different approaches. The accuracy of these approaches is testified by experiments and corresponding simulations of the packing, heap forming, and the flow in a rotating drum with two kinds of biconvex tablets firstly. Then the simulations of the flow of two kinds of biconvex tablets in a horizontal rotating drum are carried out by DEM. The simulation results are compared to discuss the effect of different approaches, which include the repose angle, the tablet orientation, the axial movement and mixing, the contact number, the percentage of the tablets reaching the free surface of the granular bed, and the computational efficiency. The results show that the simulations using multi-super-ellipsoid approach and polyhedron approach have some differences with those using multi-sphere approach.

Size-controllable double-shell hollow TiO2@SiO2 spheres (DHTSs) were fabricated using a simple sol-gel reaction. The size of DHTSs was controlled by using PS spheres with different size as templates. Moreover, DHTSs was also incorporated into waterborne polyurethane (WPU) matrix to prepare WPU/DHTSs composite film as glass coating. The effect of the diameter of DHTSs on the transparency, thermal insulation and UV-shielding properties of WPU/DHTSs composite film were investigated in detail. And the results revealed that the composite film with 230 nm-sized DHTSs exhibited the optimum performance. In addition, the temperature rise rate in the chamber fitted with the glass coated by WPU/DHTSs composite film (26%) was lower than that fitted with the common glass without coated by anything (48%). Therefore, the transparent coating with excellent thermal insulation and good UV-shielding properties will become a potential energy saving building glass coating.

The Hertz contact law for two linear elastic spheres plays a very important role in the discrete element method (DEM). Within the classic Hertz contact theory, the contact strain energy distribution in the two contacting spheres is analytically derived, which states that the ratio between the strain energies stored in the two spheres is solely dependent on their material properties, regardless of their radii. This strain distribution law is generally valid for non-spherical and other contact cases, provided that the two surfaces in contact can be reasonably treated as two elastic half-spaces and that the deformation is small. The independence feature of the law from the contact geometry also greatly facilitates the computation of the contact strain energy stored at particle level. As a direct consequence of this law, the contact point between two particles in DEM could also be determined. The numerical simulations demonstrate good agreement between the theoretical prediction and the numerical results for the tested cases involving spheres and ellipsoids with varying sizes and material properties.

This paper aims to establish the relationships between microscopic and macroscopic properties for uniform sphere packings under gravity. The packings are generated by the discrete element method under different conditions with the packing density ranging from about 0.2 to 0.74. The microscopic properties are the structural properties commonly used, including coordination number and various topological and metric properties from the Voronoi-Delaunay tessellation. The results show that these properties can be correlated with packing density. The correlations can be used to estimate different structural properties which are otherwise difficult to obtain in practice.

This paper is dedicated to the effective viscosity of suspensions without inertia, at low solid volume fraction ϕ. The goal is to derive rigorously a o ( ϕ 2 ) formula for the effective viscosity. In [17] , [19] , such formula was given for rigid spheres satisfying the strong separation assumption d m i n ≥ c ϕ − 1 3 r , where d m i n is the minimal distance between the spheres and r their radius. It was then applied to both periodic and random configurations with separation, to yield explicit values for the O ( ϕ 2 ) coefficient. We consider here complementary (and certainly more realistic) random configurations, satisfying softer assumptions of separation, and long range decorrelation. We justify in this setting the famous Batchelor-Green formula [3] . Our result applies for instance to hardcore Poisson point process with almost minimal hardcore assumption d m i n > ( 2 + e ) r , e > 0 .

