Size Distribution Of Spherical Particles Research Articles

Kinetics of the Acid Digestion of Serpentine with Concurrent Grinding. 1. Initial Investigations

The rapid extraction of magnesium from serpentine is critical to novel low-pressure mineral carbonation methodology. Though almost any acid can dissolve the magnesium, the rate plays a critical role in the industrialization of the process. It has been demonstrated that including a low-energy, attrition-type grinding with the chemical attack of the acid can more than double the extraction rate. However, the dissolution mechanism and rate law were elusive. It was found that the dissolution mechanism changes through the reaction progress and with particle size. A model was developed that combines the effects of surface reaction, surface speciation, the electrical double layer, particle size distribution, and ash layer diffusion. Because of the highly irregular particle geometry, a semiempirical spherical particle size distribution was used. The resulting model was able to fit the data with reasonable parameters, and it was demonstrated that the effect of grinding is to change the diffusivity of the ash layer. Further development of the model is underway.

Retrieval of complex refractive index and size distribution of spherical particles from Dual-Polarization Polar Nephelometer data

An algorithm to retrieve the complex refractive index and size distribution of spherical particles from Dual-Polarization Polar Nephelometer data are presented. The assessment of the refractive index is based on the lookup-table approach, which is safe against converging to a local minimum, i.e. false solutions. The results of tests of the algorithm against real experimental data are outlined. The retrieved characteristics are in the expected ranges and in good agreement with the nature of particles and the specifications of the aerosol generators. It is demonstrated that, when a population of small particles, e.g., atmospheric aerosols, is dealt with and a gradient algorithm is employed to estimate the complex refractive index, either the algorithm must be able to overcome the problem of local minima or one should have some a priori information about credible ranges of the real and imaginary parts.

Evaluation of dynamic image analysis for characterizing pharmaceutical excipient particles

The capability of the newly developed dynamic image analysis instrument QicPic equipped with the high-speed dry-powder-dispersing device was investigated systematically using various MCC particles. Instrument cross-validation was conducted by comparing the particle size distribution of spherical particles obtained with the QicPic and with a conventional laser diffraction instrument (HELOS). While good agreement was observed with spherical particles, significant differences were found when analyzing rod-shaped Ceolus™ KG-1000 particles, revealing the intrinsic difference in operating principles between these two techniques. Particle shape distributions of several spherical and rod-shaped samples obtained with the QicPic were compared to scanning electron micrographs (SEMs), and semi-quantitative agreement was obtained. The particle size and particle shape of a series of binary particulate systems composed of both spherical (CP-102) and rod-shaped (KG-1000) particles of varying mass ratios were analyzed using the QicPic. The particle size and shape distributions of these binary mixtures were also computed using the distributions of the pure components weighted by their respective mass fractions. Comparisons between the measured and computed distributions appeared to indicate that the QicPic overestimated the amount of KG-1000 particles present in all the mixtures. Further analysis revealed that the observed discrepancy might be caused by a particle porosity effect.

Anomalous diffraction approximation method for retrieval of spherical and spheroidal particle size distributions in total light scattering

Using total light scattering technique to measure the particle size distribution has advantages of simplicity in measurement principle and convenience in the optical arrangement. However, the calculation of extinction efficiency based on Mie theory for a spherical particle is expensive in both time and resources. Thus, a simple but accurate approximation formula for the exact extinction efficiency may be very desirable. The accuracy and limitations of using the anomalous diffraction approximation (ADA) method for calculating the extinction efficiency of a spherical particle are investigated. Meanwhile, the monomodal and bimodal particle size distributions of spherical particles are retrieved using the genetic algorithm in the dependent model. Furthermore, the spheroidal model in the retrieval of non-spherical particle size distribution is also discussed, which verifies the non-sphericity has a significant effect on the retrieval of particle size distribution compared with the assumed homogeneous isotropic sphere. Both numerical computer simulations and experimental results illustrate that the ADA can be successfully applied to retrieve the particle size distributions for spherical and spheroidal particles with high stability even in the presence of random noise. The method has advantages of simplicity, rapidity, and suitability for in-line particle size measurement.

Retrieval of particle size distribution in the dependent model using the moment method

The problem of determining particle size distribution using the moment method in the spectral extinction technique is studied. The feasibility and reliability of the retrieval of spherical particle size distribution using the moment method are investigated. The single spherical particle extinction efficiency, which is derived theoretically using the Mie's solution to Maxwell's equation, is approximated with a higher order polynomial in order to apply the moment method. Simulation and experimental results indicate that a fairly reasonable representation of the particle size distribution can be obtained using the moment method in the dependent model algorithm. The method has advantages of simplicity, rapidity, and suitability for in-line particle size measurement.

