Log-normal Particle Size Distribution Research Articles

Numerical simulation of polydisperse particle segregation based on a bubble-based drag model

This work is devoted to the development of a novel polydisperse drag model based on particle type for bubbling fluidized beds. Traditional homogeneous drag models do not take into account the heterogeneous mesoscale structures, while this model is a mesoscale-structure-dependent drag model. The model combined with Energy Minimum Multiscale (EMMS) theory has been successfully applied to the simulation of polydisperse particle segregation. Four particle size distribution (PSD) systems (including a binary system with different sizes, a binary system with different sizes and densities, a normal PSD and a lognormal PSD) were selected to validate the model under various superficial gas velocities. The PSD was decomposed into several types of solids, each governed by its own set of hydrodynamic equations. The solution algorithm was able to find the heterogeneous index for each solid, which was dependent on both slip velocity and solid concentration. Experiments were subsequently conducted under identical conditions to compare the experimental data with the simulated data. The average relative error between the simulation data and the experimental data about the mean particle size distribution was less than 5%. These results indicated that the proposed model outperformed other drag models in accurately predicting particle segregation behavior.

Particle Size Distributions and Extinction Coefficients of Aerosol Particles in Land Battlefield Environments

In land battlefield environments, aerosol particles can cause laser beams to undergo attenuation, thus deteriorating the operational performance of military laser devices. The particle size distribution (PSD) and extinction coefficient are key optical properties for assessing the attenuation characteristics of laser beams caused by aerosol particles. In this study, we employed the laser diffraction method to measure the PSDs of graphite smoke screen, copper powder smoke screen, iron powder smoke screen, ground dust, and soil explosion dust. We evaluated the goodness of fit of six common unimodal PSD functions and a bimodal lognormal PSD function employed for fitting these aerosol particles using the root mean square error (RMSE) and adjusted R2, and selected the optimal PSD function to evaluate their extinction coefficients in the laser wavelength range of 0.249~12 μm. The results showed that smoke screens, ground dust, and soil explosion dust exhibited particle size ranges of 0.7~50 µm, 1~400 µm, and 1.7~800 μm, respectively. The lognormal distribution had the best goodness of fit for fitting the PSDs of these aerosol particles in the six unimodal PSD functions, followed by the gamma and Rosin–Rammler distributions. For the bimodal aerosol particles with a lower span, the bimodal lognormal PSD functions exhibited the best goodness of fit. The graphite smoke screen exhibited the highest extinction coefficient, followed by the copper and iron powder smoke screens. In contrast, the ground dust and soil explosion dust exhibited the lowest extinction coefficients, reaching their minimum values at a wavelength of approximately 8.2 μm. This study provides a basis for analyzing and improving the detection and recognition performance of lasers in land battlefield environments.

A new modelling approach for dissolution of polydisperse powders

A new modelling approach for dissolution of polydisperse powders is developed within the framework of the classical Noyes–Whitney/Nernst–Brunner analysis. Its distinguishing feature is that the underlying continuous particle-size distribution is retained. Two different but related dependencies of the diffusion-layer thickness on particle size are considered. First, a power-law dependence that interpolates between a thickness that is proportional to (or equals) the particle radius (obtained when the exponent equals 1) and a constant thickness (obtained when the exponent is 0). Second, a piecewise linear function such that the thickness equals the particle radius for sufficiently small particles and is constant for larger ones. The modelling approach is exemplified by consideration of a lognormal particle-size distribution. Highly accurate closed-form expressions for the fraction of dissolved drug are obtained for dissolution under sink conditions (which are exact if the diffusion-layer thickness is radius-independent). Moreover, it is demonstrated that any result derived under sink conditions can be reused to determine the fraction of dissolved/absorbed drug under non-sink conditions, using the concept of a retarded time. Comparison with literature data and experiments are used to validate the modelling approach and to demonstrate its usefulness in a practical context.

