Complex-shaped Particles Research Articles

Gaussian random ellipsoid geometry-based morphometric recovery of irregular particles using light scattering spectroscopy

The purpose of this study is to extend the capabilities of multispectral optical imaging techniques for morphological characterization of irregular particles, encountered in several applications. We have utilized the Gaussian random ellipsoid model to quantize the shape elongation and deviation in complex-shaped particles. Compared with the Gaussian random sphere model, it is more realistic and is applicable to wider range of irregular particles with minimum possible of free parameters. By processing the reduced light scattering spectra, the proposed inverse technique can simultaneously recover the size, volume fraction, elongation, and shape deformation of particles that are randomly oriented within a colloidal suspension. The discrete dipole approximation is employed in forward light scattering calculations and input synthetic data generation. To investigate the robustness of our algorithm in coping with real scenarios, we have added different levels of noise to the observed scattering spectra. The results demonstrate the potential of our technique to non-invasively recover the morphology parameters of irregular particles.

Efficient synthesis of asymmetric particles by sol-gel process

This paper presents a novel and facile method of synthesizing polymer/silica particles with controlled asymmetric morphologies. Our approach is based on the sol–gel process in which cross-linked polystyrene particles (CPS) are adopted as templates and 3-mercaptopropyltriethoxysilane is used as a single silica source. The reaction process causes silane oligomer to preferentially grow on the local surface of CPS, giving rise to polystyrene/thiol-functionalized silica composite particles with a tunable shape. It is found that the morphologies of particles can be easily tailored by changing the ratio of ethanol/water in the reaction medium. In addition, the amount of cross-linker used during the polymerization also plays a key role in the formation of various complex-shaped particles. Controlled geometries of these organic/inorganic composite particles will allow a broad range of potential applications, such as photonic crystals, Pickering emulsifier, sensors, and so on.

Optimal description of two-dimensional complex-shaped objects using spheropolygons

Recent advances in the morphological description of particles in granular material systems allow two-dimensional complex-shaped particles to be realistically simulated using spheropolygons, i.e., the Minkowski sum of a disk and a polygon. For identical numbers of vertices, spheropolygons achieve a better description of shapes than polygons, but require that the optimal spheroradius be determined. Here we propose a method for generating spheropolygons that optimizes the description of particle morphologies, i.e., minimizes the error images and the numbers of vertices. Because the error images of individual particles are a proxy for the accuracy of granular matter flow calculations, while the numbers of vertices are a proxy for the computational time, the method is optimally applicable to discrete element methods. We demonstrate the proposed method using pebbles, gravel, and crushed shells.

Elastic moduli of composites containing a low concentration of complex-shaped particles having a general property contrast with the matrix

There are diverse materials science problems concerned with how the presence of a low concentration of particulate inclusions having mechanical properties distinct from the matrix in which they are placed influences the elasticity of the resulting composite material. There is a classical treatment of the calculation of the leading order virial coefficient for the bulk modulus K and shear modulus G, or intrinsic moduli [K] and [G], for ellipsoidal inclusions having a general contrast between the elastic properties of the particle inclusions and the matrix. However, the treatment of more physically interesting shapes, such as gravel in concrete, is analytically intractable. With literal concrete applications in mind, we treat construction gravel as being composed of block-like particles having an equivalent length, width, and thickness, and we develop numerical approximants for [K] and [G] for these block structures based on finite element calculations and limiting analytic information. The approach generalizes our previous treatment of the electrical conductivity and elastic moduli of composites containing complex-shaped objects, in the dilute limit, having a general property contrast with the suspending matrix, and corrects an error in the previous elastic moduli calculation. We verify that our approximants provide an accurate description of [K] and [G] for general property contrast conditions and extensive tabulations of data based on finite element calculation for a wide range of object shapes.