A new algorithm of relaxation method for particle analysis from forward scattered light

A new algorithm of the relaxation method is developed for the inversion of forward scattered light to obtain the size distribution of spherical particles. Numerical tests are performed for a laser particle analyzer using the Mie theory and the diffraction approximation. The algorithm efficiency, in the presence of experimental noises, is studied. The results show that the technique is fast in convergence, stable against random noise and insensitive to the distribution of particles and the initial trial distribution.

Photopyroelectric measurement of thermal conductivity of metallic powders

The effective thermal diffusivity of metal powders in air at room temperature is measured by the photopyroelectric technique. The thermal conductivity is calculated from the diffusivity, the relative density, and the specific heat obtained from literature. Maxwell’s model is a good prediction but underestimates the measured effective thermal conductivity, especially for irregular particles. Due to the large difference between the thermal conductivity of metals and air, the effective conductivity is mainly determined by the relative density of the powder bed but not by the properties of the powder material. A theoretical model showing the influence of grain size and gas pressure is presented. The dependence on the particles’ size and pressure is explained by the gradual transition from the free molecular to conductive mechanism of heat transfer in gaps between particles. The theory gives a precise estimation of effective thermal conductivity for metallic powders with a narrow size distribution of spherical particles and it underestimates this value in the case of a wide size distribution or in the case of irregular particles.

Polar stratospheric cloud microphysical properties measured by the microRADIBAL instrument on 25 January 2000 above Esrange and modeling interpretation

The balloonborne microRADIBAL instrument is a radiometer that measures the radiance and polarization of the sunlight scattered by the atmosphere, gas, and aerosols in a horizontal plane in the near‐infrared range. It was launched from Esrange, Sweden, on 25 January 2000 in the framework of the Third European Stratospheric Experiment on Ozone (THESEO) 2000 campaign, and performed measurements in the vicinity of a large polar stratospheric cloud (PSC). The measurements provide diagrams of the radiance versus scattering angle at several altitudes. The aerosol signature, derived from the radiance measurements, has been modeled via Mie theory and the T‐Matrix code. Three different size distributions of aerosols have been tested: monomodal and bimodal size distributions of spherical particles, and bimodal size distributions including a mode of spherical and a mode of nonspherical particles. The best agreement between the measured and modeled signatures is obtained considering a bimodal size distribution composed by a mode of medium spherical particles (median radius about 0.15 μm) and a second mode of larger nonspherical particles (median radius about 1.1 μm, aspect ratio about 0.6). Concentrations and surface densities of the PSC particles have been estimated. The existence of such particles has been tentatively explained using the Lagrangian Microphysical and Photochemical Lagrangian Stratospheric Model of Ozone (MiPLaSMO) model. On 25 January 2000 the polar stratospheric cloud detected by microRADIBAL is associated with a lee‐wave event. Temperature perturbations due to lee‐wave events were calculated using the National Research Laboratory Mountain Wave Forecast Model (MWFM) and have been included along trajectories. They are localized in a large region between the Norwegian mountains and Esrange. Their amplitude varies from 3 to 7 K. Detailed comparisons between measured and modeled surfaces and dimensional distributions of PSCs' particles are achieved. The two modes of particles detected by microRADIBAL can be interpreted from MiPLaSMO results considering different air masses located along the lines of sight. The air masses are characterized by two different temperature perturbations due to lee‐wave events. With a small temperature perturbation (∼3 K) that occurred just before the time of the measurement, supercooled ternary solution particles are predicted, and with a strong temperature perturbation (∼6 K) that occurred four hours before the measurement, nitric acid trihydate particles are formed.

Particle Size Distribution of Nanospheres by Monte Carlo Fitting of Small Angle X-Ray Scattering Curves

A method for recovering the size distribution of spherical particles from small angle scattering data by using a Monte Carlo interference function fitting algorithm is presented. The method is based on the direct simulation of the small angle scattering data upon the assumption of non-interacting hard sphere ensembles (“dilute” solution approximation). The algorithm for retrieving the particle size distribution does not require any additional parameters apart from the input of the scattering data. The fitting strategy necessarily implies positive particle size distributions, while preserving the advantage of the indirect transformation method for data desmearing. Furthermore, the present approach does not use any regularisation procedures of the best fit solution and favours smooth particle size distributions. The Monte Carlo procedure has been tested against several simulated cases with various types of mono- and bi-modal size distributions and different noise levels. In the special case of non-interacting spheres, the Monte Carlo fitting algorithm had the same retrieving ability as the well assessed indirect transformation, structure interference and maximum entropy methods. Finally, the algorithm was applied to retrieve the distribution of spherical nanopowders produced by gas-to-particle conversion both as free powder and as reinforcing second-phase agent in polymer nanocomposites.