Accounting for hydrolysis in the modeling of titanium dioxide nanoparticle synthesis in laminar TiCl[formula omitted]-seeded flames

The description of TiO2 synthesis in TiCl4-seeded flames is most often based on phenomenological models that qualitatively reproduce experimental trends in terms of final production but they do not provide chemical insights into the actual kinetic pathways. Alternatively, thermodynamically-consistent detailed TiCl4 oxidation kinetics are available. However, since they have been developed under dry conditions they still need to be challenged and validated when employed for flame synthesis where the presence of water molecules may potentially activate TiCl4 hydrolysis. To derive accurate chemical descriptions for TiO2 flame synthesis, it is essential to evaluate the possible contribution of TiCl4 hydrolysis. For this, numerical simulations of TiO2 flame synthesis in laminar flames are carried out in this article using different chemical descriptions for TiCl4 conversion into TiO2. Detailed oxidation kinetics neglecting hydrolysis are shown to predict an extremely slow formation of TiO2 particles in flames when the O2 concentration is small. As a consequence, a significant underestimation of the conversion yield is observed compared to experimental evidences and to trends deduced from phenomenological models. To correct this behavior, a new scheme is proposed by combining a detailed oxidation kinetics with a five-reaction mechanism describing the first steps of TiCl4 hydrolysis. Conversion of TiCl4 is found to be faster and more efficient with this new combined scheme, leading to log-normal particle size distributions in agreement with the experimental data for nanoparticles flame synthesis.

Impact of the Non-Uniform Catalyst Particle Size on Product Selectivities in Consecutive Reactions

The analysis of consecutive reactions A→B→C in porous catalyst particles, where the simultaneous processes of diffusion and chemical reactions take place and both reactant and products are subjected to diffusion limitations, was performed for catalyst particles with non-uniform sizes, a fact that has not been considered so far. The system comprises first-order consecutive irreversible reactions that proceed on spherical catalyst particles with a log-normal volume particle size distribution (PSD), which is typical in many catalytic applications. Regardless of the prevailing diffusion regime (chemical control, transition situation or intraparticle diffusion control), the yield of the intermediate product (B) reaches a maximum value as a function of the conversion of reactant (A), then decreases as a consequence of the prevalence of the secondary reaction that converts it into the secondary product (C). If intraparticle diffusion resistances affect the reactant species, given the relationship between the kinetic constants and the mean particle size, the selectivity to the intermediate product is negatively affected by the dispersion in PSD. The larger the dispersion in PSD, the stronger the negative impact.

Characterization of the Emissions and Crystalline Silica Content of Airborne Dust Generated from Grinding Natural and Engineered Stones.

In this study, we systematically characterized the airborne dust generated from grinding engineered and natural stone products using a laboratory testing system designed and operated to collect representative respirable dust samples. Four stone samples tested included two engineered stones consisting of crystalline silica in a polyester resin matrix (formulations differed with Stones A having up to 90wt% crystalline silica and Stone B up to 50wt% crystalline silica), an engineered stone consisting of recycled glass in a cement matrix (Stone C), and a granite. Aerosol samples were collected by respirable dust samplers, total dust samplers, and a Micro-Orifice Uniform Deposit Impactor. Aerosol samples were analyzed by gravimetric analysis and x-ray diffraction to determine dust generation rates, crystalline silica generation rates, and crystalline silica content. Additionally, bulk dust settled on the floor of the testing system was analyzed for crystalline silica content. Real-time particle size distributions were measured using an Aerodynamic Particle Sizer. All stone types generated similar trimodal lognormal number-weighted particle size distributions during grinding with the most prominent mode at an aerodynamic diameter of about 2.0-2.3 μm, suggesting dust formation from grinding different stones is similar. Bulk dust from Stone C contained no crystalline silica. Bulk dust from Stone A, Stone B, and granite contained 60, 23, and 30wt% crystalline silica, respectively. In Stones A and B, the cristobalite form of crystalline silica was more plentiful than the quartz form. Only the quartz form was detected in granite. The bulk dust, respirable dust, and total dust for each stone had comparable amounts of crystalline silica, suggesting that crystalline silica content in the bulk dust could be representative of that in respirable dust generated during grinding. Granite generated more dust per unit volume of material removed than the engineered stones, which all had similar normalized dust generation rates. Stone A had the highest normalized generation rates of crystalline silica, followed by granite, Stone B, and Stone C (no crystalline silica), which likely leads to the same trend of respirable crystalline silica (RCS) exposure when working with these different stones. Manufacturing and adoption of engineered stone products with formulations such as Stone B or Stone C could potentially lower or eliminate RCS exposure risks. Combining all the effects of dust generation rate, size-dependent silica content, and respirable fraction, the highest normalized generation rate of RCS consistently occurs at 3.2-5.6 µm for all the stones containing crystalline silica. Therefore, removing particles in this size range near the generation sources should be prioritized when developing engineering control measures.

