Polydisperse Spherical Particles Research Articles

Refractive index matching of large polydisperse silica spheres in aqueous suspensions

Standard synthesis protocols produce silicon dioxide (SiO2) particles with an inhomogeneous material distribution, which defines their optical properties. The inner structure and effective refractive index of the particles can be investigated by light scattering and optical contrast variation techniques. The standard analysis relies on scattering models for particles smaller than the wavelength of the scattering probe, thus restricting its use for a large variety of particle systems of academic and industrial interest. However, to overcome this difficulty should be possible by using the appropriate scattering model in the analysis. Here, SiO2 particles of size comparable to the wavelength of the illuminating source are dispersed at low particle number concentration in different mixtures of polar solvents to study the optical contrast. The angle-dependent scattered intensity from SiO2 particles suspended in different mixtures of water and DMSO are obtained by static light scattering (SLS) and the effective refractive index of the particles is estimated from refractometry experiments. The measured angle-dependent scattered intensity is well described by the Aden-Kerker theory for coated polydisperse spherical particles. Fitting of experimental data is performed by using a non-linear least squares routine assuming that the core-to-shell ratio remains constant from where the refractive index and radius of the particles shell are obtained. Additionally, we use the structural characterization to estimate the effective refractive index of SiO2 particles, which allows identification of the solvent composition that produces the minimal optical contrast between colloids and suspending medium. This is, to our knowledge, the first report describing the interplay between internal structure and optical properties of core-shell spherical colloids of size comparable to the wavelength of the scattering probe. Consequently, our study provides an experimental scheme that could be useful in the structural and optical characterization of large complex colloids.

Development of a geometric surface area monitor (GSAM) for aerosol nanoparticles

Although geometric surface area (GSA) of nanoparticles has received much attention in many fields (drug delivery, catalysts, inhalation exposure, toxicity, etc.), no appropriate instruments and methods for online measurements of GSA are readily available. Therefore, this study intends to develop a Geometric Surface Area Monitor (GSAM) to measure the GSA of spherical as well as model agglomerate/aggregate nanoparticles in nearly real-time. The GSAM consists of several existing techniques in series, including inertial impaction, unipolar charging, electrostatic precipitation, and electrical current measurement. The GSAM was first evaluated and calibrated by measuring the GSA of monodisperse nanoparticles. Spherical, aggregate, and agglomerate nanoparticles were tested in the calibration. It was found that the measured electrical current was proportional to the surface area concentration. The calibration curves obtained from the measurements of monodisperse particles was then applied for polydisperse spherical particles and compared the measured GSA with that determined by the well-known scanning mobility particle sizer (SMPS) where the GSAM had less than 10% of deviation compared with SMPS.

A collision model for grain-resolving simulations of flows over dense, mobile, polydisperse granular sediment beds

We present a collision model for phase-resolved Direct Numerical Simulations of sediment transport that couple the fluid and particles by the Immersed Boundary Method. Typically, a contact model for these types of simulations comprises a lubrication force for particles in close proximity to another solid object, a normal contact force to prevent particles from overlapping, and a tangential contact force to account for friction. Our model extends the work of previous authors to improve upon the time integration scheme to obtain consistent results for particle–wall collisions. Furthermore, we account for polydisperse spherical particles and introduce new criteria to account for enduring contact, which occurs in many sediment transport situations. This is done without using arbitrary values for physically-defined parameters and by maintaining the full momentum balance of a particle in enduring contact. We validate our model against several test cases for binary particle–wall collisions as well as the collective motion of a sediment bed sheared by a viscous flow, yielding satisfactory agreement with experimental data by various authors.

A pore-scale method for hydromechanical coupling in deformable granular media

A pore-scale numerical method for simulating multiphase granular media is described, in which the solid skeleton is represented by a dense random packing of poly-disperse spherical particles and the pore space is discretized as a network of pores. The underlying idea is to build an efficient method for analyzing the hydro-mechanical behavior of such materials. We design the model specifically for simulating the quasi-static primary drainage, using a criterion for the displacements of the invading fluid and expressions of the forces exerted on the solid grains by fluid’s pressure and surface tension. The model can reproduce some features of drainage, including fluid phase entrapment and capillary fingering. We illustrate the method by simulated primary drainage in oedometer conditions, highlighting the deformation induced by partial saturation.

