Log-normal Particle Size Distribution Research Articles

Demagnetization factor for a powder of randomly packed spherical particles

The demagnetization factors for randomly packed spherical particle powders with different porosities, sample aspect ratios, and monodisperse, normal, and log-normal particle size distributions have been calculated using a numerical model. For a relative permeability of 2, comparable to room temperature Gd, the calculated demagnetization factor is close to the theoretical value. The normalized standard deviation of the magnetization in the powder was 6.0%–6.7%. The demagnetization factor decreased significantly, while the standard deviation of the magnetization increased, for increasing relative permeability.

Radar-radiometer retrievals of cloud number concentration and dispersion parameter in nondrizzling marine stratocumulus

Abstract. The retrieval of cloud microphysical properties from remote sensors is challenging. In the past, ground-based radar-radiometer measurements have been successfully used to retrieve the liquid water content profile in nondrizzling clouds but offer little constraint in retrieving other moments of the cloud particle size distribution (PSD). Here, a microphysical condensational model under steady-state supersaturation conditions is utilized to provide additional constraints to the well-established radar-radiometer retrieval techniques. The coupling of the model with the observations allows the retrieval of the three parameters of a lognormal PSD, with two of them being height dependent. Two periods of stratocumulus from the Azores are used to evaluate the novel technique. The results appear reasonable in two nondrizzling periods: continental-like number concentrations are retrieved, in agreement with the drizzle-free cloud conditions. The cloud optical depth derived from the retrieved distributions compares well in magnitude and variability with the one derived independently from a narrow field of view zenith radiometer. Uncertainties coming from the measurements are propagated to the retrieved quantities to estimate their errors. In general, errors smaller than 20% should be attainable for most parameters, demonstrating the added value of the new technique.

Temperature dependence of electron magnetic resonance spectra of iron oxide nanoparticles mineralized in Listeria innocua protein cages

Electron magnetic resonance (EMR) spectroscopy was used to determine the magnetic properties of maghemite (γ-Fe(2)O(3)) nanoparticles formed within size-constraining Listeria innocua (LDps)-(DNA-binding protein from starved cells) protein cages that have an inner diameter of 5 nm. Variable-temperature X-band EMR spectra exhibited broad asymmetric resonances with a superimposed narrow peak at a gyromagnetic factor of g ≈ 2. The resonance structure, which depends on both superparamagnetic fluctuations and inhomogeneous broadening, changes dramatically as a function of temperature, and the overall linewidth becomes narrower with increasing temperature. Here, we compare two different models to simulate temperature-dependent lineshape trends. The temperature dependence for both models is derived from a Langevin behavior of the linewidth resulting from "anisotropy melting." The first uses either a truncated log-normal distribution of particle sizes or a bi-modal distribution and then a Landau-Liftshitz lineshape to describe the nanoparticle resonances. The essential feature of this model is that small particles have narrow linewidths and account for the g ≈ 2 feature with a constant resonance field, whereas larger particles have broad linewidths and undergo a shift in resonance field. The second model assumes uniform particles with a diameter around 4 nm and a random distribution of uniaxial anisotropy axes. This model uses a more precise calculation of the linewidth due to superparamagnetic fluctuations and a random distribution of anisotropies. Sharp features in the spectrum near g ≈ 2 are qualitatively predicted at high temperatures. Both models can account for many features of the observed spectra, although each has deficiencies. The first model leads to a nonphysical increase in magnetic moment as the temperature is increased if a log normal distribution of particles sizes is used. Introducing a bi-modal distribution of particle sizes resolves the unphysical increase in moment with temperature. The second model predicts low-temperature spectra that differ significantly from the observed spectra. The anisotropy energy density K(1), determined by fitting the temperature-dependent linewidths, was ∼50 kJ/m(3), which is considerably larger than that of bulk maghemite. The work presented here indicates that the magnetic properties of these size-constrained nanoparticles and more generally metal oxide nanoparticles with diameters d < 5 nm are complex and that currently existing models are not sufficient for determining their magnetic resonance signatures.