Large-area optoelastic manipulation of colloidal particles in liquid crystals using photoresponsive molecular surface monolayers

Noncontact optical trapping and manipulation of micrometer- and nanometer-sized particles are typically achieved by use of forces and torques exerted by tightly focused high-intensity laser beams. Although they were instrumental for many scientific breakthroughs, these approaches find few technological applications mainly because of the small-area manipulation capabilities, the need for using high laser powers, limited application to anisotropic fluids and low-refractive-index particles, as well as complexity of implementation. To overcome these limitations, recent research efforts have been directed toward extending the scope of noncontact optical control through the use of optically-guided electrokinetic forces, vortex laser beams, plasmonics, and optofluidics. Here we demonstrate manipulation of colloidal particles and self-assembled structures in nematic liquid crystals by means of single-molecule-thick, light-controlled surface monolayers. Using polarized light of intensity from 1,000 to 100,000 times smaller than that in conventional optical tweezers, we rotate, translate, localize, and assemble spherical and complex-shaped particles of various sizes and compositions. By controlling boundary conditions through the monolayer, we manipulate the liquid crystal director field and the landscape of ensuing elastic forces exerted on colloids by the host medium. This permits the centimeter-scale, massively parallel manipulation of particles and complex colloidal structures that can be dynamically controlled by changing illumination or assembled into stationary stable configurations dictated by the "memorized" optoelastic potential landscape due to the last illumination pattern. We characterize the strength of optically guided elastic forces and discuss the potential uses of this noncontact manipulation in fabrication of novel optically- and electrically-tunable composites from liquid crystals and colloids.

Computational fluid dynamics in the development of catalytic reactors

Computational fluid dynamics is becoming an important tool in the study of chemical engineering processes and apparatuses (in particular, the share of works with the application of this method is nearly 6% of the total number of all chemical engineering works issued by Elsevier Science Publishers in 2010). The possibilities of computational fluid dynamics are demonstrated using examples from three different chemical engineering fields: developing a method for loading a tubular reactor for the steam conversion of natural gas, studying heat transfer in a reactor for the hydrogenation of vegetable oils upon the replacement of a catalyst, and investigating the transitional processes in an automobile neutralizer. The results from computational fluid dynamics are verified by comparing them with experimental data in developing a method for loading a tubular reactor, using the problem of decelerating a catalyst particle with a flow of air as an example. The obtained data are compared with classical measurement data on the aerodynamic drag of a ball and a cylinder and represent the further development of works on the flow around particles of complex shape. In this work, the results from inspecting a reactor for the hydrogenation of oils with allowance for the possible heating and uniform distribution of a flow before its entering the catalyst bed are presented. It is shown that the construction of the reactor does not ensure homogeneity of the reaction flow at the desired level and requires modification of heating elements. The efficiency of computational fluid dynamics for investigating fast processes with a chemical reaction is exemplified by studying the transitional processes in an catalytic automobile neutralizer (the effect of flow dynamics and heat transfer on the thermal regime in a honeycomb catalyst particle is very difficult to study by experimental methods). The application of computational fluid dynamics allows us to reduce considerably the time and cost of developing and optimizing the designs of efficient catalytic fixed-, fluidized-, or moving-bed reactors (particularly multiphase stirred (slurry) reactors), along with mixers, adsorbers, bubblers, and other chemical engineering apparatuses with moving media.

Influence of the Hydrophobicity of Polyelectrolytes on Polyelectrolyte Complex Formation and Complex Particle Structure and Shape

Polyelectrolyte complexes (PECs) were prepared by structural uniform and strongly charged cationic and anionic modified alternating maleic anhydride copolymers. The hydrophobicity of the polyelectrolytes was changed by the comonomers (ethylene, isobutylene and styrene). Additionally, the n−/n+ ratio of the molar charges of the polyelectrolytes and the procedure of formation were varied. The colloidal stability of the systems and the size, shape, and structure of the PEC particles were investigated by turbidimetry, dynamic light scattering (DLS) and atomic force microscopy (AFM). Dynamic light scattering indicates that beside large PEC particle aggregates distinct smaller particles were formed by the copolymers which have the highest hydrophobicity (styrene). These findings could be proved by AFM. Fractal dimension (D), root mean square (RMS) roughness and the surface profiles of the PEC particles adsorbed on mica allow the following conclusions: the higher the hydrophobicity of the polyelectrolytes, the broader is the particle size distribution and the minor is the swelling of the PEC particles. Hence, the most compact particles are formed with the very hydrophobic copolymer.