Preparation and evaluation of physicochemical properties and anti-leishmanial activity of zirconium/tioxolone niosomes against Leishmania major

Due to the limitations of current chemotherapy for the treatment of leishmaniasis, there is an urgent requirement to search for new anti-leishmanial compounds and nano-drug delivery systems including niosomes. Therefore, the aim of this study was to prepare zirconium/tioxolone niosomes using the film hydration method and evaluate the physicochemical properties of the produced niosomes including morphology, size distribution, stability, and encapsulation efficiency. The best formulation was chosen as Span/Tween 40 (NZT 1 ) due to its physicochemical properties, and leishmanicidal activity against promastigotes and amastigotes was measured using both 3-(4,5-dimethylthiazol2yl)-2,5-diphenyltetrazolium bromide (MTT) and flow cytometry methods. In addition, to assess the mechanism of action of the prepared niosomes, apoptosis, levels of gene expression, reactive oxygen species (ROS) generation, superoxide dismutase (SOD) activity, and nitrite production were evaluated. The prepared formulation indicated log-normal particle size distribution curves, high encapsulation efficiency (more than 95.72 %), and good physical stability after one week, three months, and six months. Our findings demonstrated that amphotericin B was more effective than Zr/tioxolone niosomes (NZTs) due to the selectivity index (SI). However, the niosomal formulation of Zr/tioxolone showed no cytotoxic effect within the range of our experimental concentrations (CC 50 of 308.21 μg/mL). Moreover, the prepared niosomes increased the expression level of interleukin (IL)-12 and inducible nitric oxide synthase (iNOS) and significantly decreased the expression level of the IL-10 gene, which confirms the immunomodulatory role of NZTs. According to our findings in this study, the niosomal form of this combination can be considered for further therapeutic approaches against L. major in future planning.

Atmospheric aerosol particle size distribution from Lidar data based on the lognormal distribution mode

Analysis of the atmospheric Aerosol Particle Size Distribution (APSD) retrieved from Light Detection and Ranging (Lidar) data is one of the popular fields in atmospheric remote sensing. An APSD retrieval method based on the lognormal particle size distribution, the Mie theory, and the Second Simulation of the Satellite Signal in the Solar Spectrum (6S) were studied. According to the 6S, this method divides the main body of the aerosols into four basic components and calculates the APSD from Lidar data and the optical and microphysical characteristics of these components. Numerical simulation and experimental observations reveal that this method can obtain the APSD for particle sizes of >0.15 μm in the different vertical layers with good reliability.

Synchrotron-based characterization of arthroprosthetic CoCrMo particles in human bone marrow

Particles released from cobalt-chromium-molybdenum (CoCrMo) alloys are considered common elicitors of chronic inflammatory adverse effects. There is a lack of data demonstrating particle numbers, size distribution and elemental composition of bone marrow resident particles which would allow for implementation of clinically relevant test strategies in bone marrow models at different degrees of exposure. The aim of this study was to investigate metal particle exposure in human periprosthetic bone marrow of three types of arthroplasty implants. Periprosthetic bone marrow sections from eight patients exposed to CoCrMo particles were analyzed via spatially resolved and synchrotron-based nanoscopic X-ray fluorescence imaging. These analyses revealed lognormal particle size distribution patterns predominantly towards the nanoscale. Analyses of particle numbers and normalization to bone marrow volume and bone marrow cell number indicated particle concentrations of up to 1 × 1011 particles/ml bone marrow or 2 × 104 particles/bone marrow cell, respectively. Analyses of elemental ratios of CoCrMo particles showed that particularly the particles’ Co content depends on particle size. The obtained data point towards Co release from arthroprosthetic particles in the course of dealloying and degradation processes of larger particles within periprosthetic bone marrow. This is the first study providing data based on metal particle analyses to be used for future in vitro and in vivo studies of possible toxic effects in human bone marrow following exposure to arthroprosthetic CoCrMo particles of different concentration, size, and elemental composition.Graphical abstract