Na3(VO)2(PO4)2F (NVPOF) has been considered as one potential candidate for sodium-ion batteries because of its high operating voltage and theoretical capacity. However, the poor intrinsic electronic conductivity significantly restricts its widespread application. In response to this drawback, we adopt the optimization strategy of tuning the morphology and structure to boost the electrical conductivity and mitigate the capacity fading. In this paper, NVPOF microspheres with unique porous yolk-shell structure were fabricated via a facile one-step solvothermal method for the first time. By monitoring the morphological evolution with time-dependent experiments, the self-sacrifice and Ostwald ripening mechanism from rough spheres to yolk-shell structure was revealed. Benefited from the favorable interwoven nanosheets shell, inner cavity and porous core structure, the resulting NVPOF electrode exhibits superior rate capability of 63 mA h g−1 at 20 C as well as outstanding long-cycling performance with the capacity retention up to 92.1% over 1000 cycles at 5 C.

Nano-oxide hollow structures have a wide range of applications in catalysis, but the preparation of multi-shelled composite oxide hollow structures still presents a major challenge. Herein, well-dispersed multi-shelled MnO2–Co3O4 hollow spheres have been successfully prepared via a facile “Kirkendall effect” method employing carbon spheres as sacrifice templates. The shell of the hollow spheres was constructed by interconnected Co3O4 nanosheets and catkin-like MnO2 nanorods. The interdiffusion of Carbon chain and MnO4− during synthesis could be the possible formation mechanism for the special morphology. Benefiting from the hierarchical porous structure, high surface area and strong synergistic effect between Co3O4 and MnO2 was obtained, the as-prepared Co–Mn composite hollow spheres showed reliably high activity and recycle stability for CO oxidation, achieving the complete CO conversion at 137 °C without significant decrease in activity after five cycles and 10h constant-temperature reaction. We believe that this work will provide a new method for the preparation of multi-shell composite hollow spheres.

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

Ammonia borane (AB) is considered to be a promising solid hydrogen carrier. In this work, poly(N-vinyl-2-pyrrolidone) (PVP)-protected platinum nanoparticles are supported on γ-methacryloxypropyltrimethoxysilane (γ-MPS) modified silica spheres (Pt-PVP/SiO2(M)), which are firstly used as highly efficient catalysts for hydrolysis of AB. Platinum nanoparticles possess a tiny size of 2–3 nm and are uniformly dispersed over modified silica spheres. Pt-PVP/SiO2(M) catalysts with a Pt loading amount of 1.30 wt% show the highest catalytic activity with a turnover frequency (TOF) value of 371 molH2 molPt−1 min−1 (866 molH2 molPt−1 min−1 corrected for the surface atoms) at 25 °C. The activation energy is calculated to be 46.2 kJ/mol. Furthermore, owing to the synergistic effect between the modifier of silica spheres and the capping agent of metal nanoparticles, Pt-PVP/SiO2(M) catalysts have a higher loading amount (8.7 and 6.5 times) and TOF value (4.8 and 5.5 times) than the counterparts prepared without γ-MPS and PVP, respectively.

Improved knowledge of cyclic contact behaviour of brittle particle can deepen the understanding of cyclic behaviour of brittle particle assembly and help to obtain more realistic numerical simulations. The cyclic compression tests of rock spheres were performed and the results were analyzed through elastoplastic contact theory. Three modified contact models and a semi-theoretical cyclic contact model were proposed. Local plastic deformation and macroscopic tensile cracks were observed. The cyclic compression tests reveal the significant difference of cyclic contact behaviour between the first cycle and the subsequent cycles. The modified Kogut and Etsion loading model and modified Etsion unloading model perfectly agree with the experimental force-displacement curve of the first cycle. The equivalent modulus of elasticity increases with the increasing number of cycle and decreases with the increasing maximum contact force. All the main characteristic of cyclic contact behaviour can be well reproduced by the proposed semi-theoretical cyclic contact model

Inhomogeneous structures have significant impact on the drag. In this work, direct numerical simulations of flows past fluidized spheres are performed to investigate the effect of inhomogeneities on the drag at low Reynolds numbers. The inhomogeneities are quantified using various sub-grid quantities including a newly defined quantity named the solid drift flux, which is a measure of the correlation between the gas volume fraction and the particle phase velocity. Following the methodology of Rubinstein et al. (2017), a new drag model that depends simultaneously on the solid drift flux and the scalar variance of solid volume fraction is then developed. Given that these two sub-grid quantities are readily available in Eulerian-Lagrangian (EL) simulations, the developed model can be directly used in EL simulations without any additional closures for sub-grid quantities. An a priori analysis demonstrates that this model achieves satisfactory performance in predicting the drag in inhomogeneous structures.