Light absorption and scattering by aggregates: Application to black carbon and snow grains

A geometric-optics surface-wave approach has been developed for the computation of light absorption and scattering by nonspherical particles for application to aggregates and snow grains with external and internal mixing structures. Aggregates with closed- (internal mixing) and open-cell configurations are constructed by means of stochastic procedures using homogeneous and core-shell spheres with smooth or rough surfaces as building blocks. The complex aggregate shape and composition can be accounted for by using the hit-and-miss Monte Carlo geometric photon tracing method. We develop an integral expression for diffraction by randomly oriented aggregates based on Babinet's principle and a photon-number weighted geometric cross section. With reference to surface-wave contributions originally developed for spheres, we introduce a nonspherical correction factor using a non-dimensional volume parameter such that it is 1 for spheres and 0 for elongated particles. The extinction efficiency, single-scattering albedo, and asymmetry factor results for randomly oriented columns and plates compare reasonably well with those determined from the finite-difference time domain (FDTD) and the discrete dipole approximation (DDA) computer codes for size parameters up to about 20. The present theoretical approach covers all size ranges and is particularly attractive from the perspective of efficient light absorption and scattering calculations for complex particle shape and inhomogeneous composition. We show that under the condition of equal volume and mass, the closed-cell configuration has larger absorption than its open-cell counterpart for both ballistic and diffusion-limited aggregates. Because of stronger absorption in the closed-cell case, most of the scattered energy is confined to forward directions, leading to a larger asymmetry factor than the open-cell case. Additionally, light absorption for randomly oriented snowflakes is similar to that of their spherical counterparts under the condition of equal geometrical cross section area for both external and internal mixing states; however, nonspherical snowflakes scatter less light in forward directions than spheres, resulting in a substantial reduction of the asymmetry factor. We further demonstrate that small soot particles on the order of 1 μm internally mixed with snow grains could effectively reduce snow albedo by as much as 5–10%. Indeed, the depositions of black carbon would substantially reduce mountain-snow albedo, which would lead to surface warming and snowmelt, critical to regional climatic surface temperature amplification and feedback.

Comparison of the multi-sphere and polyhedral approach to simulate non-spherical particles within the discrete element method: Influence on temporal force evolution for multiple contacts

In this paper a multi-sphere as well as a polyhedral approach is investigated as method of shape-approximation within the discrete element method. The two approaches are compared against each other using an ellipsoidal particle impacting on a flat wall as a reference scenario. In general it is shown that there is a non-negligible effect of shape approximation on the temporal force evolution in normal and tangential direction. The occurrence of multiple contacts between the particles when approximated by a multi-sphere or a polyhedral approach is detected as a main source of differences between the exact solution and the solution of the approximated particles. A method to account for these effects is provided in order to increase the accuracy when complex particle shapes are used. Moreover the effect of shape-approximation accuracy on the accuracy of the results is investigated. For both approximation procedures higher accuracy levels in terms of particle shape representation do not automatically lead to more accurate results for normal and tangential forces in the investigated collision scenarios. It will be shown that the effects of a more accurate ellipsoid-surface approximation and higher numbers of contact points influence the quality of the results in opposite directions.

Digital holographic imaging of aerosol particles in flight

This work describes the design and application of an apparatus to image aerosol particles using digital holography in a flow-through, contact-free manner. Particles in an aerosol stream are illuminated by a triggered, pulsed laser and the pattern produced by the interference of this light with that scattered by the particles is recorded by a digital camera. The recorded pattern constitutes a digital hologram from which an image of the particles is computationally reconstructed using a fast Fourier transform. This imaging is validated using a cluster of ragweed pollen particles. Examples involving mineral-dust aerosols demonstrate the technique's in situ imaging capability for complex-shaped particles over a size range of roughly 15–500 μ m micrometers. The focusing-like character of the reconstruction process is demonstrated using a NaCl aerosol particle and is compared to a similar particle imaged with a conventional microscope.