Discrete dynamic modelling of the mechanical behaviour of a granular soil

This paper investigates the interaction between a falling rock boulder and a granular medium through numerical modelling based on a discrete element method. The boulder is modelled as a single sphere with an incident velocity, and the medium is modelled as an assembly composed of poly-disperse spherical particles. A classical elastic-plastic contact law is implemented with rolling resistance to consider the particle shape effects. The numerical modelling is validated by comparison with results from the literature in terms of impact force, impact duration and the boulder’s penetration depth of the boulder. Then the model is used to investigate the energy propagation within the impacted medium as well as the boulder bouncing. The energy propagation processes are investigated by analysing the space distribution of kinetic energy, elastic strain energy and energy dissipation within the medium over time. The boulder bouncing occurrence is studied, varying the impact conditions in terms of medium thickness and boulder size. Relations between the bouncing of the boulder and the response of the granular medium are finally discussed.

Capturing of the internal mechanics of liquid-granular flows comprised of polydisperse spherical particles

This paper presents a series of flume experiments designed to examine the motion and arrest of concentrated granular-fluid flows, with a view to understanding the role of polydispersity in debris flows. A non-intrusive technique is used to investigate the internal behaviour of small scale experimental flows. Three different particle size distributions comprised of polydisperse spherical particles and one with the finer component made of angular particles were analysed. The choice of using spherical shaped particles was made to improve the visualization of the internal mechanics without reducing overmuch the complexity involved in the study of these flows. We examined and compared the internal velocities of the flows and their depositional spreads. While the optical performance of the non-intrusive technique was improved, some of the characteristics commonly seen in these types of granular flows were not observed. Velocity profiles obtained in the body of the flows were similar in shape but with differences in velocity magnitude depending on the amount of fines and the angularity of the particle in one case. Depositional runouts between flows were similar at low inclinations when little internal energy was supplemented to the system or when the viscous effects dominated the mechanics at steeper angles.

Numerical simulation of the dynamic response due to discharge initiation of the grain silo

The evolution of the stress distribution inside storage silos is an inherent effect in the dynamic operations of handling granular materials. Opening a discharge gate may result in a sudden increase in the lateral pressure with a simultaneous ramp down of vertical pressure, which generates severe pulsations of bin structures.In the reported study, numerical simulations of the discharge initiation of a grain silo were performed. Discrete element method (DEM) simulations were carried out in a flat-bottomed cylindrical container 0.12 m in diameter and 0.5 m high. One hundred eighteen thousand polydisperse spherical particles with a diameter of 3.79 ± 0.05 mm and material parameters of wheat were used. Based on DEM modeling, the propagation of a rarefaction–compaction wave up the silo height during the start of the bin discharge was studied. It was found that the passage of the rarefaction wave resulted in dynamic changes of all considered micro- and macro- variables describing the behavior of the bulk of solids: particle-to-particle forces, averaged stress tensor, pressure exerted by particles on the bin structure and bulk characteristics of the material: the mobilization of particle–wall and particle–particle frictions and the lateral-to-vertical pressure ratio.

Polydisperse spherical colloidal silica particles: Preparation and application**Project supported by the National Major Scientific and Technological Special Project during the Twelfth Five-year Plan Period of China (Grant No. 2009ZX02030-1), the National Natural Science Foundation of China (Grant No. 51205387), the Science and Technology Commission of Shanghai, China (Grant No. 11nm0500300), and the Science and Technology Commission of Shanghai, China (Grant

A new industrial method has been developed to produce polydisperse spherical colloidal silica particles with a very broad particle size, ranging from 20–95 nm. The process uses a reactor in which the original seed solution is heated to 100°C, and then active silicic acid and the seed solution are titrated to the reactor continuously with a constant rate. The original seeds and the titrated seeds in the reactor will go through different particle growth cycles to form different particle sizes. Both the particles’ size distribution and morphology have been characterized by dynamic light scattering (DLS) and the focus ion beam (FIB) system. In addition, the as-prepared polydisperse colloidal silica particle in the application of sapphire wafer’s chemical mechanical polishing (CMP) process has been tested. The material removal rate (MRR) of this kind of abrasive has been tested and verified to be much faster than traditional monodisperse silica particles. Finally, the mechanism of sapphire CMP process by this kind of polydisperse silica particles has been investigated to explore the reasons for the high polishing rate.

