Arrays Of Spherical Particles Research Articles

Light absorption by a planar array of spherical particles and a matrix in which they are embedded: statistical approach.

The fractions of light energy absorbed by a 2D array of spherical particles and the matrix in which they are embedded are determined. The solution is based on a volume integral equation and a statistical approach. The absorption coefficient of the array is found via the internal fields of the particles. The absorption coefficient of a matrix is found as the difference between the absorption coefficients of the composite structure and the particles. Numerical results are presented for arrays of metal, semiconductor, and dielectric nano- and microparticles of short-range order and imperfect long-range order in the absorbing media at normal and oblique incidence of a plane wave.

Morphological structure of the Pb island films melted on the Ta layer surface

An effective way to create self-organizing arrays of metal particles is to melt thin layers of substance on a poorly wetted surface. Such arrays may improve the technological properties of functional structures, and are themselves functional elements of modern devices and systems. During the melting of a solid layer on a poorly wetted substrate, an array of spherical particles is formed, which are evenly distributed over the surface of the substrate. The distribution of particles by size is determined by the thickness of the fusible layer and conditions of the deposition. The location of islands, formed after the melting of vapour-crystal deposited solid films, is determined primarily by the initial stages of de-wetting, when the thin continuous film starts to decay while remaining in solid state. This work studied self-organizing processes during the melting of Pb films deposited on a Ta substrate. The films were deposited on glass plates in a high vacuum and then after deposition were heated to a temperature slightly above the Pb melting point. After the heat treatment the samples were removed from the vacuum chamber and examined using SEM microscopy and EDS analysis. It was discovered that arrays of spherical particles are formed during the melting of micron-thick Pb films. The histograms of the size distribution of such particles are quite wide and can be represented as bimodal with partially overlapping maxima. This can be explained by active coalescence processes in thicker samples. This study demonstrated that small temperature gradients can cause noticeable kinetic effects that allow separate particles to move macroscopic distances and capture the surrounding substance. The study also estimated the energy associated with the optimization of the morphological structure of vacuum condensate and which is a physical factor of de-wetting.

Drag force of compressible flows past random arrays of spheres

We perform particle-resolved simulations of subsonic and transonic flows past random arrays of spherical particles. The particle Reynolds number is held at Re≈300 to ensure the flow remains in the continuum regime. At low volume fractions, the drag force increases sharply near a critical Mach number due to the formation of shock waves and reaches a maximum value when the bulk flow is supersonic. Neighbor-induced aerodynamic interactions reduce the critical Mach number at higher volume fractions. An effective Mach number is introduced to capture the increase in compressibility effects on drag. A new drag correlation is proposed valid for subsonic and weakly supersonic flow from dilute to moderately dense suspensions.

Wireless portable transducer for nondestructive evaluation applications based on highly nonlinear solitary waves

A novel technique based on highly nonlinear solitary waves (HNSWs) has recently emerged to inspect / monitor engineering structures. The method is based on the actuation and detection of solitary waves propagating along a monoperiodic array of spherical particles, the last of which is in dry point contact with the material to be evaluated or monitored. The technique relies on the proved hypothesis that the dynamic interaction between the waves and the element to be inspected is dependent upon the mechanical properties and the integrity of the element. The method makes use of the so-called HNSW transducer, which consists of the array held within a rigid frame, an electromagnet that enables the excitation of the solitary waves through mechanical impact, and a sensor to detect the waves. The transducer is typically wired to a data acquisition system that controls the excitation and detection of the waves and stores the time series for post-processing. In the study presented in this paper, a portable, small wireless transducer was designed, assembled, and tested. The new instrument enables the characterization of small or soft samples without any wired connection to electronic test equipment. The reliability of the new device was proven by completing a comparative test in which the conventional wired and the novel wireless configuration were used to probe three samples made of different materials, namely steel, PDMS membrane, and Sawbones®. Then, the instrument was used to test the same membrane subjected to different pressures. The results of the experiments successfully proved that the instruments can accurately operate without the support of electronic equipment and can be used to identify subtle differences in soft materials.

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.

