Identical Spherical Particles Research Articles

Experimental Study on Coefficient of Restitution of Small-Sized Spherical Particles during Low-Speed Impact

This study presents experimental investigations on the normal restitution coefficients of a titanium bead (Ti), zirconia bead (ZrO2), and amorphous zirconium alloy sphere (Amor). The research explores the influence of particle diameter and collision velocity on the normal restitution coefficient between two independent, identical spherical particles of different materials. The experimental findings demonstrate that increasing the particle diameter results in more effective plastic deformation, leading to higher energy losses and, subsequently, smaller coefficients of restitution. Similarly, higher particle velocities cause more energy dissipation during collisions, resulting in smaller restitution coefficients. Comparing particles of different materials, those with larger yield strengths exhibit more elastic behavior, experience less initial energy loss due to deformation, and reach the maximum restitution coefficient (elastic state) with fewer collisions. This finding suggests that material properties significantly influence the overall energy dissipation and elastic response in the particles. To validate the experimental results, existing models are compared and discussed. Furthermore, potential physical mechanisms responsible for the observed behavior are explored, providing valuable insights into the collision dynamics in spherical particle interactions. Overall, this study contributes to a better understanding of the factors affecting the normal restitution coefficient in particle collisions, enabling the design and optimization of particle systems for diverse applications in condensed matter and related fields.

Direct numerical simulations of oscillatory boundary layers over rough walls

Numerical simulations of turbulent oscillatory flow over a bed made of fixed, identical spherical particles have been performed. Oscillations are imposed through a shear-driven forcing by means of an harmonic velocity boundary condition on the bed. A parametric study on the effect of the particle size and Reynolds number, spanning from the laminar to the fully-turbulent regimes, has been performed. Results show that the temporal evolution of the flow over the rough bed is modified compared to the classical Stokes’ solution for smooth-wall laminar boundary layers. In the turbulent cases, the phase shift in the velocity at various distances from the bed is reduced compared to the laminar case. The phase shift reduction seems predominantly dependent on the Reynolds number rather than the bed morphology, which suggests that a unique curve may exist for large enough values of the Reynolds number. Turbulence is observed during the deceleration phases of the cycle, with the presence of a logarithmic layer in the velocity profile, and “canonical” distribution of Reynolds shear stress and turbulent kinetic energy production. During the acceleration, the logarithmic region is suppressed and the Reynolds shear stress changes sign. Nevertheless, the turbulent kinetic energy production becomes only slightly negative, because the shear is also very small during these phases. A good correlation between Reynolds and shear stresses is also evidenced from the eddy viscosity profiles, which show the presence of plateau in the outer layers approximately constant across the phases of the cycle. Turbulence in the outer layers is related to structures which develop during previous cycles and propagate from the bed to the bulk of the channel. When the flow is fully developed, anisotropy maps show similar distributions to unidirectional wall-bounded flows, while departures from canonical distributions during the transient phases are mild, because the flow responds very rapidly to the time-varying forcing.

Optical characteristics of a monolayer of identical spherical particles in an absorbing host medium.

The problem of light interaction with a 2D ensemble of homogeneous spherical particles embedded into an unbounded homogeneous absorbing host medium is considered. Based on the statistical approach, the equations are derived to characterize optical response of such a system with taking into account multiple scattering of light. Numerical data are presented for the spectral behavior of coherent transmission and reflection, incoherent scattering, and absorption coefficients of thin dielectric, semiconductor, and metal films containing a monolayer of particles with various spatial organization. The results are compared with the characteristics of the inverse structure: particles consist of the host medium material and vice versa. Data for the redshift of the surface plasmon resonance of the monolayer of gold (Au) nanoparticles in the fullerene (C 60) matrix are presented as a function of the monolayer filling factor. They are in qualitative agreement with the known experimental results. The findings have potential applications in the development of new electro-optical and photonic devices.