Prediction of saturated hydraulic conductivity of sandy soil using Sauter mean diameter of soil particles

AbstractSaturated hydraulic conductivity of soil, Ksat, is a critical parameter for mathematical modelling of groundwater and soil water flow. Current empirical Ksat models, such as Kozeny–Carman model, Hazen models, or empirical approaches based on soil pedotranfer functions (PTFs) rely on the specific surface area, certain characteristic particle size(s), for example, d5, d10, d15, d50, etc., or the fractionation of sand, silt and clay. In this study, we proposed an alternative modelling framework to estimate Ksat from void ratio and arithmetic mean diameter of soil particles. We suggested to describe the particle size distribution (PSD) using a continuous mathematical distribution function, for example, the lognormal distribution function, and to obtain the Sauter mean diameter (dS) by calculating the moments of the PSD function. The proposed empirical equations were tested against the measured Ksat values for 54 sand samples with available measured PSD and void ratio as reported in Toumpanou et al. and validated using 49 sandy soil samples obtained from the Unsaturated Soil Database (UNSODA). We found that the dS was more relevant to Ksat than the number mean diameter (dN) and mass mean diameter (dM) (the RMSE was 0.486 for Ksat ‐ dN; 0.187 for Ksat ‐ dS; and 0.212 for Ksat ‐ dM, respectively). We also found that the proposed equation with dS had superior performance over the Hazen equation and PTF‐based models. Our results indicated that the Ksat calculated using dS, which was either estimated from discrete experimental data or calculated from a continuous lognormal PSD function, best matched with the measured values for coarse‐textured soils. Future studies should focus on developing empirical relationships for soil water retention curves and other soil properties based on continuous PSD functions.Highlights A modelling framework to estimate Ksat from the void ratio and arithmetic mean diameter is proposed. Sauter mean diameter, dS, can be obtained by calculating the moments of the PSD function. Ksat model using dS performs better than that using dN, dM, d5, d10, or d50 or PTF‐based models.

Effect of polydispersity on bubble characteristics of Geldart Group B particles

In order to enhance the understanding of the influences of bubble characteristics in bubbling fluidized beds of Gaussian and lognormal particle size distributions (PSDs) of Geldart Group B particles, machine learning tools were harnessed. The PSDs had the same Sauter-mean diameter and widths (i.e., ratio of standard deviation to Sauter-mean diameter) of between 10 and 30% and 10 – 70%, respectively. Self-organizing maps (SOMs) analysis of more than a thousand data rows each of Gaussian and lognormal PSD data indicate that bubble velocity, frequency, length, and probability are highly correlated. The optimal number of data assemblies that either the Gaussian or lognormal dataset can be divided into per the Calinski-Harabasz criterion was determined to be three, and it was found that the critical parameter that underlies the demarcation of the datasets was PSD width. This agrees with an earlier study on clusters, wherein the non-monodispersity of the particle systems was also responsible for the division of the dataset into distinct data assemblies. Furthermore, the number-based frequency of the particle species was better correlated with the bubbles than the mass-based one. The key highlight is the predominant influence of PSD width in demarcating the datasets into distinct data assemblies, which underscores the need to account for the polydispersity of particle systems and provides valuable insights towards model development.

