Particle Size Distribution Function Research Articles

Optimal analysis of the proportion between modified lime mud and active mineral additive in mortar: Insights from particle size distribution and packing density modeling

The use of lime mud in building materials is becoming more popular. However, its application has been limited by optimizing the proportion of lime mud and other active admixtures. In this study, the lime mud was firstly modified by a mechanochemical method to refine the grain size. Secondly, various particle size distribution functions were used to described the particle size distribution of cementitious materials. Further, based on the modifier Anderson and Andreasen (MAA) function, the optimal mixing proportion of cementitious materials was designed, and its feasibility was confirmed by the orthogonal test and range analysis. According to the hydration analysis through X-Ray Diffraction analysis (XRD), Thermogravimetry-Derivative Thermogravimetry (TG-DTG), Scanning Electron Microscope (SEM), and Mercury Intrusion Porosimetry (MIP), a significant increase in the harmless pore content was observed in the mortar with the optimal blend of MLM, MK, and SF.

Combining performances of E(m)-corrected LII and absorption for in situ measurements of the volume fraction of 2–4 nm soot particles.

Determining the soot volume fraction (fv) in combustion environments requires detailed knowledge of the optical properties of the soot particles, and in particular of their absorption function E(m). This study addresses a fundamental lack of information on the optical properties of 2–4 nm soot particles. Recent works based on the modeling of the photoelectron emission yields and UV-vis-NIR-absorption measurements found a sharp decrease of E(m) with the particle size in the vis-NIR spectral region, which is inconsistent with the in situ detection of 2–4 nm particles in the near-infrared region by laser-induced incandescence (LII) or sensitive absorption methods like cavity ring-down extinction (CRDE). The objective of this study is twofold: first, an original method for the determination of E(m) of soot particles, including 2–4 nm particles is proposed. Then, the dynamic of two widespread in situ diagnostics, LII and CRDE, are compared over three orders of magnitude of fv in atmospheric premixed ethylene/air flames with different flow rates and C/O. The determination of the absolute value of E(m) and of its variation in the flames is derived from an original analysis, which does not require complex LII modeling. This analysis is based on the comparison between the experimental and calculated LII/LIImax signals in the low fluence regime, LIImax being the plateau value of the fluence curve, which is reached at fluence larger than 1 J/cm2 for the smallest C/O. E(m) is found to vary between 0.15 at low C/O up to 0.36 for the richest flames. Concerning the comparison of the dynamics of LII and CRDE, an excellent agreement is found above a threshold (C/O)limit, while LII exhibits a stronger decrease with C/O below (C/O)limit. This discrepancy is attributed to the spectral dependence of E(m) which is negligible above (C/O)limit, but increases when C/O decreases below (C/O)limit. The particle size distribution function (PSD), measured by scanning mobility particle sizing, reveals monomodal or bimodal PSDs with soot having mobility diameter in the range 2.3–7.5 nm depending on the flame conditions. It is suggested that the particles contained in the first PSD mode, which is dominant in the low C/O range, could be affected by a significant spectral dependence of E(m) in comparison with the second PSD mode.

Response of mineral particles in inland lakes to water optical properties and its influence on chlorophyll-a estimation.

Many chlorophyll-a (Chl-a) remote sensing estimation algorithms have been developed for inland water, and they are proposed always based on some ideal assumptions, which are difficult to meet in complex inland waters. Based on MIE scattering theory, this study calculated the optical properties of mineral particles under different size distribution and refractive index conditions, and the Hydrolight software was employed to simulate remote sensing reflectance in the presence of different mineral particles. The findings indicated that the reflectance is significantly influenced by the slope (j) of particle size distribution function and the imaginary part (n') of the refractive index, with the real part (n) having a comparatively minor impact. Through both a simulated dataset containing 18,000 entries and an in situ measured dataset encompassing 2183 data from hundreds of lakes worldwide, the sensitivities of band ratio (BR), fluorescence baseline height (FLH), and three-band algorithms (TBA) to mineral particles were explored. It can be found that BR showed the best tolerance to mineral particles, followed by TBA. However, when the ISM concentration is less than 30 g m-3, the influence of CDOM cannot be ignored. Additionally, a dataset of over 400 entries is necessary for developing the BR algorithm to mitigate the incidental errors arising from differences in data magnitude. And if the amount of developing datasets is less than 400 but greater than 200, the TBA algorithm is more likely to obtain more stable accuracy.

