Arrays Of Spherical Particles Research Articles

Turbulent channel flow past a moving array of spheres

We have performed a particle-resolved direct numerical simulation of a turbulent channel flow past a moving dilute array of spherical particles. The flow shares important features with dilute vertical gas solid flow at high Stokes number, such as significant attenuation of the turbulence kinetic energy (TKE) at low particle volume fraction. The flow has been simulated by means of an overset grid method, using spherical grids around each particle overset on a background non-uniform Cartesian grid. The main focus of the present paper is on the TKE budget, which is analysed both in the fixed channel frame of reference and in the moving particle frame of reference. The overall (domain-integrated) TKE and turbulence production due to mean shear are reduced compared to unladen flow. In the fixed frame, the interfacial term, which represents production due to relative (slip) velocity, accounts for approximately 40 % of the total turbulence production in the channel. As a consequence, the total turbulence production and the overall turbulence dissipation rate remain approximately the same as in the unladen flow. However, a comparison with laminar flow past the same particle configuration reveals that significant parts of various fixed-frame statistics are due to non-turbulent structures, spatial variations that are steady in the moving particle frame. In order to obtain a clearer picture of the modification of the true turbulence and in order to reveal the rich three-dimensional (3-D) statistical structure of turbulence interacting with particles, time averaging in the moving frame of reference of the particle is used to extract the fluctuations entirely due to true turbulence. In the moving frame, the turbulence production is positive near the sides and in the wake, but negative in a region near the front of the particle. The turbulence dissipation rate and even more the dissipation rate of the 3-D mean flow attain very large values on a large part of the particle surface, up to approximately 400 and 4000 times the local turbulence dissipation rate of the unladen flow, respectively. Very close to the particle, viscous diffusion is the dominant transport term, but somewhat further away, in particular near the front and sides of the particle, pressure diffusion and also convection provide large and positive transport contributions to the moving-frame budget. A radial analysis shows that the regions around the particles draw energy from the regions further away via the surprising dominance of the pressure diffusion flux over a large range of radii. Spectra show that (very) far away from the particles all scales of the (true) turbulence are reduced. Near the particles enhancement of small scale turbulence is observed, for the streamwise component of the velocity fluctuation more than for the other components. The most important reason for turbulence reduction and anisotropy increase appears to be particle-induced non-uniformity of the mean driving force of the flow.

The effects of microstructure on wave velocity and wavefront in granular assemblies with binary-sized particles

The nonlinear behavior of highly ordered granular materials is due to their inability to transfer tensile loads and the Hertzian contact between particles. We investigated the propagation of stress waves excited by impulsive loadings in granular assemblies composed of an uncompressed, centered square array of spherical particles the radii of which are gradually increased. Systematic variations in the radius ratio of the surrounding and intruder particles lead to large variations in the characteristics of the wave velocity and propagating stress wavefronts traveling through the system. By assuming the dissipating rate of the contact interface, the pulse energy dissipation is obtained, which provides a solution to the calculation of the frictional energy consumption. The relationship between the microstructure and the wavefront shape is of concern. Finally, equations of the wavefront in hexagonal assemblies were analytically given which substantiated reasonable prediction of the wave propagation process through the assemblies.

Magnetostriction effect in soft magnetic elastomers

We discuss the magnetostriction effect in soft magnetic elastomers: stretching/shrinking of a sample under the action of uniform magnetic field in the absence of mechanical loads. Qualitative analysis shows that the field has a twofold effect on the medium; one of those mechanisms works at the macroscopic scale whereas the other one stems from the mesoscopic processes. Essentially, the latter one is defined by the “architecture” of short-range spatial order existing in the ferromagnet particle assembly. This conclusion is illustrated with the aid of numerical modeling. First, it is done on a 2D elastic array filled with linearly magnetizable particles. It is shown that it is indeed the presence of clusters that controls both the sign and magnitude of magnetostriction in the composite. In other words, two composites with the same matrix/filler content may behave very differently depending on their mesoscale structure. Further on, to get a more realistic description, the modeling is extended to a 3D array of spherical particles randomly distributed in an elastic matrix. Although the general conclusions hold, the quantitative results differ substantially.

Opal-like Multicolor Appearance of Self-Assembled Photonic Array.