Effect of lognormal particle size distributions on particle spreading in additive manufacturing

Additive manufacturing (AM) has attracted much attention worldwide in various applications due to its convenience and flexibility to rapidly fabricate products, which is a key advantage compared to the traditional subtractive manufacturing. This discrete element method (DEM) study focusses on the impact of particle polydispersity during the particle spreading process on parameters that affect the quality of the final product, like packing and bed surface roughness. The particle systems include four lognormal particle size distribution (PSD) widths, which are benchmarked against the monodisperse system with the same mean particle diameter. The results reveal that: (i) the solid volume fraction of the initial packed particle bed in the delivery chamber increases then plateaus as the PSD width increases; (ii) regardless of PSD width, the solid volume fraction of the particle bed increases with spreading layer height before compression, but decreases with layer height after compression; (iii) the bed surface roughness increases with PSD width or layer height both before and after the compression of the spreading layer; (iv) the extent of increase in solid volume fraction during compression is correlated with the extent of decrease in bed surface roughness; and (v) the broader PSDs exhibit larger fluctuations of solid volume fraction of the particle bed and bed surface roughness due to greater variability in the arrangement of particles of different sizes. The results here have important implications on the design and operation of particle-based AM systems.

Analysis of terahertz wave attenuated by sand and dust storms with different modes

The research on space transmission characteristics of terahertz wave is of great significance for the application of terahertz wave in space. In order to study the transmission characteristics of terahertz wave in sand and dust storm weather, according to the lognormal distribution of dust particle sizes, Mie scattering theory and Monte Carlo method are used to analyze the attenuation characteristics of six dry sand modes of sand and dust storm in different regions of China in a frequency band of 1–10 THz, and the relationship of the extinction parameters and attenuation rate to the frequency is given. The results show that with the increase of frequency, the attenuation rate of 1–10 THz terahertz wave first increases and then decreases. Different mode of sand and dust storm leads to different frequency range of strong attenuation of terahertz wave. In order to analyze the influence of sand dust particle moisture content on terahertz wave propagation attenuation, the relationship of three efficiency factors to water content of sand dust particles with different sizes is calculated. The results show that the influence of water content on extinction is different from that of the particle size. Monte Carlo method is used to calculate the attenuation of terahertz wave by sand and dust storm in two kinds of wet sand modes, and the relationship of the attenuation rate and water content to the frequency is given, the results are compared with those from the dry sand mode, showing that the albedo of wet sand mode is obviously lower than that of dry sand mode with the same size distribution. The absorption of wet sand particles increases with water content increasing. The extinction of wet sand and dust storm results from scattering and absorption. With the increase of water content in sand particles, the frequency band with strong attenuation of terahertz wave by wet sand and dust storm moves toward low frequency. When the water content is less than 5%, the attenuation rate of terahertz wave increases significantly with the increase of water content. Sand and dust storms with higher humidity have a greater influence on the transmission attenuation of terahertz wave.

Simulation Informed Design and Performance of In Vitro Bioequivalence Trials for Particle Size Distributions.

This study used statistical simulations to investigate the performance of the population bioequivalence test applied to image-based particle size measurements (such as morphologically directed Raman spectroscopy) and methods for designing in vitro bioequivalence trials using prior information. Simulations of in vitro population bioequivalence trials were conducted across a range of representative D50 (number-weighted median particle diameter from a log-normal particle size distribution) and span (which is defined as [Formula: see text] where D90 and D10 are the number-weighted 90th and 10th percentiles in particle diameters sampled from a log-normal particle size distribution) values respectively. The performance of the population bioequivalence test in the simulations was driven by an interplay between overall test variability and the widening or narrowing of the bioequivalence region due to variance terms in the test statistic definition. These findings were dependent upon differences in the variability of D50 and span and may generalise to a wider range of in vitro metrics. Trial design optimisation using power and assurance approaches followed patterns consistent with these findings. As more novel scientific methods are applied to the development of complex generic drug products, the procedures outlined in this study may be used at the inception stage of future in vitro bioequivalence trials to reduce the risk of conducting costly trials with low probabilities of success.