Statistical Analysis of Microstructures in Materials Science

Dedication to G?nter Bach. Preface. Series Preface. Acknowledgements. List of Notation. List of Source Codes. Introduction. Methodological Tools. Statistical Estimation of Basic Characteristics. Basic Characteristics and Digitalization. Covariance and Spectral Density. Size Distribution of Spherical Particles. Nonspherical Particles of Constant Shape. Size-Shape Distribution of Particles. Arrangement of Objects. Single-Phase Polyhedral Microstructures. Appendix A: Characteristics of Geometric Objects. Appendix B: Software Utilities. References. Index.

Quantitative measurements of spherical particle size distribution in a phase separated matrix

In many multicomponent polymeric blend systems micro-phase separation takes place to form dispersed phases within a continuous matrix phase. The mechanical and physical properties of this type of material are often dependent on the number, size, interspacing and volume fraction of the dispersed phase particles. These morphological parameters can be estimated once a correct three-dimensional distribution is established. The use of microscopy for the quantitative study of these parameters presents difficulties arising from the fact that it provides only two-dimensional information. Several statistical treatments to convert two-dimensional distributions to three-dimensional distributions have been developed. These methods were tested with known systems by a computer simulation. Error analysis for estimated distributions as well as suggestions of experimental procedures to more quantitatively deal with this problem are discussed. ©

The impact of subvisible cirrus clouds near the tropical tropopause on stratospheric water vapor

The radiative impact of subvisible cirrus ice clouds at and just below the tropical tropopause has been studied using a zonally averaged interactive chemistry‐radiation‐dynamics model. Model runs have been performed with and without the inclusion of the radiative heating of these thin ice clouds, and with and without sedimentation. Near‐infrared optical depths of 0.005–0.08 were computed for assumed log‐normal size distributions of spherical particles having mode radii of 2–10 µm. Particles with 6 µm mode radii have computed scattering ratios of 3–15 at 603 nm, in good agreement with lidar observations. The increased radiative heating of these clouds, 0.1–0.2 K/day, results in temperature increases of 1–2 K and vertical velocity increases of 0.02–0.04 mm/s. As a consequence of the warmer tropopause, lower stratosphere water vapor increases by as much as 1 ppmv. The dehydration resulting from sedimentation was found to be a much smaller effect.

Nanopowder of silicon nitride produced in radio frequency modulated glow discharges from SiH 4 and NH 3

Square-wave modulated radio frequency (RF) plasmas have been shown to be a suitable source of nanometric size powder with high purity and controllable nanostructure. This paper reports the production of SiN nanopowder at room temperature and low pressure by RF glow discharge decomposition of SiH 4 and NH 3 gases. The RF power was modulated at 0.5 Hz with a duty cycle of 20% in order to control the size of the expelled particles. A study of the particle formation process using in-situ monitoring of the RF dissipated power is presented. Transmission electron microscopy showed a narrow size distribution of spherical particles from 25 to 45 nm and their electron diffraction provided evidence of a short range order in Si or SiN units depending on the precursor gas mixture. Analysis by Fourier transform infrared spectroscopy revealed the presence of SiN, NH and SiH bonds and the elemental analysis of the powder determined its chemical composition.

Analysis of Small-Angle Scattering Data from Spherical Particles by both the Indirect Transform Method and the Maximum-Entropy Method

In this paper extensive comparison studies of the indirect transform method (ITM) and the maximum-entropy method (MEM) were made for recovering the size distribution of spherical particles. Simulated small-angle scattering (SAS) data with different noise levels for various size distributions are tested. It is found that both the MEM and ITM are capable of accurately recovering the original size distributions for various types of size distributions from simulated SAS data with a 1% noise level. When the noise level of the simulated SAS data is increased to 6%, the size distributions recovered by both the ITM and MEM begin to have many noisy oscillations. It is also found that the MEM is more vulnerable to termination effects, i.e. when low-Q or high-Q data are not available. On the other hand, even for cases with limited-Q-range data the ITM can still accurately recover the original size distribution. This was clearly shown in the analysis of the measured small-angle X-ray scattering data, with a limited Q range, from a β-quenched zircaloy-4 specimen.