Packing properties are determined by the dynamic deposition history and affected by many variables. In this work, DEM is used to study the effects of dropping height, deposition intensity and friction coefficient on the dynamic response and stable-state packing properties of ellipsoidal particles. The results demonstrate that with dropping height increasing, packing density increases but the bed becomes less ordered. Dropping height affects the densification process of ellipsoids more significantly than spheres. At high dropping height, the transition period of the orientation angle in the densification process almost disappears for oblate particles, while it becomes longer for prolate particles. With the increase of deposition intensity, packing density decreases significantly, but orientational order changes slightly. With the increase of sliding friction coefficient, packing density and orientational order decrease dramatically. The difference in packing density is mainly caused by dynamic pouring process rather than the densification process.

Particle-resolved computational fluid dynamics simulations of flow and pressure drop in fixed beds of spheres give poor accuracy at higher Reynolds number (Re) under turbulent conditions. The influence of meshing is investigated for two cases, a face centered cubic packing with no wall effects, and a narrow bed of tube-to-particle diameter ratio three with strong wall effects. Local approaches to meshing at contact points were compared, using both surface flattening (caps) and bridging between spheres. Accurate results for pressure drop at moderate to high Re > 1000 required computationally expensive fine uniform meshes, however at highest Re pressure drop appeared to be low. The use of boundary adaption improved results with less expensive meshes. The aspect ratio of surface prisms and the sizes of the bridges used at contact points had strong effects. Velocity profiles were much less sensitive to the mesh refinement and could be obtained at reasonable cost.

In this work, we aim at the study of the statistical and thermal properties of the oil-in-water Pickering emulsions which are stabilized by strongly adsorbed charged nanoparticles on the surfaces of their droplets. In this study, we have adopted a pair-potential of Sogami-Ise type which is the sum of a repulsive part and an attractive one; and depends, in particular, on the salt-concentration. In this work, we were interested in two kinds of problems, namely (1) the determination of the structural and thermal properties of Pickering emulsions, and (2) the investigation of the scaling of cluster aggregation of the oil-droplets, as the salt-concentration is varied, keeping the other pertinent factors (surface-charge of oil-droplets, their size and density and bath temperature) fixed. For the two problems, we regarded the oil-droplets as monodisperse small spheres assimilated to charged soft-colloids. First, we have computed all of the structural properties (through the radial-distribution-function) versus the salt-concentration using the Integral-Equation Theory with the Hybridized-Mean-Spherical Approximation. Second, using the same numerical appoach, we have determined the thermal properties (through pressure, internal energy and isothermal compressibility). Finally, we have demonstraded that the oil-droplets aggregate has a fractal structure, with the help of an elaborated scaling model which was found to be in good agreement with Integral-Equation Theory.

The feasibility of using electrostatic forces to stabilize a close-proximity leader-follower formation is investigated. The leader craft is equipped with a set of affixed spheres whose charge is modulated to hold the charged follower craft along a proscribed trajectory to its nominal leader-relative position. This charge structure and the follower craft are constrained to remain in the plasma wake generated behind all LEO craft because the more-dense ambient plasma outside the wake prevents object charging and electric field propagation. Once the formation is achieved, a controlled electric field is generated by the leader to counter relative accelerations from perturbations like differential drag and solar radiation pressure, holding the follow near its nominal position. Two controllers are derived for the system described, incorporating Coulomb accelerations and linearized gravity and drag accelerations. Simulations are run under unmodeled perturbations and sensor noise for different scenarios, demonstrating the challenges and benefits associated with electrostatic actuation.