Discrete pore and particle size distributions during pore blocking and cake filtration

Modeling membrane filtration is important for plenty industrial applications. The understanding of the phenomena and related mechanisms aims at the improvement of techniques in different areas. Therefore, different authors have proposed models to describe the mechanisms related to the filtration process involving either cake build-up or blocking processes, a few of them however have proposed both concepts simultaneously, although none considered pore and particle size distribution during the process, which is the proposal brought up in this paper. Transient solutions for filtrate volume and filter cake thickness as a function of initial pore and particle size distributions are obtained. Good matching between the studied experimental data and the proposed model was observed. In general, the results showed that permeability reduction and filtrate volume are strongly influenced by the initial pore and particle size distributions. In addition, the cake build-up rate depends on both the particle size distribution and the residual flow through blocked pores. It was observed that, after all the largest particles have blocked the smaller pores, effective permeability and flow rate vary only due to cake build-up. Finally, because the proposed empirical parameters do not depend on the pore size distribution, this model can be applied for predicting permeability decline for any feed concentration.

On evaluating the hypothesis of shape similarity between soil particle-size distribution and water retention function

Two pedotransfer functions (PTFs) are available in the literature enabling the soil water retention function (WRF) to be estimated from knowledge of the soil particle-size distribution (PSD), oven-dry soil bulk density (b), and saturated soil water content (s): i) the Arya and Heitman model (PTF-AH) and ii) the Mohammadi and Vanclooster model (PTF-MV). These physico-empirical PTFs rely on the hypothesis of shape similarity between PSD and WRF, and do not require the calibration of the input parameters. In the first stage, twenty-seven PSD models were evaluated using 4,128 soil samples collected in Campania (southern Italy). These models were ranked according to the root mean square residuals (RMSR), corrected Akaike Information Criterion (AICc), and adjusted coefficient of determination (R2adj). In the second stage, three subsets of PSD and WRF data (DS-1, DS-2, and DS-3), comprising 282 soil samples, were used to evaluate the two PTFs using the best three PSD models selected in the first stage. The hypothesis of shape similarity was assumed as acceptable only when the RMSR value was lower than the field standard deviation of the WRFs (*), which is viewed as a tolerance threshold and computed from the physically-based scaling approach proposed by Kosugi and Hopmans (1998). In the first study area (DS-1), characterized by a fairly uniform, loamy textured volcanic soil, the PTF-AH outperformed the PTF-MV and both PTFs provided reasonable performance within the acceptance threshold (i.e., RMSR < *). In the other two heterogeneous field sites (DS-2 and DS-3, characterized by soil textural classes that span from clay and clay-loam to loam and even sandy-loam soils), the PTF-MV (with 3% to 6% RMSR surpassing *) outperformed the PTF-AH (with 8% to 30% RMSR surpassing *) and the majority of RMSR values were larger than those obtained in the original studies. The mean relative error (MRE) revealed that the PTF-MV systematically underestimates the measured WRFs, whereas the PTF-AH provided negative MRE values indicating an overall overestimation. The outcomes of our study provide a critical evaluation when using calibration-free PTFs to predict WRFs over large areas.

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.