Continuum representation of a continuous size distribution of particles engaged in rapid granular flow

Natural and industrial granular flows often consist of several particle sizes, approximately forming a continuous particle size distribution (PSD). Continuous PSDs are ubiquitous, though existing kinetic-theory-based, hydrodynamic models for rapid granular flows are limited to a discrete number of species. The objective of this work is twofold: (i) to determine the number of discrete species required to accurately approximate a continuous PSD and (ii) to validate these results via a comparison with molecular dynamics (MD) simulations of continuous PSDs. With regard to the former, several analytic (Gaussian and lognormal) and experimental (coal and lunar soil simulants) distributions are investigated. Transport coefficients (pressure, shear viscosity, etc.) of the granular mixture given by the polydisperse theory of Garzó et al. [“Enskog theory for polydisperse granular mixtures. I. Navier-Stokes order transport,” Phys. Rev. E 76, 031303 (2007)10.1103/PhysRevE.76.031303;Garzó et al. “Enskog theory for polydisperse granular mixtures. I. Navier-Stokes order transport,” Phys. Rev. E 76, 031304 (2007)10.1103/PhysRevE.76.031304] are compared using an increasing number of species s to approximate the given PSD. These discrete approximations are determined by matching the first 2s moments of the approximation and the given continuous distribution. Relatively few species are required to approximate moderately wide distributions (Gaussian, lognormal), whereas even wider distributions (coal and lunar soil simulants) require a larger number of species. Regarding the second objective, a comparison between MD simulations and kinetic-theory predictions for a simple shear flow of both Gaussian and lognormal PSDs reveal essentially no loss of accuracy stemming from the polydisperse theory itself (as compared to theories for monodisperse systems) or from the discrete approximations of continuous PSDs used in the polydisperse theory.

Characterization of airborne particles in an open pit mining region

We characterized airborne particle samples collected from 15 stations in operation since 2007 in one of the world's largest opencast coal mining regions. Using gravimetric, scanning electron microscopy (SEM-EDS), and X-ray photoelectron spectroscopy (XPS) analysis the samples were characterized in terms of concentration, morphology, particle size distribution (PSD), and elemental composition. All of the total suspended particulate (TSP) samples exhibited a log-normal PSD with a mean of d=5.46±0.32μm and σ(ln d)=0.61±0.03. Similarly, all particles with an equivalent aerodynamic diameter less than 10μm (PM10) exhibited a log-normal type distribution with a mean of d=3.6±0.38μm and σ(ln d)=0.55±0.03. XPS analysis indicated that the main elements present in the particles were carbon, oxygen, potassium, and silicon with average mass concentrations of 41.5%, 34.7%, 11.6%, and 5.7% respectively. In SEM micrographs the particles appeared smooth-surfaced and irregular in shape, and tended to agglomerate. The particles were typically clay minerals, including limestone, calcite, quartz, and potassium feldspar.

Multimodality of a particle size distribution of cohesive suspended particulate matters in a coastal zone

Particle size distributions (PSDs) of suspended particulate matters in a coastal zone are lognormal and multimodal in general. The multimodal PSD, which is caused by the mixing of multiple particle and aggregate size groups under flocculation and erosion/resuspension, is a record of the particle and aggregate dynamics in a coastal zone. Curve‐fitting software was used to decompose the multimodal PSD into subordinate lognormal PSDs of primary particles, flocculi, microflocs, and macroflocs. The curve‐fitting analysis for a time series of multimodal PSDs in the Belgian coastal zone showed the dependency of the multimodality on (1) shear‐dependent flocculation in a flood and ebb tide, (2) breakage‐resistant flocculation in the spring season, and (3) silt‐sized particle erosion and advection in a storm surge. Also, for modeling and simulation purposes, the curve‐fitting analysis and the settling flux estimation for the multimodal PSDs showed the possibility of using discrete groups of primary particles, flocculi, microflocs, and macroflocs as an approximation of a continuous multimodal PSD.

Magnetic behaviour of Ni0.4Zn0.6Co0.1Fe1.9O4 spinel nano-ferrite

Nanoparticles of the spinel ferrite Ni0.4Zn0.6Co0.1Fe1.9O4, have been synthesized by a co-precipitation method. The x-ray diffraction patterns of the particles confirmed the formation of single-phase cubic spinel structure. The Langevin function fitting on M-H data at 300 K gives a log-normal particle size distribution with median diameter of 59.6 nm and standard deviation of 0.6. The isothermal dc magnetization studies have been performed using the superconducting quantum interface device and vibrating sample magnetometer in the temperature range of 5-300 K. These measurements show that the sample is superparamagnetic above the blocking temperature TB ∼ 253 K when an external magnetic field of 20 Oe is applied. The reduction in saturation magnetization in case of nanoparticles may be attributed to the fact that magnetic moments in the surface layers outside the core are in the state of frozen disorder. A doublet observed in the Mössbauer study also confirms the superparamagnetic behavior and nanocrystalline formation.