On the Long-Term Performance of Solitary Wave-Based Transducers for Nondestructive Evaluation Applications

Abstract A nondestructive evaluation (NDE) technique based on highly nonlinear solitary waves (HNSWs) has been developed recently by a few groups worldwide. The technique is based on the propagation and detection of these waves along a one-dimensional monoperiodic array of spherical particles in which one end of the array is in contact with the material/structure to be inspected, and the particle at the opposite end induces the waves by means of a mechanical impact. Several studies have demonstrated that the dynamic interaction between the waves and the element to be evaluated is dependent on the geometric and mechanical properties of the structure, and such dependency can be monitored by sensing the waves reflected at the interface between the array and the structure. This NDE technique is typically performed by using the so-called HNSW transducer. The term transducer indicates a portable device that consists of a monoperiodic array of particles, a device to trigger the waves, and a sensing element to detect the waves. In the study presented in this article, the long-term performance of three transducers was investigated by placing them above a test object whose mechanical and geometric properties were left constant for a week while the transducers triggered and detected thousands of waves. Any variability of the waves was quantified by extracting simple features such as amplitude, time of flight, and cross-correlation. To investigate the cause of variabilities, 16 measurements were captured with short videos at ∼1000 fps. The results of the study demonstrate that the traveling time of the solitary waves is the most reliable parameter for long-term monitoring with the lowest variability and the least susceptibility to physical changes within the array. In addition, the findings of this study allow the framing of a valid strategy to improve the design of the transducers in order to make the HNSW-based technique suitable for long-term monitoring.

Wireless Node for Highly Nonlinear Solitary Wave Transducers

A novel nondestructive evaluation (NDE) method based on the application of highly nonlinear solitary waves has recently emerged as a leading candidate for structural health monitoring (SHM) scenarios. The method is based on the actuation and detection of solitary waves propagating along a medium made of uniform spherical particles, the last of which is in contact with the material to be inspected. The typical setup consists of a built-in transducer in dry point contact with the material. The transducer is made of a monoperiodic array of spherical particles in Hertzian contact that enables the excitation and detection of the solitary waves. The transducer is wired to a data acquisition system that controls the functionality of the transducer and store the time series for post-processing. The method relies on the proved hypothesis that the dynamic interaction between the wave and the material/structure in contact with the particle to be inspected is dependent upon the condition of the material/structure. In the study presented in this paper, a wireless node was developed to enable the solitary wave based NDE/SHM without any wired connection to electronic test equipment. Comparative tests and analyses between the measurements obtained with the designed node unit and a conventional wired configuration is provided. Advantages and limitations of the proposed node are given along with some suggestions for future developments.

Simulation of the flow past random arrays of spherical particles: Microstructure-based tensor quantities as a tool to predict fluid–particle forces

A recent challenge in the modelling of particle flows is to build microstructure-informed drag models to overcome the average description of the fluid–particle force in the drag force correlations currently used in Euler–Lagrange and Euler–Euler models. To that end, we study through particle-resolved direct numerical simulations (PR-DNS) the flow past random assemblies of mono-dispersed spherical particles at three particle Reynolds numbers (10, 50, 100) and four solid volume fractions (0.10, 0.20, 0.30, 0.40). The present methodology is validated against theoretical and numerical results for the mean drag force in Stokes flows and finite Reynolds numbers flows. PR-DNS results are then used to characterize in details the statistics of the force distribution over the particle array, highlighting the substantial dispersion of the fluid force along the streamwise and transverse directions. The microstructure formed by the solid phase is described by means of a limited number of tensor quantities inspired from the fabric tensor used in granular media. Significant correlations are identified between the force experienced by a given particle immersed in a random array and a few key quantities that describe the anisotropy of its neighbourhood. A microstructure-based multi-linear model is proposed and validated against independent test cases. The model appears to perform best in the viscous and dense regimes. The addition of a stochastic contribution to the model allows to recover the correct level of force fluctuations at the cost of a lower correlation between the model and the data.