Molecular self-assembly of short peptide building blocks leads to the formation of various material architectures that may possess unique physical properties. Recent studies had confirmed the key role of biaromaticity in peptide self-assembly, with the diphenylalanine (FF) structural family as an archetypal model. Another significant direction in the molecular engineering of peptide building blocks is the use of fluorenylmethoxycarbonyl (Fmoc) modification, which promotes the assembly process and may result in nanostructures with distinctive features and macroscopic hydrogel with supramolecular features and nanoscale order. Here, we explored the self-assembly of the protected, noncoded fluorenylmethoxycarbonyl-β,β-diphenyl-Ala-OH (Fmoc-Dip) amino acid. This process results in the formation of elongated needle-like crystals with notable aromatic continuity. By altering the assembly conditions, arrays of spherical particles were formed that exhibit strong light scattering. These arrays display vivid coloration, strongly resembling the appearance of opal gemstones. However, unlike the Rayleigh scattering effect produced by the arrangement of opal, the described optical phenomenon is attributed to Mie scattering. Moreover, by controlling the solution evaporation rate, i.e., the assembly kinetics, we were able to manipulate the resulting coloration. This work demonstrates a bottom-up approach, utilizing self-assembly of a protected amino acid minimal building block, to create arrays of organic, light-scattering colorful surfaces.

Apparent viscosity reduction during microwave sintering of amorphous silica

The sintering of arrays of spherical particles of amorphous SiO2 was investigated experimentally under microwave (24GHz) and conventional heating. The materials under study were compacts formed by gravitational sedimentation of monodisperse silica microspheres (1µm in diameter). The kinetics of neck growth between individual particles was investigated by analyzing SEM images. It was found that the rates of viscous mass transport under microwave heating were significantly higher than those under conventional heating. The values of the viscosity obtained under microwave heating were significantly (by more than an order of magnitude) lower compared to conventional heating. Possible reasons for the viscosity decrease observed under microwave heating may be associated with the influence of water vapor and the action of the electromagnetic field on impurity ions. The interrelation of the observed effect with flash sintering and microwave-enhanced mass transport is discussed.

Convergence study of the Immersed Domain method for periodic particle configurations

For large-scale discrete element (DEM) simulations, particles sizes are often scaled up to reduce the computational effort. This coarse graining is incompatible with certain types of coupling to computational fluid dynamics (CFD) simulations usually used for large-scale simulations, as they require the fluid cells to be even larger than the particles, leading to unacceptably badly resolved flows. We investigate the possibility of using an Immersed Domain method with a large cell size to perform coupled DEM-CFD simulations of dense granular flows. To this end, we calculate the drag force on a single particle of an infinite simple cubic array of spherical particles suspended in a driven flow. We consider three packing fractions and compare the results for multiple resolutions to those obtained from conformal mesh CFD. While a number of flow characteristics suffer badly from coarse resolutions, the total drag force on the particle proves surprisingly accurate even for resolutions lower than 10 cells per particle diameter.

Large-area formation of microsphere arrays using laser surface texturing technology

Many potential applications in optics and nanotechnology require arrays of spherical particles with dozens of microns diameter, but it is not easy to format microspheres in this scale using existing technologies, especially for large-area application. In this paper, we report that microspheres sized from 40 to 80 μm can be regularly arranged in arrays with the aid of micro-ridges generated by pulsed nanosecond laser texturing. After experimental comparison, it is known that final formation of microspheres is significantly related to the height and width of micro-ridges. Proposed particle arrangement technology does not have area limitation and harsh hardware requirement, simultaneously possessing low-cost and time-saving advantages.

Nonlinear wave propagation and rotational dynamics In microscale granular media

Granular media have been shown to exhibit complex dynamics stemming from dispersion and nonlinear particulate interactions. Studies of wave propagation in granular materials composed of ordered arrays of spherical particles interacting via Hertzian contact, known as “granular crystals,” have demonstrated rich nonlinear phenomena, including amplitude-dependent and tunable sound speeds, solitary waves, and discrete breathers. However, most of the past work on granular crystals has considered macroscale spheres, with diameters on the order of centimeters or millimeters. More recent works have explored wave phenomena in microscale granular crystals, having particle diameters of a few microns, which can be fabricated using self-assembly methods, and characterized experimentally using laser ultrasonic techniques. The physics of microscale granular media have been shown to vary drastically from their macroscale counterparts; for example, interparticle adhesion, which is negligible at macroscale, creates an intrinsic static load, which linearizes the contact forces at low amplitude, and can increase the importance of shear interactions and particle rotations. In this work, we present theoretical and computational analyses of nonlinear wave propagation in microscale granular crystals, examining the interplay between nonlinearity and rotational dynamics. In particular, we focus on amplitude-dependent distribution of energy into the translational and rotational modes of a hexagonally close-packed granular crystal.