Fluidized Bed Reactor Modeling and Simulation with Aspen Plus

Fluidized bed reactor is useful for heterogeneous (multiphase) reactions, separations, size enlargement, coating, and blending in chemical and pharmaceuticals industries. To develop a model and simulation of this reactor with advanced systems process engineering software (Aspen Plus). Aspen plus has the capability to simulate real factory performance, design improved plants, and intensify profitability in present plants. This modeling and simulation are applied Geldart B particle classification, GGC is used for particle size distribution function, Newton parameters for mass convergence, and Ergun equation is used for minimum fluidization velocity calculation and pressure drop through the fluidized bed reactor. Generally, most of the predictions model from Aspen plus is a reasonable agreement through the experimental results. Advantage of this investigation is used small quantity of bed particles and identified their melting point temperature is above 340°C. This fluidized bed reactor model and simulation is functional for aluminum hydroxide decomposition reaction. The feed 275 kg/hr of Al(OH)3is converted into 169.6 kg/hr of aluminum oxide (Al2O3) and 89.9 kg/hr of water. A total mass conversion percent is 94.4% of aluminum hydroxide.

A computationally efficient approach for soot modeling with discrete sectional method and FGM chemistry

A novel approach for the prediction of soot formation in combustion simulations within the framework of discrete sectional method (DSM) based univariate soot model and Flamelet Generated Manifold (FGM) chemistry, referred to as FGM-CDSM, is proposed in this study. The FGM-CDSM considers the clustering of soot sections derived from the original soot particle size distribution function (PSDF) to minimize the computational cost. Unlike conventional DSM, in FGM-CDSM, governing equations for soot mass fractions are solved for the clusters, by using a pre-computed lookup table with tabulated soot source terms from the flamelet manifold, while the original soot PSDF is re-constructed in a post-processing stage. The flamelets employed for the manifold are computed with detailed chemistry and the complete sectional soot model. A comparative assessment of FGM-CDSM is conducted in laminar diffusion flames for its accuracy and computational performance against the detailed kinetics-based classical sectional model. Numerical results reveal that the FGM-CDSM can favorably reproduce the global soot quantities and capture their dynamic response predicted by detailed kinetics with a good qualitative agreement. Furthermore, compared to detailed kinetics, FGM-CDSM is shown to substantially reduce the computational cost of the complete reacting flow simulation with soot particle transport. Primarily, the use of FGM reduces the overall calculation by about two orders of magnitude compared to detailed kinetics, which is advanced further with the clustering of sections at a low memory footprint. Therefore, the present work demonstrates the promising capabilities of FGM-CDSM in the context of computationally efficient soot calculations and provides an excellent framework for extending its application to the simulations of turbulent sooting flames.

Anomalous Absorption of Smoke Aerosol in the Visible and Near-Infrared Regions of the Spectrum

Anomalous absorption of finely dispersed smoke aerosol was recorded in large-scale smoke haze during mass fires in the boreal forests of Alaska in July 2019 in the visible and near-infrared regions of the spectrum (440‒1020 nm) according to the data of monitoring of the spectral dependences in the refractive index imaginary part on the network of AERONET stations. The variations in the spectral dependences of the aerosol optical depths (extinction and absorption), as well as the size distribution function of aerosol particles, are analyzed. During the anomalous absorption, the imaginary part of the refractive index increased by a factor of 1.8‒7.2 with an increasing optical wavelength from 440 to 1020 nm, reaching a value of 0.315 for the wavelength of 1020 nm. A power approximation is proposed for the spectral dependence of the imaginary part of the refractive index with indices of power approximately from 0.7 to 2.3.

ANOMALOUS ABSORPTION OF SMOKE AEROSOL IN THE VISIBLE AND NEAR-INFRARED OF SPECTRUM INTERVALS

In large-scale smoke haze during mass fires in the boreal forests of Alaska in July 2019 in the visible and near infrared of spectrum intervals 440–1020 nm, according to monitoring data on the network of AERONET stations of the spectral dependences of the refractive index imaginary part, anomalous absorption of the fine smoke aerosol was found. Variations in the spectral dependences of the aerosol optical extinction and absorption depths, as well as the size distribution function of aerosol particles, are analyzed. With anomalous absorption, the imaginary part of the refractive index increased by a factor of 1.8–7.2 with increasing wavelength from 440 to 1020 nm, reaching a value of 0.315 for the wavelength of 1020 nm. A power-law approximation of the spectral dependence of the refractive index imaginary part with exponents approximately from 0.7 to 2.3 is proposed.