Highly Nonlinear Solitary Waves to Estimate Orientation and Degree of Anisotropy in Rocks

This paper delves into the use of highly nonlinear solitary waves for the nondestructive identification and characterization of anisotropy in rocks. The nondestructive testing approach proposed expands upon a technique developed recently by some of the authors for the nondestructive characterization of engineering materials and structures. The technique uses the characteristics of solitary waves propagating in a periodic array of spherical particles in contact with the rock to be characterized. The features of the waves that bounce off the chain rock interface are used to infer some properties of the geomaterial under consideration. Numerical models and experimental validation were conducted to explore the feasibility of the method and to standardize the methodology for future widespread applications.

Angle Resolved Scattering Measurement of Multiple Spherical Particles by Fourier Transform

In this paper, we report that the far field diffraction pattern of a specimen which is consisting of an array of spherical particles enables the determination of the size and refractive index of each scattering sphere. The far field 2D angular resolved diffraction pattern, of which the diffraction angle reaches tens of degrees, is measured by CCD camera. On one hand, the diffraction pattern distorted obviously at high angles is corrected for curvature. The amplitude and phase images of the specimen are reconstructed by difference map iterative algorithm. The size of each scattering microsphere is calculated according to its pixel numbers and the image resolution. On the other hand, the diffraction pattern without curvature correction is used to reconstruct the amplitude and phase images of the specimen by HIO algorithm. The amplitude and phase images of each sphere are isolated. Then the angular resolved scattering signals of the individual spheres are quantitatively indicated by Fourier transform. Finally, the refractive index of each microsphere is obtained by fitting the experimental results using Mie theory.

Polarization of light scattered by a two-dimensional array of dielectric spherical particles

The polarization state of light scattered by a two-dimensional array of spherical particles is considered based on the statistical approach. The impact of filling factor, particle size, and the type of their spatial order is analyzed for arrays of silicon and silica scatterers. The conditions are formulated to suppress the p and s components of light specularly reflected by the array of any size and concentration of particles. It is shown that at an angle of suppression of the coherent component of the reflected wave, its incoherent component is also suppressed.

Effect of Stefan flow on the drag force in flow past random arrays of spheres

Stefan flow is a mass flow perpendicular to the particle surface induced by the reaction or component diffusion occurring inside particles. It significantly affects the interphase transfer process in gas–solid reacting flows. In this work, a second-order immersed boundary-lattice Boltzmann method (IB-LBM) is adopted for analyzing the influence of Stefan flow on the drag force in flows past fixed random arrays of spherical particles. The effect of Stefan flow is introduced by assigning specific fluid velocities at Lagrangian markers on the sphere surface. The simulation results show that the drag force exerting on particles decreases as the Stefan Reynolds number increases. The drag force reduction caused by Stefan flow is weakened as the solid volume fraction increases. This is because the thick boundary layer caused by Stefan flow on each particle is suppressed by Stefan flow from their neighboring particles. Based on the simulation results, a novel drag correction coefficient is developed, which considers the joint influence of the Stefan Reynolds number, particle Reynolds number and solid volume fraction.

Methods for ray-tracing thermal modelling of Saturn's main rings

The thermal emission and temperatures of the main rings of Saturn depend on the energy the ring particles absorb, reflect and scatter and/or on their Bond albedo, emissivity, thermal inertia, rotation rate and porosity. However, the energy that each particle absorbs also depends on the amount of energy (e.g., solar energy) that reaches its surface and this latter on the local optical depth, that controls the mutual eclipsing between neighbouring particles and, in general, all shadowing effects on the rings. On the other hand, thermal models of the rings of Saturn based on the energy balance equation strongly depend on a function that described how the non-shadowed area of ring particles changes with solar elevation. Experimental and analytical shadowing functions have been proposed by [6] and [1], respectively. In this work, we propose shadowing functions based on the creation of 3D arrays of spherical particles that simulate specific regions of the main rings of Saturn. The methods implemented to obtain these shadowing functions follow the next general steps:• Arrays are created as a collection of spherical particles with a size distribution that follows a power law constrained to the optical depth of the region of study based on the UVIS instrument data.• The particles of the arrays are then reordered to add some relevant dynamical features observed in actual rings (e.g., wake structures in the case of optically-thick rings).• Under different illumination geometries, images of these arrays are rendered using ray tracing. From these images, an analysis of their pixel brightness values allows us to determine the non-shadowed fractional area of the particles in order to compose the corresponding shadowing functions.