3-d numerical simulation of particle concentration effect on a single-wire ESP performance for collecting poly-dispersed particles

In this paper a simple one stage wire-plate electrostatic precipitator is analyzed to predict particle transport and charging, and airflow patterns under the influence of EHD and external flows, assuming various particle concentrations. The investigated numerical model includes the governing equations describing the motion of ions, gas, solid particles and the effect of particle space charge. The complicated mutual interaction mechanisms between the three coexisting fields of gas flow, particle trajectories and electrostatic field, which affect an industrial ESP process, have been implemented using the User Defined Functions (UDFs) in commercial FLUENT 6.2 software. The electrostatic field and ionic space charge density due to corona discharge were computed by numerical solution of Poisson and current continuity equations using a hybrid Finite Element - Flux Corrected Transport method. The model takes into account the particle space charge density effect on the ionic charge density distribution. The airflow equations were solved inside FLUENT using the Finite Volume Method and the turbulence effect was included by using the k-e model. The Lagrangian random walk approach was used to determine particle motion, as affected by EHD flows and turbulence effects. This part was performed with the aid of Discrete Phase Model (DPM) in FLUENT. The performance of the discussed ESP in the removal of particulates and the effect of different particle concentration on the gas flow pattern and corona discharge current was evaluated numerically assuming poly-dispersed particles with lognormal particle size distribution.

Polydispersity effects on the magnetization of diluted ferrofluids: a lognormal analysis

Based on a lognormal particle size distribution, this paper makes a model analysis on the polydispersity effects on the magnetization behaviour of diluted ferrofluids. Using a modified Langevin relationship for the lognormal dispersion, it first performs reduced calculations without material parameters. From the results, it is extrapolated that for the ferrofluid of lognormal polydispersion, in comparison with the corresponding monodispersion, the saturation magnetization is enhanced higher by the particle size distribution. It also indicates that in an equivalent magnetic field, the lognormally polydispersed ferrofluid is magnetically saturated faster than the corresponding monodispersion. Along the theoretical extrapolations, the polydispersity effects are evaluated for a typical ferrofluid of magnetite, with a dispersity of σ = 0.20. The results indicate that the lognormal polydispersity leads to a slight increase of the saturation magnetization, but a noticeable increase of the speed to reach the saturation value in an equivalent magnetic field.

Static and dynamic magnetic properties of monodispersed Mn0.5Zn0.5Fe2O4 nanomagnetic particles

Static and dynamic magnetic properties of oleic acid/oleyamine coated Mn–Zn ferrite nanoparticles of diameter 82 Å are reported. The zero-field-cooled peak temperature decreases with increasing magnetic field and obeys the well known de Almeida–Thouless line. The zero-field-cooled magnetization data are simulated by assuming noninteracting magnetic particles with uniaxial anisotropy and lognormal particle size distribution. The relevant parameters give the values of particle diameter (D) 80 Å, standard deviation 0.3 in ln(D), and the anisotropy constant K to be 5.8×105 erg/cm3. The observed higher value of standard deviation is due to the interparticle interaction. The complex magnetic susceptibility was measured as a function of temperature for frequencies ranging from 67 to 1800 Hz. The temperature at which the maximum in the ac-susceptibility curve is observed is well accounted by the Vogel–Fulcher law for both χ′ and χ″. The peak is also observed in a plot of χ″/χ′ versus temperature, which may mean the existence of magnetic aftereffect, and furthermore, it has an Arrhenius as well as Vogel–Fulcher law type dependence. An observed nonthermal activation type relaxation mechanism at 12 K is attributed to possible quantum tunneling effect in Mn–Zn ferrite nanoparticles.

Approximated Solution of Estimating Cyclone Efficiency for Polydispersed Aerosol

A simplified analytic solution for calculating overall collection efficiency of polydispersed aerosol by a cyclone separator was studied. The generalized Lapple's collection efficiency was modified for polydispersed aerosol under the assumption of lognormal particle size distribution. Approximate overall collection efficiency was compared with numerically estimated results in various size distribution parameters, and showed good agreement. This study evaluated the effect of polydispersity on overall collection efficiency in a cyclone separator. Results can be applied to the estimation of collection efficiency of a cyclone separator and in the error analysis of cyclone separation of polydispersed aerosol.