Optimization of 10 N Monopropellant High Test Peroxide Thruster for Space Applications

Monopropellant thruster is one of the most propulsion system types developed in the space industry. This system uses a single type of propellant that reacts in porous medium catalytic packed bed to generate thrust in the form of hot gases. The last decade, green propellant hydrogen peroxide (H2O2), also known as High Test Peroxide (HTP), thanks to its low cost and easy to store as liquid, is used as an alternative solution of hydrazine which is very toxic and not environmentally friendly. In the current study, hydrogen peroxide monopropellant thruster is investigated for application in the future satellites. A numerical simulation is performed using the Computational Fluid Dynamics (CFD) software ANSYS Fluent in order to simulate fluid flow of hydrogen peroxide in thruster, and the finite volume method was employed for resolving the governing equation. Species transport model is applied in the single-phase reaction simulation using the Eddy Dissipation model (EDM) for turbulence-chemistry interaction. A mathematical approach based on the local thermal non-equilibrium (LTNE) model is used to describe the heat transfer through solid and fluid phases in the packed bed consisting of identical spherical silver particles. Several simulations performed allowed an optimal design of the injector, catalyst bed length and diameter and nozzle geometry, to achieve a 10N monopropellant thruster with hydrogen peroxide at 87.5% concentration.

Resonant absorption of light by a two-dimensional imperfect lattice of spherical particles.

The light absorption and scattering by an infinite two-dimensional array with an imperfect lattice of identical spherical particles is considered based on the statistical approach to a description of electromagnetic wave interaction with particulate media. Absorption resonances due to the coherent component of scattered light (zeroth order of diffraction) and resonances arising from the excitation of a flux of incoherently scattered light (higher diffraction orders) propagating at grazing angles to the array plane are studied. The dependence of absorption on the degree of positional ordering of particles is considered. It is shown that with an increase in ordering, the spatial coherence of the light flux along the array plane increases and the absorption resonance becomes more pronounced. Data are presented for silver wavelength-sized particles for s- and p-polarized incident waves. It is shown that at small angles of incidence, the first diffraction order can arise at the wavelength of zeroth-order resonance. In this case, the contributions to absorption created by the coherent and incoherent components of scattered light are summed up. The value of the absorption coefficient can be close to 0.95. A comparison with data for a partially ordered array is carried out.

Аbsorption of diffuse light by 2D arrays of spherical particles

The problem of absorption of diffuse light by a 2D array of identical spherical particles is considered. The equations to solve this problem are derived on the basis of statistical approach. They can be used to match parameters of the array and the illumination system to get maximum absorption. The numerical results are presented for absorption coefficients of arrays with the imperfect triangular lattice and partially ordered structures of crystalline silicon and silver particles embedded in nonabsorbing medium, in the wavelength range 0.35 μm – 0.80 μm. The size of particles and their concentration are chosen so as to illustrate the dependence of light absorption on the angle of incidence under conditions of resonances due to the high spatial ordering of particles. The absorption coefficients of the arrays at diffuse and directional light illumination are compared.

The influence of Stefan flow on the flow and heat-transfer characteristics of spherical-particle pair in supercritical water

For any flow process of mixtures containing dispersed reactive particles, especially highly concentrated particles, the particle-particle, and fluid-particle interactions are very complex and affect the overall flow. Supercritical water gasification technology is a complex multiphase-flow process that occurs in high-temperature reactors. Under these conditions, the components of the particle surface are heated and gasify to form a Stefan flow (i.e., a mass flow), which modifies fluid-particle interactions. The interaction between particles and the influence of Stefan flow cannot be ignored. In this work, we consider the simplest case of two identical spherical particles with different relative orientations and particle distances and discuss the flow and fluid-particle heat-transfer characteristics by numerical simulation of supercritical water flowing around the fixed two-particle system. We are particularly interested in the fluid-particle interactions with different particle configurations under the influence of Stefan flow. Three particle configurations are possible: tandem, cross, and parallel. The flow field, Nusselt number, drag coefficient, and temperature distribution around the particles are all analyzed. In comparison with a single particle, the two-particle configurations significantly affect the drag coefficient, Nusselt number, and vortex structure and Stefan flow strongly affects the wake vortex structure of two particles with small particle distance, reducing the drag coefficient and Nusselt number.