Fokker–Planck equation for the particle size distribution function in KJMA transformations

The Fokker–Planck (FP) equation has been derived for describing the temporal evolution of the particle size probability density function (PDF) for KJMA (Kolmogorov–Johnson–Mehl–Avrami) transformations. The classical case of transformations with constant rates of both nucleation and growth, in 3D space, has been treated. Integration of the equation shows that the PDF is given by the superposition of one-parameter gamma distributions with time-dependent mean size given by the KJMA theory. The asymptotic behavior of the FP solution offers a demonstration of the conjecture, previously proposed by Pineda et al. (2004), according to which the set of crystals formed at the same time are gamma-distributed, with the parameter depending on crystal birth time. Computer simulations of the transformation with constant nucleation and growth rates show that the temporal evolution of the PDF, in volume domain, is in good agreement with the Johnson–Mehl PDF. The approach based on the FP equation provides a particle size PDF that exhibits such behavior.

Magnetic neutron scattering from spherical nanoparticles with Néel surface anisotropy: atomistic simulations.

A dilute ensemble of randomly oriented non-interacting spherical nanomagnets is considered, and its magnetization structure and ensuing neutron scattering response are investigated by numerically solving the Landau-Lifshitz equation. Taking into account the isotropic exchange interaction, an external magnetic field, a uniaxial magnetic anisotropy for the particle core, and in particular the Néel surface anisotropy, the magnetic small-angle neutron scattering cross section and pair-distance distribution function are calculated from the obtained equilibrium spin structures. The numerical results are compared with the well known analytical expressions for uniformly magnetized particles and provide guidance to the experimentalist. In addition, the effect of a particle-size distribution function is modelled.

Phase-field model of grain boundary diffusion in nanocrystalline solids: Anisotropic fluctuations, anomalous diffusion, and precipitation

The anisotropic phase-filed model of grain boundary diffusion and precipitation of solute in nanocrystalline solids has been developed. In this model, the Cahn–Hilliard equation is generalized for the anisotropic phase-field diffusion of solute and anisotropic compositional fluctuations. It is found that dynamics of solute concentration profile demonstrates the anomalous diffusion behavior with scaling parameters depending on the mobility ratio and microstructure of a solid solution. It is noteworthy that the increase in source concentration can slow down the concentration front propagation due to uphill diffusion or formation of a new phase. Parameters of grain boundary diffusion control the precipitation dynamics. In particular, a decrease in transverse diffusion coefficient is responsible for longer incubation time, and lower rates of nucleation and nuclei growth in comparison with the case of isotropic solute transport near grain boundaries. Transport properties of boundary and bulk are responsible for the formation of the bimodal size distribution function of second phase particles and specific kinetics of average radius and number density.

Image histogram decomposition method for particle sizing – A numerical simulation study

Scanning probe microscopy is a useful tool in nanoscience. The effective application of nanotechnologies in various fields requires a knowledge of the characteristic attributes of nanoparticles such as shape, dimensions and statistical distribution, and a wide spectrum of experimental and theoretical methods based on various principles have been developed to determine these characteristics. Image histograms offer a global overview of the characteristics of an image. Their shape can encode specific statistical properties of displayed objects such as the distribution function in the case of similar and scalable objects. The model of height histogram presented here proposes a method which solves the long-term problem of processing images of extremely dense particle distributions. The method is based on the principle of the superposition of histograms of individual particles whose topographic surface is described by a parametric model. The resulting height histogram is defined by a convolution of the model of the particle histogram with the distribution function of particle size, with this construction forming the basis of the regression model. The parameters of the distribution function can be obtained via the optimization of the model. The method has been tested on artificially generated configurations of particles of various shapes and size distributions. Each of these configurations creates a topographic surface which is transformed into an image, and the heights obtained from the image allow a histogram to be calculated. Firstly, various configurations of particles are simulated without the presence of any disruptive influences. Next, several experimental effects are evaluated separately (for example, the background, particle shape irregularity and particle overlap). The decomposition of the histogram by the regression model on artificially generated images shows the robustness of the method with respect to particle density, partial horizontal overlap, randomly generated backgrounds and random fluctuations in particle shape. However, the method is sensitive to uniform changes in particle shape, a factor which limits its use to particles with known parametric models of their shape which allow the means of their parameters to be estimated.