The rapid development of internet and internet of things brings new opportunities for the expansion of intelligent sensors, and acetone as a major disease detection indicator (i.e., diabetes) making it become extremely important clinical indicator. Herein, uniform mesoporous ZnO spheres were successfully synthesized via novel formaldehyde-assisted metal-ligand crosslinking strategy. In order to adjust the pore structure of mesoporous ZnO, various mesoporous ZnO spheres were synthesized by changing weight percentage of Zn(NO3)2·6H2O to tannic acid (TA). Moreover, highly active heterojunction mesoporous ZnO/Co3O4 has been fabricated based on as-prepared ultra-small Co3O4 nanocrystals (ca. 3 nm) and mesoporous ZnO spheres by flexible impregnation technique. Profit from nano-size effect and synergistic effect of p-n heterojunction, mesoporous ZnO/Co3O4 exhibited excellent acetone sensing performance with high selectivity, superior sensitivity and responsiveness. Typically, 5 wt% Co3O4 embedded mesoporous ZnO sphere showed prominent acetone response (ca. 46 for 50 ppm), which was about 11.5 times higher than that in pure ZnO sensing device, and it was also endowed high cyclic stability. The nanocrystals embedded hybrid material is expected to be used as promising efficient material in the field of catalysis and gas sensing.

This paper proposes a sphere-triangle contact model for three-dimensional sphere discontinuous deformation analysis to simulate complex boundary face problems often encountered in engineering. First, the detection of sphere-triangle contact and the calculation of corresponding sphere-triangle contact submatrices for building a sphere-triangle contact model are described. Then, the correctness of the proposed model is preliminarily verified by simulating the sphere-plane/edge/vertex contact, sphere-triangle friction problem and a complex boundary face problem. Furthermore, a rigorous open-close iteration is proposed to guarantee the correctness of setting penalty springs for sphere-triangle contacts, to ensure computational stability of three-dimensional sphere discontinuous deformation analysis. Meanwhile, two imperceptible fatal errors (i.e., direction deflection error and oscillation error) hidden in the sphere-triangle contact model are estimated, which reveals that a larger sphere or a higher collision velocity at a sphere-triangle contact leads to larger errors. In addition, an algorithm for excluding invalid contacts is proposed to avoid these fatal errors, enhancing the robustness of the proposed contact model. Finally, a landslide simulation with 80,974 spheres, 76,382 triangles and 150,000 calculation steps is conducted, further validating the proposed model in large-scale simulations. This work indicates the feasibility of the proposed model for simulating complex boundary face problems.

Accurate asymptotic solutions are presented for axisymmetric deformation of thin layers constrained by either two rigid plates or two rigid spheres. Those solutions are developed using Saint-Venant's principle and the layer thinness as the only assumptions. The solutions are valid in the entire range of Poisson's ratios, and allow one to distinguish among compressible, nearly incompressible, and incompressible layers. That classification involves both material and geometric parameters., 38 pages, 4 figures

Welded hollow spherical joints are comprehensively used in spatial steel structures. However, the original joints cannot meet the strength requirements in some conditions, such as the corrosion, the fire and the change of structural load. Therefore, it is necessary to explore effective methods of strengthening the joints to maintain the durability and safety of the structures. This paper proposes and investigates the method of strengthening welded hollow spherical joints using unidirectional annular ribs. Experiments were conducted to study the failure modes, axial load–displacement curves and ultimate bearing capacity under axial compressive and tensile load. Nonlinear finite element (FE) model was established and verified to study the failure mechanism and bearing capacity of the test joints using ABAQUS. Based on the accurate FE model, parametric studies were performed to study the influence of the thickness and height of unidirectional annular rib, the dimensions of the steel tubes and the welded hollow spheres on the capacity of the joints. Practical design formulas were proposed based on the test and the FE analysis. The conclusions presented in this study can provide theoretical and numerical basis for the design of welded hollow spheres strengthened with unidirectional annular ribs in spatial steel structures.