Numerical study of a pair of spheres in an oscillating box filled with viscous fluid

When two identical spherical particles are submerged in an oscillating fluid, they align themselves perpendicularly to the direction of the flow, leaving a small gap between them. The formation of this structure is attributed to a non-zero residual flow known as steady streaming. We performed direct numerical simulations of a fully resolved, oscillating flow in which the pair of particles is modeled using an immersed boundary method. In equilibrium, the particles oscillate both parallel and perpendicularly to the oscillating flow. Two scaling regimes for the particle dynamics, which are related to changes in the (average) flow field, are observed.

Revisiting the Theory of Coagulation of Colloidal Dispersions: An Improved Expression for the Stability Ratio.

The stability of a colloidal dispersion has long been expressed in terms of the stability ratio. Based on the available theories of coagulation of colloidal dispersions, a novel expression, complying with the classical definition, is developed for the stability ratio. It accounts for the contributions of both primary and secondary minimum coagulations to the overall rate of coagulations. In addition, it can also be regarded as the result of a combination of the kinetic theory of an ideal gas and the Smoluchowski theory with Fuchs' correction, considering the interaction between identical spherical particles and their surfaces immersed in a symmetrical electrolyte solution. The agreement with experimental data suggested that it is superior to the classical ones in describing the weak dependence of the stability ratio on the particle size and the valence of the counterion, by emphasizing the importance of the secondary minimum coagulation in dispersion stability and the complementation between the two modes of coagulation.

Broadband antireflective random metasurfaces

In this work, we propose and numerically investigate broadband antireflective random metasurfaces. We demonstrate that a random monolayer of identical metallic subwavelength spherical particles, deposited on a substrate, is able to suppress the reflection in a broadband spectral region over a wide range of incident angles and that it is insensitive to the polarization. From the optical properties of a single spherical particle, we show that the annihilation of the reflectivity is due to the constructive interference between the radiated electromagnetic waves from the electric dipole and the electric quadrupole induced within the particles. The metasurfaces we propose in this work have significant opportunities in many technological areas, including display technologies, glass windows, automobile industries, solar harvesting, and detectors. Furthermore, they are suitable for fabrication; hence, experimental validation of our theoretical predictions is feasible.

Inviscid Suspension Flow along a Flat Boundary

A previously developed self-consistent field method is used to study an arbitrary finite set of identical spherical particles of arbitrary density moving in a uniform inviscid incompressible flow specified at infinity in the presence of a flat wall. For a given initial particle distribution in space, expressions for the particle and fluid velocities are derived taking into account the collective hydrodynamic interaction of the particles with each other and the wall. For a statistically uniform particle distribution in a semibounded inviscid fluid, analytical averaged particle and fluid velocity profiles are obtained in the first approximation with respect to the particle volume fraction in the suspension.

The influence of Einstein's effective viscosity on sedimentation at very small particle volume fraction

We investigate the sedimentation of identical inertialess spherical particles in a Stokes fluid in the limit of many small particles. It is known that the presence of the particles leads to an increase of the effective viscosity of the suspension. By Einstein's formula this effect is of the order of the particle volume fraction ϕ. The disturbance of the fluid flow responsible for this increase of viscosity is very singular (like |x|−2). Nevertheless, for well-prepared initial configurations and ϕ→0, we show that the microscopic dynamics is approximated to order ϕ2|log⁡ϕ| by a macroscopic coupled transport-Stokes system with an effective viscosity according to Einstein's formula. We provide quantitative estimates both for convergence of the densities in the p-Wasserstein distance for all p and for the fluid velocity in Lebesgue spaces in terms of the p-Wasserstein distance of the initial data. Our proof is based on approximations through the method of reflections and on a generalization of a classical result on convergence to mean-field limits in the infinite Wasserstein metric by Hauray.