Influence of particle lattice effect on stability of suspensions: application to self-consolidating concrete

One of the parameters influencing the stability of a granular skeleton in a fluid is particle-size distribution (PSD). This phenomenon partially originates from the particle lattice effect (PLE) where in a given fluid the sedimentation behavior of one particle or a group of particles is modified in the presence of other particles. The PLE is of particular interest for the design of highly flowable concrete in which given the high fluidity of the paste, segregation of coarse aggregate is of concern. In the present study, the stability of several groups of bidisperse and polydisperse spherical glass particles (3–19 mm in diameter) suspended in limestone filler pastes designed with different rheological properties is investigated. Test results show that regardless of the PSD in the suspension, the PLE of any size-class is proportional to the volume fraction of such class. The main contribution of PLE to the enhancement of the stability of the overall system can be attributed to the stabilization of individual fine classes as the volume fractions of such classes are increased, instead of simply the interaction between different particle classes. Two indices are proposed to quantify the PLE potential of a given PSD and to predict the risk of segregation of a mixture of particles suspended in a yield stress fluid. The predictions made by the segregation index are shown to be feasible to apply to self-consolidating concrete (SCC) mixtures.

Nonlinear electroelastic deformations of dielectric elastomer composites: I—Ideal elastic dielectrics

This paper puts forth homogenization solutions for the macroscopic elastic dielectric response—under finite deformations and finite electric fields—of ideal elastic dielectric composites with two-phase isotropic particulate microstructures. Specifically, solutions are presented for three classes of microstructures: (i) an isotropic iterative microstructure wherein the particles are infinitely polydisperse in size, (ii) an isotropic distribution of polydisperse spherical particles of a finite number of different sizes, and (iii) an isotropic distribution of monodisperse spherical particles. The solution for the iterative microstructure, which corresponds to the viscosity solution of a Hamilton–Jacobi equation in five “space” variables, is constructed by means of a novel high-order WENO finite-difference scheme. On the other hand, the solutions for the microstructures with spherical particles are constructed by means of hybrid finite elements.Prompted by the functional features shared by all three obtained solutions, a simple closed-form approximation is proposed for the macroscopic elastic dielectric response of ideal elastic dielectric composites with any type of (non-percolative) isotropic particulate microstructure. As elaborated in a companion paper, the proposed approximate solution proves particularly useful as a fundamental building block to generate approximate solutions for the macroscopic elastic dielectric response of dielectric elastomer composites made up of non-Gaussian dielectric elastomers filled with nonlinear elastic dielectric particles.

The role of force chains in granular materials: from statics to dynamics

This paper investigates the role of force chains in granular materials under both quasi-static biaxial loading and dynamic impact loading conditions. This study is mainly interested in investigating the role of force chains on the global mechanical responses of samples as well as on the microstructure of granular materials. For this purpose, discrete element methods are adopted to perform different loading tests. Granular materials are modelled as aggregations of poly-disperse spherical particles. Results first show that force chains are responsible for the strength of the sample: in 2D biaxial test, the establishment and buckling of force chains are responsible for the evolution in terms of deviatoric stress; in 3D dynamic impact test, the development and the buckling of force chains are responsible for the evolution of impact force on the impacting projectile. Second, force chains are found to play an important role in the microstructure of granular materials: in statics, the buckling of force chains mainly locates inside the shear band, and is related to the increase in local void around the buckling grain as well as the increase in kinetic energy inside the sample; in dynamic test, the number of buckled force chains is correlated with the energy dissipation inside the sample.

The permeability prediction of beds of poly-disperse spheres with applicability to the cake filtration

Abstract The interactions between the cake and depth filtration of poly-disperse spherical particles is examined by comparing experimentally measured cake permeability to the permeability predictions of analytical models. In the experiments, the influence of the cake forming history on the cake permeability is investigated, where the parameters as (i) different filtration materials, (ii) test suspension flow rates, and (iii) particle concentrations in the suspension are varied. The permeability models are given as product of preset constant, porosity function and square of characteristic particle size. For the poly-disperse porous media, the characteristic particle size has to account for the distribution of particle sizes which is typically accomplished through the use of various moments of the distribution. Clearly, the size distribution function of particles forming the cake has to be utilized which is obtained after correcting the original distribution function of particles used in the test suspension for the particles which pass through the cake. This implies that the particles have to be counted after the test suspension passes the filtering material. Following this framework, a set of experiments is carried out to determine the permeability of poly-disperse cake. For each experiment, the permeability is also evaluated analytically using four different long-established models in combination with different averages for the particle diameter of the poly-disperse particle sample, trying to identify an averaging rule for which the analytical predictions are most close to the experimental results.