Ray-tracing thermal modelling of Saturn's main rings

The observations of the Cassini spacecraft gave new perspectives to our understanding of the rings of Saturn and their thermal studies due to their large variety of observation geometries. However, we still know little about the ring particles' physical and, particularly, thermal properties, which is the reason why a number of observations are not easy to explain. Nevertheless, the observed temperature profiles of the rings can be reproduced by considering the rings' general structural properties like local optical depth, τ, and, for the optically-thick rings, wake properties like the ratios H/W or wake thickness to wake width, and S/W or wake separation to wake width; as well as their main energy input sources (e. g., direct and reflected solar energy and Saturn's infrared energy).In this work, we assume that the main rings (C, B, Cassini Division and A rings) are monolayers and study the temperature variations with solar elevation angle, B′, of ten of their regions with a simple thermal balance equation that depends on the rings' shadowing behaviour due to the illumination geometry (B′) and the arrangement of particles across the rings (τ). The shadowing is a key feature, which we reproduce with a numerical function obtained via ray tracing from arrays of spherical particles (C(B′,τ)). Using the former model, we fit Cassini Composite Infrared Spectrometer (CIRS) temperature data with the Bond albedo, AV, and the so-called rotation parameter, f (which represents the rotation status of the ring particles) as only parameters. These parameters are two of the most important physical properties that define the rings' temperatures.With our method, we are able to reproduce the CIRS data temperature trends of the selected regions reasonably well. For evaluation purposes we compare the derived Bond albedo values with those obtained with the Cassini Imaging Science Subsystem (ISS) at wavelengths in the range 451 ≲ λ ≲ 650nm. The comparison suggests a dominance of slow rotators. Additionally, we evaluate the differences obtained when using either a numerical or an analytical shadowing function (in particular, that by (Altobelli et al., 2008)) in the thermal model. The differences between these two approaches reflect some details of the structure of the ring regions we study.

Investigation of a thin permeable layer effect on turbulent flow and passive scalar transport in a channel

Large eddy simulations of turbulent flow and passive scalar transport in a channel partially filled with an array of spherical particles, mimicking a layer of deposited material over a surface, are carried out to investigate the effect of turbulence mixing on the passive scalar transfer rate from the channel wall. It is observed that large turbulence structures generated at the permeable layer-fluid interface penetrate into the porous media and enhance the scalar transport from the channel wall. The small gap between the layer of particles and the wall also induces a channeling effect that implies turbulence mixing and high velocity near the wall resulting in an enhancement in scalar transport from the channel wall. The influence from the distance between the particles in one layer, particle diameter and the gap thickness on the passive scalar transport is also investigated. It is found that the highest Stanton number is derived for the largest distance between particles since this facilitates the motion of the large turbulent structures into the porous layer. Such motions will affect the scalar transport from the channel wall into the bulk. The channeling effect is observed to be the most important parameter when the particle diameter and the gap thickness are varied, and the highest Stanton number is achieved for the cases with the most effective channeling effect.

Molecular dynamics simulation study of a polymer droplet transport over an array of spherical nanoparticles

The dynamic behavior of a partially wetting polymer droplet driven over a nanostructured interface is studied using molecular dynamics simulations. We consider the bead-spring model to represent a polymeric liquid that partially wets a rough surface composed of a periodic array of spherical particles. It is shown that at sufficiently small values of the external force, the droplet remains pinned at the particles’ surface, while above the threshold, its motion consists of alternating periods of pinning and rapid displacements between neighboring particles. The latter process involves large periodic variation of the advancing and receding contact angles due to attachment and detachment of the contact line. Finally, upon increasing external force, the droplet center of mass is displaced steadily but the oscillation amplitude of the receding contact angle as well as the maximum contact angle hysteresis remain relatively unaffected.

Wireless Module for Nondestructive Testing/Structural Health Monitoring Applications Based on Solitary Waves.