Improving constant-volume simulations of undrained behaviour in DEM

In order to simulate undrained conditions using the discrete element method, a constant sample volume is often assumed. There are well-recognised problems with these constant-volume triaxial simulations, particularly of dense samples, which inhibit quantitative comparison with laboratory experiments. In this paper, four possible explanations for these problems with conventional constant-volume simulations of ideal spherical particles are explored, each of which has a physical basis: particle crushing, the presence of highly compressible air within the sample, or the reduction in stiffness due to particle surface asperities or non-spherical particle shapes. These options are explored independently and in combination through implementation in the open-source LAMMPS code. In situations where a significant amount of particle crushing occurs, it is important to incorporate this in the simulations so that stresses are not over-estimated. There is experimental evidence that irregular particles have lower Young’s moduli than the Hertzian spheres often used in DEM. In the absence of particle crushing, the most effective method to achieve more realistic stress–strain responses is to reduce the particle shear modulus substantially. This approach has the added computational benefit of enabling an increase in the simulation time-step.

Periodic particle arrangements using standing acoustic waves

We determine crystal-like materials that can be fabricated by using a standing acoustic wave to arrange small particles in a non-viscous liquid resin, which is cured afterwards to keep the particles in the desired locations. For identical spherical particles with the same physical properties and small compared to the wavelength, the locations where the particles are trapped correspond to the minima of an acoustic radiation potential which describes the net forces that a particle is subject to. We show that the global minima of spatially periodic acoustic radiation potentials can be predicted by the eigenspace of a small real symmetric matrix corresponding to its smallest eigenvalue. We relate symmetries of this eigenspace to particle arrangements composed of points, lines or planes. Since waves are used to generate the particle arrangements, the arrangement's periodicity is limited to certain Bravais lattice classes that we enumerate in two and three dimensions.

ARISE: A granular matter experiment on the International Space Station

We developed an experiment to study different aspects of granular matter under microgravity. The 1.5U small experiment was carried out on the International Space Station. About 3500 almost identical spherical glass particles with 856 μm diameter were placed in a container of 50 × 50 mm cross section. Adjusting the height between 5 and 50 mm, the filling factor can be varied. The sample was vibrated under different frequencies and amplitudes. The majority of the data are video images of the particles’ motion. Here, we first give an overview of the general setup and a first qualitative account of different phenomena observed in about 700 experimental runs. These phenomena include collisional cooling, collective motion via gas-cluster coupling, and the influence of electrostatic forces on particle-particle interactions.

Static and dynamic effective moduli of elastic-perfectly plastic granular aggregates under normal compression

Based on an existing simplified theoretical model for the normal contact interaction between two elastic-perfectly plastic spherical particles, we derived explicit expressions for the static and dynamic normal and dynamic tangential contact stiffnesses of elastic-perfectly plastic two-particle combination at pre-yield, yield, and post-yield conditions of normal loading. We used “static stiffness” or “loading stiffness” to refer to the slope of the force-displacement curve during monotonically increasing load. The “dynamic stiffness” or “unloading stiffness” refers to the stiffness that controls the speed of infinitesimal strain elastic waves propagating through the contacts. The static and dynamic contact stiffnesses are compared with numerical modeling of a two-sphere combination using the finite-element method. Furthermore, we used the explicit expressions for contact stiffnesses with the commonly used statistical averaging scheme to derive the static and dynamic effective bulk and shear moduli of a dry, random packing of identical elastic-perfectly plastic spherical particles. Elastic contact/mechanics-based effective medium models are unable to model the growth of contact area between inelastic (e.g., plastic) particles under normal force, which results in inaccurate predictions of contact stiffnesses and effective moduli. Once the particle reaches the limit of elasticity with onset of plastic deformation (yielding), further loading of two elastic-perfectly plastic spherical particles leads to a larger contact area than for two elastic particles under the same normal loading. As a result, after yielding, the dynamic effective moduli become stiffer than the corresponding moduli in the elastic case, whereas the static effective moduli remain constant, rather than increasing as in the elastic case.