Self-assembly of polyethyleneamine-intercalated H2Ti2O5 nanoparticles into spherical agglomerates

Abstract

On the radiative properties of soot aggregates – Part 2: Effects of coating

The effects of weakly absorbing material coating on soot have attracted considerable research attention in recent years due to the significant influence of such coating on soot radiative properties and the large differences predicted by different numerical models. Soot aggregates were first numerically generated using the diffusion limited cluster aggregation algorithm to produce fractal aggregates formed by log-normally distributed polydisperse spherical primary particles in point-touch. These aggregates were then processed by adding a certain amount of primary particle overlapping and necking to simulate the soot morphology observed from transmission electron microscopy images. After this process, a layer of WAM coating of different thicknesses was added to these more realistic soot aggregates. The radiative properties of these coated soot aggregates over the spectral range of 266–1064nm were calculated by the discrete dipole approximation (DDA) using the spectrally dependent refractive index of soot for four aggregates containing Np=1, 20, 51 and 96 primary particles. The considered coating thicknesses range from 0% (no coating) up to 100% coating in terms of the primary particle diameter. Coating enhances both the particle absorption and scattering cross sections, with much stronger enhancement to the scattering one, as well as the asymmetry factor and the single scattering albedo. The absorption enhancement is stronger in the UV than in the visible and the near infrared. The simple corrections to the Rayleigh–Debye–Gans fractal aggregates theory for uncoated soot aggregates are found not working for coated soot aggregates. The core–shell model significantly overestimates the absorption enhancement by coating in the visible and the near infrared compared to the DDA results of the coated soot particle. Treating an externally coated soot aggregate as an aggregate formed by individually coated primary particles significantly underestimates the absorption enhancement by coating in the visible and the near infrared.

The overall elastic dielectric properties of a suspension of spherical particles in rubber: An exact explicit solution in the small-deformation limit

A solution is constructed for the homogenization problem of the elastic dielectric response of rubber filled with a random isotropic distribution of polydisperse spherical particles in the classical limit of small deformations and moderate electric fields. In this limit, the overall elastic dielectric response is characterized by five (two elastic, one dielectric, and two electrostrictive) effective constants. Explicit formulas are derived for these constants directly in terms of the corresponding constants describing the elastic dielectric response of the underlying rubber and the filler particles, as well as the concentration of particles. By means of comparisons with finite-element simulations, these formulas are shown to also be applicable to isotropic suspensions of monodisperse spherical particles, provided that the particle concentration is sufficiently away from percolation. With the aim of gaining physical insight into the extreme enhancement in electrostrictive properties displayed by emerging dielectric elastomer composites, specific results are examined for the case of suspensions wherein the rubber is incompressible and the particles are mechanically rigid and of infinite permittivity.

Numerical and analytical description of the mechanical properties of quasi tetrahedral agglomerates

Quasi tetrahedral agglomerates consist of four spherical primary particles, of which three primary particles generally form a mechanically stable base on which the fourth primary particle is arranged centrally (as in the regular case, where the primary particles have equal radii) forming an apparent trigonal pyramid.The coordinates of the centers of the primary particles are derived for agglomerates composed of monodisperse spherical primary particles (regular tetrahedron) and polydisperse spherical primary particles (skewed tetrahedron). Moreover, the force distribution within the agglomerates at compression is described and an analytical model for elastic contact deformation is derived on the basis of the Hertz model [1].Following, the regular structure of the agglomerates is experimentally analyzed using compression tests and the recorded force–displacement curves are evaluated with the new analytical model. Additionally, mechanical properties like the modulus of elasticity and the yield point of the primary particles as well that as of the tetrahedral agglomerates are also derived.Subsequently, tetrahedral agglomerates are modeled using the discrete element method (DEM) and their compression behavior between two rigid plates is simulated. The received numerical force–displacement curves are compared with the model-based approximated analytical force–displacement curves. Force–displacement curves of agglomerates composed of poly-disperse spherical primary particles are recorded and evaluated as well. It was found that the regular tetrahedron represents the most stable configuration, with an upper threshold force–displacement curve on varying the upper primary particle size and limiting curves on varying the size of one of the lower primary particles.

Flexible tool for simulating the bulk optical properties of polydisperse spherical particles in an absorbing host: experimental validation.