Minkowski-Voronoi diagrams as a method to generate random packings of spheropolygons for the simulation of soils

Minkowski operators (dilation and erosion of sets in vector spaces) have been extensively used in computer graphics, image processing to analyze the structure of materials, and more recently in molecular dynamics. Here, we apply those mathematical concepts to extend the discrete element method to simulate granular materials with complex-shaped particles. The Voronoi-Minkowski diagrams are introduced to generate random packings of complex-shaped particles with tunable particle roundness. Contact forces and potentials are calculated in terms of distances instead of overlaps. By using the Verlet method to detect neighborhood, we achieve CPU times that grow linearly with the body's number of sides. Simulations of dissipative granular materials under shear demonstrate that the method maintains conservation of energy in accord with the first law of thermodynamics. A series of simulations for biaxial test, shear band formation, hysteretic behavior, and ratcheting show that the model can reproduce the main features of real granular-soil behavior.

Molecular dynamics simulations of complex-shaped particles using Voronoi-based spheropolyhedra

The spheropolyhedra method has been used earlier for efficient and accurate molecular dynamics simulations of granular matter with particles with complex shapes. Also the Voronoi construction is a tool of proved utility for the virtual representation of powders and grains. In this paper a technique that combines the two methods and provides a framework for the study of the three-dimensional mechanical behavior of granular matter is proposed. In order to understand the capabilities of the new method, a number of computer simulations of the cubic (true) triaxial test, measuring the mechanical behavior of packing of particles, is carried out. Results from tests with packing of complex-shaped particles represented by "Voronoi particles" are compared with corresponding results of packing of spherical particles. Features such as the saturation value for the macroscopically observed coefficient of friction, as reported in the literature, are compared for the packing of spheres and for the packing of "Voronoi particles," showing that the difference in shape strongly affects the results. The proposed technique and simulation results can be used to help understand how the individual shape of grains affects the macroscopic mechanical behavior of granular matter such as cohesionless soils.

Investigating the effect of shape on particle segregation using a Monte Carlo simulation

A Monte Carlo simulation has been used to investigate the segregation potential of a range of particulate systems under conditions in which the particles undergo high amplitude low frequency shaking. These systems involve a wide range of binary powder mixtures in which complex particle shapes have been investigated, including plates and rods which represent the real world materials encountered in pharmaceutical systems such as those which include crystalline components. Previous simulations on the segregation propensity of systems with different shapes were limited to spheres and spherocylinders, with relatively low vibrational amplitude drops. A commercial computer application for particle packing—called MacroPac—has been successfully employed here, as it has been able to model systems that are more complex where the shape variation is much wider. These simulations apply to the case of macroscopic particles, in the absence of air resistance and inter-particle forces. For non-spherical shapes, an ‘effective size’ which relates to the radius of gyration of the particles is determined. Our studies indicate that with high amplitude low frequency shaking, in a mixture of particles with different shapes but with equal volumes, the particles with the larger ‘effective size’, which tend to have a lower packing fraction, segregate to the top.

Method for determining the aerodynamic diameter of complex-shaped aerosol particles within the Reynolds-number range from 0.1 to 6.0

In the present paper, we introduce an experimental technique for evaluating the equivalent aerodynamic diameter dae of non-spherical aerosol particles upon their sedimentation in a gravity field within the Reynoldsnumber range from 0.1 to 6.0. A description of the sedimentometer is given, and aerodynamic diameters dae of plexiglass powder particles measured on this sedimentometer are reported.

An efficient algorithm for granular dynamics simulations with complex-shaped objects

One of the most difficult aspect of the realistic modeling of granular materials is how to capture the real shape of the particles. Here we present a method to simulate two-dimensional granular materials with complex-shaped particles. The particle shape is represented by the classical concept of a Minkowski sum, which permits the representation of complex shapes without the need to define the object as a composite of spherical or convex particles. A well defined interaction force between these bodies is derived. The algorithm for identification of neighbor particles reduces force calculations to O(N), where N is the number of particles. The method is much more efficient, accurate and easier to implement than other models. We prove that the algorithm is consistent with energy conservation, which is numerically verified using non-dissipative granular dynamics simulations. Biaxial test simulations on dissipative granular systems demonstrate the relevance of shape in the strength and stress fluctuations at the critical state.