Carbon nanotubes (CNTs) have important application in electromagnetic wave absorption due to their unique tubular structure, lightweight feature and high electrical conductivity. However, sole CNTs suffer from bad impedance matching characteristic, leading to unsatisfactory absorption performance. Herein we propose a universal SiO2-assisted strategy to fabricate Ni nanoparticle-encapsulated nitrogen-doped CNTs on the SiO2 spheres (Ni@NCNT@SiO2). Due to the spatial separating effect, the formation of large metal aggregates and large-sized NCNTs in the products are avoided effectively. In the meanwhile, the ideal impedance matching characteristic is also achieved due to the introduction of the non-conductive SiO2 spheres. As a result, even with a low matching thickness (1.3–2.0 mm), the reflection loss values of Ni@NCNT@SiO2 reaches −30 dB. Furthermore, the proposed method can be also used to fabricate Fe3C/Fe@NCNT@SiO2 and Co@NCNT@SiO2 with satisfactory absorption properties, demonstrating its universality for synthesis of high-performance absorbers based on CNTs.

Float-sink of large objects (on order of cm) in a gas-solid fluidized bed of powder (on order of 100 s of microns) based on density difference has been utilized for dry density separation in industry. The air velocity u0/umf is one of the important factors operating the fluidized bed, where u0 and umf are the superficial air velocity and the minimum fluidization air velocity, respectively. It is empirically known that the sinking of heavy objects is “occasionally” unstable in the fluidized bed combustor, for which the higher air velocity u0/umf > 4 is used. Unstable sinking means heavy objects that are expected to sink but sometimes do not. However, the precise conditions at which the unstable sinking occurs are not clear. In this study, we investigated the float-sink characteristics at a given air velocity u0/umf = 2–7 using glass beads of size Dgb = 425–600 μm and 600–850 μm as the fluidized powder bed media. The float-sink experiments were carried out at the bed height hgb = 150 mm and 75 mm using density adjusted spheres (diameter = 30 mm). We found that the spheres stably float or sink based on density difference at Dgb = 425–600 μm & hgb = 150 mm and at Dgb = 600–850 μm & hgb = 75 mm. However, the unstable sinking does occur at u0/umf > 4 at Dgb = 600–850 μm & hgb = 150 mm. These results indicate that the powder size and the bed height are key factors to induce the unstable sinking at the higher air velocity.

The separation behavior of two bodies was experimentally investigated in a shock tunnel. Simple-shaped bodies, including a cylinder, cube, and sphere, with a size of 3 or 5 mm were used as the test models. The two contact models with a plane-exposed configuration were mounted using a thin wire, and the separation behavior was observed and analyzed using the shadowgraph technique. The surface roughness effect on the separation of two spheres was also considered. Particularly, attention was given to the lateral velocity. It was found that the spheres had a constant final lateral velocity after the shock interaction, whereas the velocities of the cylinders and cubes were determined by the rotational motion of the body. Based on the experimental data, a reentry trajectory analysis was conducted using Monte Carlo simulation. The results showed large ground footprint and downrange differences depending on the characteristics of the body, implying the importance of separation behavior for a reentry analysis.

Particle-unresolved Eulerian/Lagrangian simulations (DEM/CFD) of static homogenous particle ensembles are compared to direct numerical simulations (DNS) performed with the Lattice-Boltzmann method (LBM). Eliminating particles’ motion, the accuracy of the CFD can be examined in a targeted way. Local quantities at the particle scale such as drag, lift and Nusselt numbers are thus evaluated in detail. In particular, the influence of particles’ shape on numerical accuracy of the non-resolved DEM/CFD utilizing different correlations is studied. As particle shapes spheres, cylinders and cubes are examined applying the widely used multi-sphere method (MSM) for particle approximation. The simulations are conducted for two different exemplary voidages of e = 0.6 and e = 0.8 in the Reynolds number range of Re p = 10 - 300 and the Prandtl number Pr = 1 . The study reveals issues related to non-resolved DEM/CFD simulations especially in the case of non-spherical particles and provides important details for general DEM/CFD applications as well as for future closure derivations.