In this study, a flexible tool to simulate the bulk optical properties of polydisperse spherical particles in an absorbing host medium is described. The generalized Mie solution for Maxwell's equations is consulted to simulate the optical properties for a spherical particle in an absorbing host, while polydispersity of the particle systems is supported by discretization of the provided particle size distributions. The number of intervals is optimized automatically in an efficient iterative procedure. The developed tool is validated by simulating the bulk optical properties for two aqueous nanoparticle systems and an oil-in-water emulsion in the visible and near-infrared wavelength range, taking into account the representative particle sizes and refractive indices. The simulated bulk optical properties matched closely (R2 ≥ 0.899) with those obtained by reference measurements.

Modeling of the random packing of a loose layer of polydisperse spherical particles

A method for calculating the loose packing structure of polydisperse spherical particles with a predetermined size distribution function is proposed. The coordinates of the particle centers in the loose layer are determined as the result of random fall of single spheres on a substrate under the action of gravity, assuming the inelastic collision of the spheres and considering the force of their adhesive interaction, and also assuming that the motion of one sphere on the surface of the other is pure slip. Numerical simulation is used to obtain the pattern of arrangement of polydisperse spherical particles in the loose powder layer, whose porosity depends on the particle size distribution function. The results are compared with experimental data.

Use of Statistically Inhomogeneous Screens in Calibration of Lidar from the Parameters of Images of Particles for the Bottom Layer of the Atmosphere

There has been practically no discussion of the problem of remote measurement of the microstructure of scattering media consisting of polydisperse and nonspherical particles. This may be attributed to the great diversity of particles of the bottom layer of the atmosphere possessing undetermined optical and physical properties. Lidar functioning at several wavelengths with subsequent solution of an ill-posed inverse problem is usually used to determine the microstructure of polydisperse spherical particles (fog, haze, etc.). The process of solving the problem requires a priori information concerning the scattering object (for example, the assumption that the distribution function is close to a lognormal distribution). Information about the ranges of the real and imaginary components of the coefficient of diffraction is also important. A particular optimal distribution function of the particles by size, to which the measured spectral dependence of the lidar signals corresponds, is selected as the solution of the ill-posed inverse problem. The radial moments of the particle distribution function by size [1] are used to compare the results of the modeling with the microstructure of the scattering object being studied. A significant volume of adjustment parameters and a priori information about the probed object are needed to solve the ill-posed inverse problem. These features prevent us from performing remote measurements of the parameters of the microstructure of a scattering object. Methods that are used for the solution of an ill-posed inverse problem are not applicable to nonspherical objects (dust, soot, pollen, etc.), since for such particles it is important to determine the transverse dimension of a particle. Cases of thread-like inhomogeneities are also possible. Thus, for existing methods an evaluation of the reliability of the sizes of particles is critical. There is now no indicator of the size of particles available, since an optical scheme of probing cannot be adjusted to particles with given sizes. Multiwave probing is a technically complex procedure for this problem, since calibration of signals to several wavelengths is a necessary condition for its realization. A method that uses lidar operating at a single wavelength (elastic scattering lidar) is quite promising. The problem may be solved with the use of an equivalent scattering object consisting of monodisperse inhomogeneities whose basic optical parameters are the back-scatter factor and the transmission coefficient, as well as the distortion of the beam, as in the case of a scattering object [1]. The measured backscattering signal will then determine the concentration of these particles in the

Porosity Distribution in Monodisperse and Polydisperse Fixed Beds and Its Impact on the Fluid Flow

This work is devoted to the numerical study of the porosity distribution and gas flow within randomly packed fixed beds comprising polydisperse spherical particles with Rosin–Rammler particle size distribution in a cylindrical container. The fixed bed is numerically generated using gravity-forced sedimentation modeled utilizing the discrete element method. The radial porosity distribution of monodisperse fixed beds was validated against published experimental data and good agreement was achieved. The diameter ratio of smallest to largest particle was varied from 1:2 to 1:5 and then 1:10. The simulation revealed overall porosities of 0.38 for the monodisperse bed and 0.345 and 0.33 for polydisperse beds with ratios of 1:2 and 1:10, respectively. In the second part, the fluid flow within the generated fixed beds was examined using a numerical solution to the incompressible Navier–Stokes equations in the Brinkman–Forcheimer formulation. An analysis of the results showed that in the case of a monodisperse fixed bed and low Reynolds numbers (Re) the pressure drop predicted numerically is close to the values calculated using Ergun's relation. The increase inRe leads to the deviation between the numerical and analytical predictions. This effect is because of channeling due to the sinusoidal distribution of the void fraction close to the wall.