On convergence of the generalized Maxwell scheme: conductivity of composites containing cubic arrays of spherical particles

The Maxwell concept of equivalent inhomogeneity generalized to account for the interactions between the particles in the cluster and combined with recently reported results on the polarizability of a cube is used to evaluate the effective conductivities of the materials reinforced by cubic arrays of spherical particles. New numerical results demonstrate that the estimates of the effective properties based on the generalized Maxwell scheme with the equivalent inhomogeneity of cubic shape converge to the accurate periodic benchmark solutions, unlike spherical shape-based estimates.

Energy Harvesting Using an Array of Granules

In the last decade, there has been an increasing attention on the use of highly and weakly nonlinear solitary waves in engineering and physics. These waves can form and travel in nonlinear systems such as one-dimensional chains of particles. One engineering application of solitary waves is the fabrication of acoustic lenses, which are employed in a variety of fields ranging from biomedical imaging and surgery to defense systems and damage detection. In this paper, we propose to couple an acoustic lens to a wafer-type lead zirconate titanate (PZT) transducer to harvest energy from the vibration of an object tapping the lens. The lens consists of an ordered array of spherical particles in contact with a polycarbonate material where the nonlinear waves become linear and coalesce ideally into a focal point. The transducer located at the designed focal point converts the mechanical energy carried by the stress waves into electricity to power a load resistor. The performance of the designed harvester is compared to a conventional nonoptimized cantilever beam, and the experimental results show that the power generated with the nonlinear lens has the same order of magnitude of the beam.

Platinum Ordered Porous Electrodes: Developing a Platform for Fundamental Electrochemical Characterization

High surface area platinum electrodes with an ordered porous structure (Pt-OP electrodes) have been prepared and characterized by electrochemical methods. This study builds a foundation upon which we can seek an in-depth understanding of the limitations and design considerations to make efficient and stable Pt-OP electrodes for use in electrochemical applications. A set of Pt-OP electrodes were prepared by controlled electrodeposition of Pt through a self-assembled array of spherical particles and subsequent removal of the spherical templates by solvent extraction. The preparation method was shown to be reproducible and the resulting electrodes were found to have clean Pt surfaces and a large electrochemical surface area (A ecsa) resulting from both the porous structure, as well as the nano- and micro-scale surface roughness. Additionally, the Pt-OP electrodes exhibit a surface area enhancement comparable to commercially available electrocatalysts. In summary, the Pt-OP electrodes prepared herein show properties of interest for both gaining fundamental insights into electrocatalytic processes and for use in applications that would benefit from enhanced electrochemical response.

Added mass of dispersed particles by CFD: Further results

The added mass coefficient C is calculated for dispersed particles in different flow situations using the CFD simulations. Several geometrical configurations are considered, which are physically relevant and difficult to treat analytically. We study a single spherical and ellipsoidal particle near a gas/liquid interface, a pair of ellipsoidal particles in both the in-line and side-by-side arrangements, and an infinite array of spherical particles at different vertical and horizontal spacing. The effect of the key control parameters on the added mass is demonstrated. Where possible, easy-to-use closed formulas (correlations) are provided for the value of C.

Three-dimensional particle-resolved models of Li-ion batteries to assist the evaluation of empirical parameters in one-dimensional models

Li-ion batteries are frequently modeled using variants of the one-dimensional approach that was initially developed by Newman and colleagues (e.g., [2]). Necessarily such an approach is based upon assumptions about the electrode microstructure, and quantitative predictions depend upon empirical parameters such as effective conductivities and diffusion coefficients. The present paper develops a three-dimensional model that can resolve electrode structure at the submicron scale. Although the three-dimensional model is capable of representing arbitrary electrode microstructure, the present paper considers regular arrays of spherical particles. The model is applied to evaluate approximations in one-dimensional models and to assist in establishing empirical relationships that can be used in reduced-dimension models. General relationships for effective particle radius in one-dimensional models are derived from the three-dimensional simulations. The results also provide a basis for estimating the empirical Bruggeman exponents that affect Li-ion transport within electrolyte solutions.