Mobile robots find now more and more applications in Space science and technology. So prototypes of mobile robots (bodies with magnetizable materials) being controlled by an alternating uniform magnetic field are proposed. An easy-to-implement alternating (pulsating) uniform magnetic field inclined to a horizontal plane is used to control prototypes. In experiments two samples of mobile robots are used: a spiral with a magnetizable elastomer and two magnetizable spheres with a non-magnetic elastic coupling. Size of proposed mobile robots can be quite small. The directed motion of these mobile robots in different surrounding viscous fluids along a horizontal bottom of a vessel in an alternating magnetic field is investigated experimentally and theoretically. Interesting effects are found experimentally: movement direction of robots dependents on viscosity of the surrounding fluid, and velocity value of robots in glycerin (high viscosity) are greater than in water (low viscosity). The mathematical model well describing experimental effects is proposed. Numerical calculations show that the motion of such robots occurs in opposite directions, when they move in water and glycerin.

This paper presents a numerical study on the self-assembly of mono-size granular spheres with periodic boundary conditions under uniform and non-uniform 3D vibration. For uniform 3D vibration, the vibration conditions for self-assembly are similar to those under 1D vertical vibration. For non-uniform 3D vibration, slight horizontal vibration added to 1D vertical vibration can significantly promote or depress self-assembly. Moreover, under 1D or uniform 3D vibration, self-assembly results in a RHCP (random hexagonal close packed) structure, while under certain non-uniform vibration, a packing can self-assemble into a nearly pure FCC (face centered cubic) or HCP (hexagonal close packed) crystal structure. The microscopical analyses on the local structures, dynamics and forces provide rich insight into the different self-assembly processes under different vibration modes. These results can help understand the self-assembly of granular materials under vibration and guide how to control the structure of packed beds.

It has been a longstanding question how stars are packed or distributed in the universe. Here we show that the spatial distribution of stars follows some geometric rules although there may be local inhomogeneities. The topological and metric properties of their Voronoi tessellations exhibit a lognormal distribution. Moreover, these distributions can be connected with those established for the packing of spheres, corresponding to the loosest packing state. The findings provide a new angle to understand the packing structure of stars in the universe.

The discrete element method (DEM) which is used to simulate granular flows often assumes spherical shape for particles. This assumption is legitimized by the added complexity of non-spherical shape representation, contact detection and computational cost. In this work, the difference between the dynamics of non-spherical and spherical particles was studied in detail by a combined physical and DEM modeling approach. An in-house developed DEM software called KMPCDEM©, which was coded to handle non-spherical particles, was used to simulate the behavior of particles. To calibrate the model parameters, a model tumbling mill (100 cm diameter and 10.8 cm length) with one transparent end was used which made accurate photography possible. The tests were performed at filling of 20% and mill speed of 85% of critical speed with steel balls and wood cubes. In the simulation, each cubical particle was represented with clusters of spheres (with identical size) by particle packing algorithm for contact detection and contact-force calculation. Comparison of the simulation and experimental results showed that the difference between the measured and predicted impact toe, shoulder angle and bulk toe angle were 3, 4 and 5°, respectively. The significant change in the charge movement and structure on account of non-spherical particles was reflected in the amount of in-flight charge, and positions of shoulder, impact toe and bulk toe. It found that there was a 17% difference in the amount of in-flight of charge between cubical and spherical particles. The marked difference was attributed to higher interlocking of non-spherical particles in comparison to spherical balls. The results showed that cubical particles participated 5% more in the high energy impact action compared to that of the spherical particles. The simulation computation time increased by 35 times when the shape of particles changed from spherical to cubical.