Effect of lognormal particle size distributions of non-spherical particles on hopper discharge characteristics

This study focusses on the hopper discharge characteristics of lognormal particle size distributions (PSDs) of non-spherical particles (namely, ellipsoids, cylinders and cuboids). Discrete element method is employed to understand the coupled effects of sphericity and lognormal PSD width. The results reveal that: (i) the ellipsoids have the most similar discharge behaviors with the spheres, but the differences increase as the PSD width increases; (ii) the packing density in the hopper increases as PSD width increases and particle sphericity decreases; (iii) regardless of sphericity, the discharge rate decreases and the jamming probability increases as the PSD width increases; (iv) for the same PSD width, the jamming probability is the greatest for cuboids and least for the ellipsoids; and (v) the lower-sphericity cylinder and cuboid have some residual particles left in the hopper upon complete discharge, and the number of residues is greater and increases with PSD width for the latter. The results provide new insights regarding the behavior of wide PSDs of non-spherical particles in the hopper, highlighting the non-negligible impact of the coupled effect of PSD and particle non-sphericity.

PARAMETERIZATION OF MAGNETIC NANOPARTICLES MATHEMATICAL MODEL USING EVOLUTIONARY ALGORITHMS

In this paper, the evolutionary algorithms approach is applied to the parameterization of a mathematical model describing the Mössbauer spectra of nanogranular (or nanoparticle) magnetic systems. These systems exhibit physical properties very different from bulk specimens being of great interest for material science and its use as biosensors, magneto sensors, data storage, and magnetic fluids. The purpose of this work is to compare the performance between the Differential Evolution and the Evolutionary Strategies algorithms to optimize the model parameters which best fit the experimental Mössbauer spectra of nanoscale magnetic particles. Spectra of two samples (??iron foil and NiFe2O4 nanoparticles) were recorded, at room temperature, by a conventional Mössbauer spectrometer using a scintillation detector in transmission geometry with a 57Co/Rh source. Fits to Mössbauer spectra were done using spin hamiltonians to describe both the electronic and nuclear interactions; a model of superparamagnetic relaxation of two levels (spin ½) and stochastic theory; a lognormal particle size distribution function as well as a dependency of the magnetic transition temperature and the anisotropy constant on particle diameter. The evolutionary algorithms have been implemented using Python programming language. For comparison, the two algorithms obey the termination criterion of 6,000 evaluations of the objective function. The results presented show the efficiency of these algorithms in the optimization of the parameters and on the fits of the spectra.

ON SPIN HAMILTONIAN FITS TO MÖSSBAUER SPECTRA OF NiFe2O4 NANOPARTICLES SYNTHESIZED BY CO-PRECIPITATION

Nanocrystalline NiFe2O4 particles prepared by chemical co-precipitation method were studied using magnetic measurements, 57Fe Mössbauer spectroscopy, X-ray diffraction, and transmission electron microscopy. Fits to Mössbauer spectra, in the range of 4.2 K – 300 K, were done using spin hamiltonians to describe both the electronic and nuclear interactions, a model of superparamagnetic relaxation of two levels (spin ½) and stochastic theory, a log-normal particle size distribution function as well as a dependency of the magnetic transition temperature and the anisotropy constant on particle diameter. We have used evolutionary strategies to fit the more complex Mössbauer spectra line shapes. The nanoparticles have an average size of 7 nm and exhibit superparamagnetism at room temperature. The saturation magnetization (Ms) at 4.2 K was determined from M vs. 1/H plots by extrapolating the value of magnetizations to infinite fields, to 24.21 emu/g and coercivity to 3.15 kOe. A magnetic anisotropy energy constant (K) 1.9´105 J/m3, at 4.2 K, were calculated from magnetization measurements. The synthesis, characterization, and functionalization of magnetic nanoparticles is a highly active area of current research located at the interface between materials science, biotechnology, and medicine. Superparamagnetic iron oxides nanoparticles have unique physical properties and have emerged as a new class of diagnostic probes for multimodal tracking and as contrast agents for magnetic resonance imaging (MRI).