Nondestructive evaluation of orthopaedic implant stability in THA using highly nonlinear solitary waves

We propose a new biomedical sensing technique based on highly nonlinear solitary waves to assess orthopaedic implant stability in a nondestructive and efficient manner. We assemble a granular crystal actuator consisting of a one-dimensional tightly packed array of spherical particles, to generate acoustic solitary waves. Via direct contact with the specimen, we inject acoustic solitary waves into a biomedical prosthesis, and we nondestructively evaluate the mechanical integrity of the bone–prosthesis interface, studying the properties of the waves reflected from the contact zone between the granular crystal and the implant. The granular crystal contains a piezoelectric sensor to measure the travelling solitary waves, which allows it to function also as a sensor. We perform a feasibility study using total hip arthroplasty (THA) samples made of metallic stems implanted in artificial composite femurs using polymethylmethacrylate for fixation. We first evaluate the sensitivity of the proposed granular crystal sensor to various levels of prosthesis insertion into the composite femur. Then, we impose a sequence of harsh mechanical loading on the THA samples to degrade the mechanical integrity at the stem–cement interfaces, using a femoral load simulator that simulates aggressive, accelerated physiological loading. We investigate the implant stability via the granular crystal sensor–actuator during testing. Preliminary results suggest that the reflected waves respond sensitively to the degree of implant fixation. In particular, the granular crystal sensor–actuator successfully detects implant loosening at the stem–cement interface following violent cyclic loading. This study suggests that the granular crystal sensor and actuator has the potential to detect metal–cement defects in a nondestructive manner for orthopaedic applications.

YIELD DESIGN HOMOGENIZATION METHOD FOR COMPACTION OF MONOSIZED SPHERICAL POWDERS

The compaction of a package of monosized spherical solid grains by rate-independent plasticity deformation is examined in this paper through the use of both yield design homogenization method and finite element simulation. Both modes of compaction, isostatic and closed die, are considered. In this study, the arrangement of powder consists of hexagonal array of identical spherical grains touching each other in its initial state. During the compaction process the response of the powder compacts is monitored in terms of behaviors of appropriate representative unit cells subject to axisymmetrical loading conditions. The kinematic approach of the yield design homogenization method has been used to determine external estimates of macroscopic strength criteria of powders at various stages of compaction. The obtained upper bound estimates are based on consideration of discontinuous incompressible velocity fields satisfying conditions of homogeneous strain rate. The shapes and sizes of the macroscopic yield surfaces are determined at various stages of compaction and it has been found that they depend upon the loading history as well as the relative density of the compact. Finite element simulations similar to those of Ogbonna N. and Fleck N. A. [1995] "Compaction of an array of spherical particles," Acta Metall. Mater.43(2), 603–620. have also been performed in order to (i) obtain the deformation modes as well as the evolution of the deformation mechanism of the powder compact during the whole process of compaction; (ii) derive the evolution of contact sizes between adjacent grains; (iii) examine the dependence of the macroscopic yield surface upon the degree of compaction, using the "yield probing technique" Gurson, A. L. and Yuan, D. W. [1995] A Material Model for a Ceramic Powder Based on Ultrasound, TRS Bend Bar, and Axisymmetric Triaxial Compression Test Results (ASME, New York), pp. 57–68, and (iv) validate, to some extent, the results provided by the kinematic approach.