In recent years, there has been an increasing interest in the use of highly nonlinear solitary waves (HNSWs) for nondestructive evaluation and structural health monitoring applications. HNSWs are mechanical waves that can form and travel in highly nonlinear systems, such as granular particles in Hertzian contact. The easiest setup consists of a built-in transducer in drypoint contact with the structure or material to be inspected/monitored. The transducer is made of a monoperiodic array of spherical particles that enables the excitation and detection of the solitary waves. The transducer is wired to a data acquisition system that controls the functionality of the transducer and stores the time series for post-processing. In this paper, the design and testing of a wireless unit that enables the remote control of a transducer without the need to connect it to sophisticated test equipment are presented. Comparative tests and analyses between the measurements obtained with the newly designed wireless unit and the conventional wired configuration are provided. The results are corroborated by an analytical model that predicts the dynamic interaction between solitary waves and materials with different modulus. The advantages and limitations of the proposed wireless platform are given along with some suggestions for future developments.

Linear and nonlinear surface waves in two-dimensional, hexagonal close-packed granular crystals

Granular crystals (GCs) are ordered arrays of spherical particles in contact, which have been shown to exhibit rich nonlinear dynamics stemming from Hertzian contact interactions. They are typically modeled as discrete networks of rigid body spheres, which may undergo translational and rotational motion, with Hertzian interactions modeled as effective nonlinear normal and shear springs. Most of the existing literature on GCs concerns one-dimensional chains of spheres, though a growing body of recent work has explored two-dimensional systems in linear and nonlinear regimes, with multiple packing geometries. In a recent analytical study, Rayleigh-like surface waves were shown to exist in the linear regime for two-dimensional GCs with square packing [Phys. Rev. E 93, 023008 (2016)]. In the present work, we report on surface waves in two-dimensional granular crystals with hexagonal close-packed (HCP) geometry. We demonstrate analytically that, in the linear regime, HCP GCs support Rayleigh-like surface waves analogous to the square-packed case, as well as a leaky surface wave mode with quasi-longitudinal polarization. Extensions of the linear surface modes into the nonlinear regime are demonstrated via numerical examples and compared to results from one-dimensional granular chains. [Work supported by the postdoctoral program at ARL:UT.]

Numerical Analysis and Experimental Validation of an Nondestructive Evaluation Method to Measure Stress in Rails

This article presents a numerical formulation and the experimental validation of the dynamic interaction between highly nonlinear solitary waves generated along a mono-periodic array of spherical particles and rails in a point contact with the array. A general finite element model of rails was developed and coupled to a discrete particle model able to predict the propagation of the solitary waves along a L-shaped array located perpendicular and in contact with the web of the rail. The models were validated experimentally by testing a 0.9-m long and a 2.4-m long rail segments subjected to compressive load. The scope of the study was the development of a new nondestructive evaluation technique able to estimate the stress in continuous welded rails and eventually to infer the temperature at which the longitudinal stress in the rail is zero. The numerical findings presented in this article demonstrate that certain features, such as the amplitude and time of flight, of the solitary waves are affected by the axial stress. The experimental results validated the numerical predictions and warrant the validation of the nondestructive evaluation system against real rails.

Modelling of the interaction between nonlinear solitary waves and composite beams

We examine numerically the interaction between solitary waves in lightly pre-compressed granular chains and laminated composite beams. A discrete element (DE) model is developed to simulate, with low computational effort, the propagation of solitary waves in a linear array of spherical particles as well as their interaction with a transversely isotropic composite beam. The derived equations allow identifying the governing dimensionless parameters and their effects on the delays and amplitudes of the reflected solitary waves are studied. It is found that the formation of reflected solitary waves is highly sensitive to the beam's geometry as well as to the elastic properties and layup of the laminate. For a beam of given dimensions, the delays and amplitudes of the reflected solitary waves are strongly affected by the flexural stiffness of the composite beam. The DE predictions are compared to those obtained from a more detailed hybrid discrete/finite element model and good agreement is reported for a wide range input parameters. The results of this study support the idea of developing a low-cost solitary wave-based diagnostic scheme for non-destructive evaluation of basic elastic properties of engineering composites.