Numerical investigation on new configurations for vapor-phase aerosol reactors

Non-ideal aerosol reactors for synthesizing nano- and micro-metal-oxide powders can currently be accurately designed by means of computational fluid dynamics (CFD) models instead of an expensive trial-and-error experimental technique. According to a multi-scale approach, fluid dynamics of the reacting volume is modeled by an appropriate population balance equation (PBE) coupled to momentum, energy and chemical species conservative equations. The present work refers to the modeling of non-ideal vapor-phase aerosol reactors, in particular to the numerical investigation on the effects of feeding nozzle arrangement, where the most significant gradients and aerosol phenomena occur. The described aerosol CFD model, which a priori assumes a log-normal particle size distribution (PSD), has been validated against both an experimental and an industrial case, and therefore it has been applied to the study of new reactor configurations. Numerical results show that traditional axial-symmetric and jet-opposed nozzle arrangements can be improved adopting a tangential geometry.

Fabrication of Fe nanoparticles with sizes ranging from 30 to 170 nm by gas flow sputtering

Fe nanoparticles were prepared by gas flow sputtering (GFS), and their sizes and size distributions were investigated as functions of the preparation parameters. The mean diameter of the particles increased with the sputtering pressure and substrate-to-target separation; the size distribution of the particles was well fitted by a log-normal function. By varying the sputtering pressure and substrate-to-target separation, Fe particles with diameters ranging from 30 to 170 nm were obtained. On the other hand, the value of S(D)/E(D), where E(D) and S(D) are the mean diameter and standard deviation of the log-normal particle size distribution, respectively, remained constant at approximately 0.2 and did not vary significantly when the sputtering pressure and substrate-to-target separation were changed, indicating that a narrow size distribution is achieved by GFS.

Computational Modeling of Silicon Nanoparticle Synthesis: I. A General Two-Dimensional Model

A two-dimensional model has been developed for silicon nanoparticle synthesis by silane thermal decomposition driven by laser heating in a tubular reactor. This fully coupled model includes fluid dynamics, laser heating, gas phase and surface phase chemical reactions, and aerosol dynamics which includes particle transport and evolution by convection, diffusion, thermophoresis, nucleation, surface growth, and coagulation processes. A moment method, based upon a lognormal particle size distribution, and a sectional method are used to model the aerosol dynamics. The simulation results obtained by the two methods are compared. The sectional method is capable of capturing the bimodal behavior that occurs locally during the process, while the moment method is computationally more efficient. The effect of operating parameters, such as precursor concentration, gas phase composition, inlet gas velocity and laser power input, on the characteristics of the particles produced are investigated. Higher temperature gene...

Mass estimations of ejecta from Strombolian explosions by inversion of Doppler radar measurements

We present a new method for estimating particle loading parameters (mass, number, volume) of eruptive jets by inversion of echo power data measured using a volcano Doppler radar (VOLDORAD) during typical Strombolian activity from the southeast (SE) crater of Mount Etna on 4 July 2001. Derived parameters such as mass flux, particle kinetic and thermal energy, and particle concentration are also estimated. The inversion algorithm uses the complete Mie (1908) formulation of electromagnetic scattering by spherical particles to generate synthetic backscattered power values. In a first data inversion model (termed the polydisperse model), the particle size distribution (PSD) is characterized by a scaled Weibull function. The mode of the distribution is inferred from particle terminal velocities measured by Doppler radar for each explosion. The distribution shape factor is found to be 2.3 from Chouet et al.'s (1974) data for typical Strombolian activity, corresponding to the lognormal PSDs commonly characteristic of other Strombolian deposits. The polydisperse model inversion converges toward the Weibull scale factor producing the best fit between synthetic and measured backscattered power. A cruder, alternative monodisperse model is evaluated on the basis of a single size distribution assumption, the accuracy of which lies within 25% of that of the polydisperse model. Although less accurate, the monodisperse model, being much faster, may be useful for rapid estimation of physical parameters during real‐time volcano monitoring. Results are illustrated for two explosions at Mount Etna with contrasted particle loads. Estimates from the polydisperse model give 58,000 and 206,000 kg as maxima for the total mass of pyroclasts, 26,400 and 73,600 kg s−1 for mass flux rates, 38 and 135 m3 (22 and 76 m3 equivalent magma volume) for the pyroclast volumes, and 0.02–0.4 and 0.06–0.12 kg m−3 for particle concentrations, respectively. The time‐averaged kinetic energy released is found to be equal to 4.2 × 107 and 3.9 × 108 J, and thermal energy is estimated at 8.4 × 1010 and 3 × 1011 J.