Analysis of polarization transformations by a planar chiral array of complex-shaped particles

Vectorial relations of field amplitudes are derived from the Lorentz lemma applied to electromagnetic fields at direct and reversed scenarios of a wave diffraction on a doubly-periodic planar array. Biorthogonality of polarization eigenstates of the waves propagating in opposite directions is shown with reference to a wave channel formed by an incident wave and a diffraction order. For a planar chiral array, an essential difference in polarization transformations of propagated waves is ascertained in the direct wave channel and in the reversed one. Numerical data are presented to demonstrate the polarization transformations by both transmitting and reflecting planar chiral arrays. A difference in polarization eigenstates inherent to a planar chiral array and a bulk chiral medium is noticed.

Smoothed profile method for particulate flows: Error analysis and simulations

We re-formulate and analyze a new method for particulate flows, the so-called “smoothed profile” method (SPM) first proposed in [Y. Nakayama, R. Yamamoto, Simulation method to resolve hydrodynamic interactions in colloidal dispersions, Phys. Rev. E 71 (2005) 036707], which uses a fixed computational mesh without conformation to the geometry of the particles. The method represents the particles by certain smoothed profiles to construct a body force term added into the Navier–Stokes equations. SPM imposes accurately and efficiently the proper conditions at the particle–fluid interface. In particular, while the original method employs a fully-explicit time-integration scheme we develop a high-order semi-implicit splitting scheme, which we implement in the context of spectral/ hp element discretization. First, we show that the modeling error of SPM has a non-monotonic dependence on the time step size Δ t ; it is a function of ν Δ t / ξ , where ν is the kinematic viscosity of fluid and ξ is the interface thickness of the smoothed profile. Subsequently, we present several steady and unsteady simulations, including flow past 3D complex-shaped particles, and compare against direct numerical simulations and the force coupling method (FCM).

A simple method to create complex particle shapes for DEM

In order to get quantitatively reliable results with the discrete element method, or DEM, it becomes more and more necessary to reproduce accurately the shape of irregular particles. A simple and fast original method to create complex shapes by assembling spheres together is proposed. This paper shows its ability to reproduce a shape, its degree of resolution and the number of spheres required.

On the use of discrete element modelling to simulate the viscoelastic deformation behaviour of an idealized asphalt mixture

The use of discrete-element modelling (DEM) to simulate the behaviour of a highly idealized bituminous mixture under uniaxial and triaxial compressive creep tests is investigated in this paper. The idealized mixture comprises single-sized spherical particles (sand) mixed with bitumen and was chosen so that the packing characteristics are known and the behaviour of the mixture is dominated by the bitumen. The bitumen is represented as shear and normal (tensile and compressive) contact stiffnesses. Numerical sample preparation procedures for specimens containing spherical particles or clumps have been developed to ensure that the final specimen is isotropic and has the correct volumetric proportions. An elastic contact was used for the compressive normal contact stiffness and a viscoelastic contact was used for shear and tensile normal contact stiffness. Simulation results show that the idealized mixture is found to dilate when the ratio of compressive to tensile contact stiffness increases as a function of loading time. Uniaxial and triaxial viscoelastic simulations have been performed to investigate the effect of stress ratio on dilation and the numerical results have been verified with experimental data. The effects of introducing a proportion of frictional contacts and a more complex particle shape (clump) on dilation have been examined.

On the Effective Constitutive Parameters of Metal-Dielectric Arrays of Complex-Shaped Particles

The problem of retrieving the effective constitutive parameters for planar arrays of metallic complex-shaped particles printed on a dielectric substrate is considered in this paper. The equivalent homogenized layer gives exactly the same complex reflection and transmission coefficients for normal incident plane waves as in the original problem.