Microstructures and Formation of Tundish Clogging Deposits in Ti-Alloyed Al-Killed Steel

The continuous casting of Ti-alloyed Al-killed steels traditionally experiences clogging in the tundish, impeding stable operation. We studied the microstructures and mode of formation of such clogging deposits in tundish skulls recovered after long cast series. We sampled the steel skull along the whole tundish bottom from under the ladle shroud (impact zone) up to the tundish well and nozzle. The microstructures imply that the steel solidifies to the refractory (gunning mass) and remains partially solid through the entire cast. Thus, a “mushy zone” of steel loaded with solid delta ferrites is present along the margins of the steel during casting. In this mushy zone, the widely observed clusters of variably sintered alumina (NMI) accumulate, along with a substantial amount of gas bubbles acting as inclusion scavengers. The clustered alumina particles show a lognormal particle size distribution (PSD) in all locations, which becomes more pronounced if correcting for the observable sintering. Sintering of alumina size distributions linearizes a PSD, and further evolution, once the deposit is locked in place, occurs by Ostwald ripening, introducing skewness to the distributions. The observed PSDs contrast with the established log-linearity of PSDs of individual floating alumina NMI in the bulk steel, and suggest that the source of the alumina in the clogging deposits is not the passing bulk steel. However, ubiquitous sedimentary features show that the alumina particles are also not grown by reoxidation in situ. An upstream source separate from the bulk stream must be inferred, which is also required by the consistent sporadic presence of oxidic materials which cannot be derived from local sidewall reaction. In summary, the development of clogging deposits in this type of steel is an example of “slurry casting” of partially solidifying steel over thermal loss surfaces of refractories in the nozzle area.

A Method for Retrieving Stratospheric Aerosol Extinction and Particle Size from Ground-Based Rayleigh-Mie-Raman Lidar Observations

We report on the retrieval of stratospheric aerosol particle size and extinction coefficient profiles from multi-color backscatter measurements with the Rayleigh–Mie–Raman lidar operated at the Arctic Lidar Observatory for Middle Atmosphere Research (ALOMAR) in northern Norway. The retrievals are based on a two-step approach. In a first step, the median radius of an assumed monomodal log-normal particle size distribution with fixed width is retrieved based on a color index formed from the measured backscatter ratios at the wavelengths of 1064 nm and 532 nm. An intrinsic ambiguity of the retrieved aerosol size information is discussed. In a second step, this particle size information is used to convert the measured lidar backscatter ratio to aerosol extinction coefficients. The retrieval is currently based on monthly-averaged lidar measurements and the results for March 2013 are discussed. A sensitivity study is presented that allows for establishing an error budget for the aerosol retrievals. Assuming a monomodal log-normal aerosol particle size distribution with a geometric width of S = 1.5, median radii on the order of below 100 nm are retrieved. The median radii are found to generally decrease with increasing altitude. The retrieved aerosol extinction profiles are compared to observations with the OSIRIS (Optical Spectrograph and InfraRed Imager System) and the OMPS-LP (Ozone Mapping Profiling Suite Limb Profiler) satellite instruments in the 60∘ N to 80∘ N latitude band. The extinction profiles that were retrieved from the lidar measurements show good agreement with the observations of the two satellite instruments when taking the different wavelengths of the instruments into account.

Modelling the Age-Hardening Precipitation by a Revised Langer and Schwartz Approach with Log-Normal Size Distribution

A new numerical modelling approach integrating the Langer and Schwartz approach and log-normal particle size distribution has been developed to depict the precipitation kinetics of age-hardening precipitates in Al alloys. The modelling framework has been implemented to predict the precipitation behavior of the key secondary phases in 6xxx and 7xxx Al alloys subjected to artificial aging. The simulation results are in good agreement with the available experimental data in terms of precipitate number density, radius, and volume fraction. The initial shape parameter of the log-normal size distribution entering the modeling framework turns to play an important role in affecting the later-stage evolution of precipitation. It is revealed that the evolution of size distribution is not significant when a small shape parameter is adopted in the modelling, while an initial large shape parameter will cause substantial broadening of the particle size distribution during aging. Regardless of the magnitude of shape parameter, a broadening of the particle size distribution as predicted by the present model is in agreement with experimental observations. It is also shown that large shape parameter will accelerate the coarsening rate at later aging stage, which induces fast decreasing of number density and increased growth rate of mean/critical radius. A comparison to the Euler-like multi-class approach demonstrates that the integration of more realistic log-normal distribution and Langer and Schwartz model make the present modelling faster and equivalently accurate in precipitation prediction.