Particle size distribution in FeAg granular alloy

A combination of Langevin and hyperbolic tangent functions weighted by a log-normal particle size distributions were used to fit the magnetization curves of Fe 10Ag 90 granular alloys, produced by a sol–gel process under different chemical conditions. The fitting technique allows one to get both the superparamagnetic and the blocked particle size distributions. The average size of the Fe particles obtained from the fit were in good agreement with those obtained by X-ray diffraction. The correlation between the coercive field and the particle distribution was also investigated. Zero-field cooling dc magnetic susceptibility measurements were fitted using a similar technique to that used for fitting the magnetization curves. The saturation magnetization and mean Fe particle size values obtained from the two fittings were in good agreement.

Bayesian assessment of uncertainty in aerosol size distributions and index of refraction retrieved from multiwavelength lidar measurements

We investigate the assessment of uncertainty in the inference of aerosol size distributions from backscatter and extinction measurements that can be obtained from a modern elastic/Raman lidar system with a Nd:YAG laser transmitter. To calculate the uncertainty, an analytic formula for the correlated probability density function (PDF) describing the error for an optical coefficient ratio is derived based on a normally distributed fractional error in the optical coefficients. Assuming a monomodal lognormal particle size distribution of spherical, homogeneous particles with a known index of refraction, we compare the assessment of uncertainty using a more conventional forward Monte Carlo method with that obtained from a Bayesian posterior PDF assuming a uniform prior PDF and show that substantial differences between the two methods exist. In addition, we use the posterior PDF formalism, which was extended to include an unknown refractive index, to find credible sets for a variety of optical measurement scenarios. We find the uncertainty is greatly reduced with the addition of suitable extinction measurements in contrast to the inclusion of extra backscatter coefficients, which we show to have a minimal effect and strengthens similar observations based on numerical regularization methods.

Impedance as a Tool for Investigating Aging in Lithium-Ion Porous Electrodes: II. Positive Electrode Examination

High-power positive composite porous electrodes are known to be the main source of impedance increase in batteries based on GEN2 chemistry. The impedance of positive electrodes, both fresh and harvested from coin cells aged in an accelerated EUCAR hybrid electric vehicle lifetime matrix, was measured in a three-electrode setup and the results fitted with a physically based impedance model. A methodology for fitting the impedance data, including an optimization strategy incorporating a global genetic routine, was used to fit either fresh or aged positive electrodes simultaneously at different states of charge down to . The fresh electrodes had an exchange current density of approximately , a solid-phase diffusion coefficient of approximately , and a log-normal active particle size distribution with a mean radius of . Aged electrode impedance results were shown to be highly dependent on both the electrode state of charge and the pressure applied to the electrode surface. An aging scenario incorporating loss of active particles, coupled with an increase both in the local contact resistance between the active material and the conductive carbon and the resistance of a layer on the current collector, was shown to be adequate in describing the measured aged electrode impedance behavior.

Laser-induced incandescence for soot-particle sizing at elevated pressure

This paper describes the applicability of laser-induced incandescence (LII) as a measurement technique for primary soot particle sizes at elevated pressure. A high-pressure burner was constructed that provides stable, laminar, sooting, premixed ethylene/air flames at 1–10 bar. An LII model was set up that includes different heat-conduction sub-models and used an accommodation coefficient of 0.25 for all pressures studied. Based on this model experimental time-resolved LII signals recorded at different positions in the flame were evaluated with respect to the mean particle diameter of a log-normal particle-size distribution. The resulting primary particle sizes were compared to results from TEM images of soot samples that were collected thermophoretically from the high-pressure flame. The LII results are in good agreement with the mean primary particle sizes of a log-normal particle-size distribution obtained from the TEM-data for all pressures, if the LII signals are evaluated with the heat-conduction model of Fuchs combined with an aggregate sub-model that describes the reduced heat conduction of aggregated primary soot particles. The model, called LIISim, is available online via a web interface.

Hydriding kinetics of ball-milled nanocrystalline MgH2 powders

The kinetics of hydride formation and decomposition described by semiempirical models generally do not involve particle and grain-size dependence. However, ball-milled nanocrystalline powders usually exhibit log-normal grain-size and particle-size distribution. Considering size dependence, a total reacted function for a multiparticle system has been developed. We show that the shape of the measured reaction fraction curves do not determine unambiguously the rate-controlling mechanism of hydrogen sorption, since the kinetics are strongly affected by the microstructure. With the application the convolutional multiple whole profile fitting procedure for nanocrystalline MgH2, the parameters, e.g., the median and variance of the log-normal grain-size distribution have been determined. Taking these values into account, the reaction constants corresponding to different sorption states are considerably modified compared with values obtained from classical single-particle models.