A two dimensional analysis of the evolution of the particle size distribution in particle laden high temperature jet flows including the effects of coagulation and buoyancy

A numerical study has been done on the evolution of particle size distribution in particle laden high temperature jet flows undergoing convection, diffusion, thermophoresis and coagulation. The dynamic behavior of these particles have been modelled by approximating the particle size distribution by a lognormal function throughout the process and the moments of the particle size distribution have been used to solve the general dynamic equation. The size distributions of spherical particles in the radial and axial direction have been obtained including the effect of buoyancy. Of particular interests are the variations of geometric mean diameter, number concentration and polydispersity. Results show that buoyancy significantly alters the size distribution in both axial and radial direction. One dimensional analysis for non-spherical particles has also been done and the results have been compared with the existing experimental data.

Random models for morphological analysis of powders

SummaryModels to estimate powder size distributions or fractions of components in a mixture of powders were developed and tested for various specimens. The models derived from the Boolean model and from the dead leaves models can be implemented on rough secondary electron scanning electron microscope images, obtained after minimal sample preparation. With the dead leaves tessellation, the size distributions of spherical particles or short fibres can be estimated either from the size distribution of intact grains, or from the area fraction measurement after binary erosions. With the dead leaves random function, there is no need for image segmentation. It provides data on the size and shape of a population of particles from an estimation of the distribution of grey‐level images after erosions by convex structuring elements of increasing size. A version of these models for long fibres is developed for estimating their diameter distribution. Allowing for superposition of particles, the proposed methods enable an unbiased estimation of the size distribution and characterization of the shape of complex particles. The approach is illustrated by applications to spherical particles obtained by simulations and from scanning electron microscope micrographs.

An Alternative Representation of the Ice Canopy for Calculating Microwave Brightness Temperatures over a Thunderstorm

Passive microwave brightness temperatures (TB's) at 92 and 183 GHz from an aircraft thunderstorm overflight are compared with values calculated from radar-derived hydrometer profiles and a modified proximity sounding. Two methods for modeling particles in the ice canopy are contrasted. The fist is a “traditional” approach employing Marshall–Palmer ice spheres. The second, or “alternative,” method partitions 20% of the ice water content into a Marshall–Palmer component for graupel and hail, and 80% into a modified gamma spherical particle size distribution function representing ice crystals. Results from the alternative approach are superior to those from the traditional method in the anvil and mature convective core. In the decaying convective region, the traditional approach yields better agreement with observed magnitude. Neither method, however, matches the geometry of the observed TB depression associated with the decaying convective core. This is likely due to the presence of graupel, which is not detected as a special signature in radar reflectivity, but does diminish TB's through scattering. Brightness temperatures at the relatively high microwave frequencies considered are shown to be very sensitive to the ice-particle size distribution.

Estimation of the Size Distribution of Closed Cell Elements from Analysis of Their Random Plane Sections

Numerical estimates of the size distribution of spherical particles derived from the distribution of their random plane section sizes (Wicksell's problem) are well known. The present paper considers problems in which the observed particles are approximated by either three-axial or ''crushed'' ellipsoids. Based on the described numerical solutions of the problems, the size distributions of some important neuron ultrastructural elements are estimated from an electron microscopic morphometrical study. Experimental evidence supporting the ''crushed'' ellipsoid paradigm is discussed.

A study of the method for measuring the local size distribution of spherical particles diffusing in a fluid by L.D.A.

This work concerns a method for measuring the local size distribution of spherical particles diffusing in a fluid. It is based on the light scattering theory and makes use of an ordinary Laser Doppler Anemometry apparatus. The required information is obtained by analyzing and processing the signal from the PM, which observes the measuring volume at the angle of 90. The pinhole is replaced by a slit oriented in such a way that the intensity of the scattered light depends only on the diameter of the particle and on a single space variable. A direct calibration of the response of the optical system is used to compute the size distribution from the scattered light probability density.

Particle size distribution from small-angle scattering data: A histogram technique

A method of reparametrizing small-angle scattered intensity spectra I(q) in terms of the q=0 contributions from populations of spheres of discrete radii I0(r) is described. The minimal assumptions are made that the scattering from a particulate system can be parameterized as a distribution of sizes of solid spheres, and that the particle positions are uncorrelated. The calculated size distribution can be used to define either the multimodal size distributions of spherical particles or the shape of monodisperse, nonspherical particles. In any case, its usefulness is limited at high concentrations where the particle–particle correlation function has significant structure. The applicability of this technique is demonstrated with calculated spectra and experimental results from water-in-oil microemulsions.