The effect of many-body interactions on the electrostatic force in an array of spherical particles

The effect of many-body interactions on the electrostatic force between spheres in an array of charged spherical particles has been quantified by solving the non-linear Poisson–Boltzmann equation (PBE) using a finite element method (FEM) model. The equation is solved for conditions of constant surface potential. The effect of the dimensionless Debye length scaled radius of the spheres on the electrostatic force between them has been determined and a significant reduction of the force is observed as the dimensionless Debye radius is decreased. Calculations based on the dimensionless separation distance between a pair of charged spheres in isolation confirm an exponential decay of the repulsive electrostatic force as the surface to surface separation distance is increased. In contrast, calculations based on an array of interacting spheres in certain critical packing conditions reveal considerable reduction in the magnitude of the repulsive electrostatic force at separation distances less than half the sphere radius. The latter results are explained by considering the directional cancellation effects of the electrical double layer between adjacent spheres placed in certain orientations within the array. This is believed to be a surprising many-body effect which has been overlooked in previous studies and whose validity can be used to explain the stability and strength of charged sphere arrays under certain critical geometric configurations.

Assemble-and-Stretch Method for Creating Two- and Three-Dimensional Structures of Anisotropic Particles

We fabricate two-dimensional ordered arrays of anisotropic particles by embedding hexagonally close-packed monolayers of spherical latex particles in polymer films and subjecting them to an extensional strain. Furthermore, by stacking several films, we create three-dimensional structures. An important advantage of this approach is the ability to independently control the particle orientation in each layer of the structure. Additionally, the symmetry of a layer is controlled by the orientation of the original array of spherical particles versus the stretch direction. This technique may be readily used to generate structures for photonic applications, as well as to aid fundamental studies of packing of anisotropic particles.

Multi-scale calculation of settling speed of coarse particles by accelerated Stokesian dynamics without adjustable parameter

The calculation of settling speed of coarse particles is firstly addressed, with accelerated Stokesian dynamics without adjustable parameters, in which far field force acting on the particle instead of particle velocity is chosen as dependent variables to consider inter-particle hydrodynamic interactions. The sedimentation of a simple cubic array of spherical particles is simulated and compared to the results available to verify and validate the numerical code and computational scheme. The improved method keeps the same computational cost of the order O(N log N) as usual accelerated Stokesian dynamics does. Then, more realistic random suspension sedimentation is investigated with the help of Mont Carlo method. The computational results agree well with experimental fitting. Finally, the sedimentation of finer cohesive particle, which is often observed in estuary environment, is presented as a further application in coastal engineering.

Particle encapsulation due to thread breakup in Stokes flow

The capillary instability of a liquid thread containing a regular array of spherical particles along the centreline is considered with reference to microencapsulation. The thread interface may be clean or occupied by an insoluble surfactant. The main goal of the analysis is to illustrate the effect of the particle spacing on the growth rate of axisymmetric perturbations and identify the structure of the most unstable modes. A normal-mode linear stability analysis based on Fourier expansions for Stokes flow reveals that, at small particle separations, the interfacial profiles are nearly pure sinusoidal waves whose growth rate is nearly equal to that of a pure thread devoid of particles. Higher harmonics suddenly enter the normal modes for moderate and large particle separations, elevating the growth rates and yielding a stability diagram that consists of a sequence of superposed pure-thread lobes. A complementary numerical stability analysis based on the boundary integral formulation for Stokes flow reveals the strong stabilizing effect of particles whose radius is comparable to the thread radius. Numerical simulations of the finite-amplitude motion based on the boundary integral method demonstrate that thread breakup leads to particles coated with annular layers of different thicknesses.

Light propagation in linear arrays of spherical particles

A propagation of dipolar radiation in a finite length linear chain of identical dielectric spheres is investigated using the multisphere Mie scattering formalism (MSMS). A frequency pass band is shown to be formed near every Mie resonances inherent in the spheres. The manifestation of the pass band depends on the polarization of the travelling radiation. To prove this effect, a point dipole placed by the end of the chain is used as an external source of radiation. It is found that, if this dipole is directed parallel to the chain axis, the frequency pass bands exist if the refractive index of dielectric spheres is sufficiently large n r > 1.9 . For the dipole normal to the chain axis, the pass band can always be formed if the chain is sufficiently long. Such a distinction is due to different behavior of the far-field dipolar interaction between the spheres induced by the external source. The edges of the pass bands are defined by the guiding wave criterion based on the light-cone constraint. The criterion of creation of the pass bands correlate with condition of formation of high quality factor modes in these systems found in our previous papers. A comparison with the results available for infinite chains is made. In particular, we clarify the nature of braking down the band structure for small enough wavevectors.