Lift Off and Breakage of the Structure of Fractal - Like Aggregate

A new mathematical model of aggregate of N identical spherical particles is proposed. Model is able to simulate aggregates with different flexibility. Mutual forces in normal direction between primary particles are described by spring-mass system with parameters related to the material properties. The flexibility of aggregate structure is controlled by harmonic interaction functions. Developed model was used to study the lift-off phenomenon of aggregates in the fluid. Simulation were performed for numerically generated few population of fractal-like aggregates by Diffusion Limited Aggregation algorithm (DLA), which differ with number of primary particles in aggregate’s structure and fractal dimension. Numerical results show that aggregates with more open morphology with fractal dimension in the range of Df = 1.6 - 1.8 are lifted-off easier, compared to aggregates with compacted structure. The effectiveness of the lift off is enhanced by the deformation of the aggregate caused by the flexibility of its structure.

Preparation of Spherical FePO4 by Chemical Co-precipitation Combined with Spray-Drying

Well-shaped spherical agglomerates of FePO4 particles were prepared by a novel method: chemical co-precipitation combined with spray-drying. Tap density analysis, Brunauer–Emmett–Teller analysis, characterizations of X-ray diffraction, scanning electron microscopy, and transmission electron microscopy confirmed that the micron-sized spherical agglomerates with high specific surface area and high tap density were composed of the uniform nano-sized particles. The effects of pH and reaction time on the morphology of the FePO4 particles were investigated by experimental and theoretical analyses. The analyses revealed that amorphous FePO4 was responsible for forming a well-shaped spherical agglomerate, and the ideal spherical particles were obtained at pH 3. The reaction time also played a significant role in controlling the size and surface morphology of the FePO4 particles, and smooth spherical FePO4 particles were obtained at a reaction time of 6 h. By this novel method, poly-porous spherical iron phosphate particles were prepared, which can be used with high efficiency in some special fields, especially as a precursor for synthesizing LiFePO4 and catalysts.

Sedimentation of particles in Stokes flow

In this paper, we consider $ N $ identical spherical particles sedimenting in a uniform gravitational field. Particle rotation is included in the model while fluid and particle inertia are neglected. Using the method of reflections, we extend the investigation of [11] by discussing the threshold beyond which the minimal particle distance is conserved for a short time interval independent of $ N $. We also prove that the particles interact with a singular interaction force given by the Oseen tensor and justify the mean field approximation in the spirit of [8] and [9].

Scale and Boundary Effects on the Effective Elastic Properties of 2‐D and 3‐D Non‐REV Heterogeneous Porous Media

AbstractA digital 3‐D representation of a heterogeneous medium can be used as an input to physics‐based numerical methods to obtain an estimate of the effective physical properties of the composite, such as transport, electrical, and elastic properties. These properties can then be used to simplify large‐scale numerical simulations of physical processes by considering the constitutive equations of the heterogeneous composite as if it was a homogenous continuum. By definition, effective physical properties do not depend on the boundary conditions applied to a medium during an experiment. In finite‐sized media, computing effective properties for a medium may not be feasible due to the boundary effects on the computed parameters. Through numerical experiments, we developed a methodology to minimize the boundary effects by considering a subdomain within a sample onto which the experiment was performed. Specifically, we analyzed the boundary effects on the computed elastic properties of 2‐D and 3‐D subdomains located within a digitized sample of a Berea sandstone and a compacted random pack of identical spherical particles. As the parent sample size increases while the size of the subdomain remains fixed, the elastic properties of the latter converge to constant values. These values correspond to the effective elastic values of the subsample, though they depend on the immediate region surrounding the subdomain. In addition, we propose a method to relate the effective elastic properties of rock samples to another microstructural parameter to be used in prediction of elastic properties of other samples having the same type and geological conditions.