Evolution of a Polydisperse Ensemble of Spherical Particles in a Metastable Medium with Allowance for Heat and Mass Exchange with the Environment

Motivated by a wide range of applications in various fields of physics and materials science, we consider a generalized approach to the evolution of a polydisperse ensemble of spherical particles in metastable media. An integrodifferential system of governing equations, consisting of a kinetic equation for the particle-size distribution function (Fokker–Planck type equation) and a balance equation for the temperature (concentration) of a metastable medium, is formulated. The kinetic equation takes into account fluctuations in the growth/reduction rates of individual particles, the velocity of particles in a spatial direction, the withdrawal of particles of a given size from the metastable medium, and their source/sink term. The heat (mass) balance equation takes into account the growth/reduction of particles in a metastable system as well as heat (mass) exchange with the environment. A generalized system of equations describes various physical and chemical processes of phase transformations, such as the growth and dissolution of crystals, the evaporation of droplets, the boiling of liquids and the combustion of a polydisperse fuel. The ways of analytical solution of the formulated integrodifferential system of equations based on the saddle-point technique and the separation of variables method are considered. The theory can be applied when describing the evolution of an ensemble of particles at the initial and intermediate stages of phase transformation when the distances between the particles are large enough, and interactions between them can be neglected.

Evolution of Statistical Characteristics of Particle Size Distribution Functions for Micropowders during Their Temporal Treatment in Planetary-Type Ball Mill

Evolution of Statistical Characteristics of Particle Size Distribution Functions for Micropowders during Their Temporal Treatment in Planetary-Type Ball Mill

Modeling soot particles as stable radicals: a chemical kinetic study on formation and oxidation. Part II. Soot oxidation in flow reactors and laminar flames

Recent experimental and theoretical studies have shed light on the persistent radical behavior of large polycyclic aromatic hydrocarbons (PAHs) and soot particles. The first detailed soot model developed based on these findings is here proposed. While its good performances in predicting soot formation and growth when soot oxidation is negligible are presented in the companion paper of this work (Part I), the model is here validated against 45 cases of particle size distribution functions (PSDF) and soot volume fraction under oxidizing conditions. Notably, we show that by considering stable radical particles and aggregates it is possible to reproduce soot oxidation by O2 in plug flow reactors under very diluted conditions, whereas existing models could not predict particle consumption in the absence of particle surface activating species. Therefore, this work paves the way for a different approach to soot modeling that could help to better interpret soot reactivity. Oxidation of soot produced from different fuels (ethylene, n-heptane, and toluene, i.e. leading to different particle graphitization) at different temperatures (950–1073 K) and O2 concentrations (1000–10000 ppm) is successfully modeled adopting reference oxidation rates of gas-phase resonantly stabilized PAH radicals, featuring analogous reactivity compared to soot species, and by also accounting for different particle hydrogenation levels. Good model performances are also obtained in both rich and lean premixed ethylene flames (Tmax∼1480–1510 K) and in two sets of counterflow ethylene soot formation/oxidation flames (SFO, Tmax∼2560–2825 K), where OH radical becomes the dominant oxidizer. Finally, model limitations emerging in some of the cases considered are discussed through a sensitivity analysis and with references to other oxidation mechanisms proposed in the literature in order to highlight possible future improvement of the model predictive capability

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.

Beneficiation properties of ash-and-slag dumps

Purpose. Development of a mathematical model for the indices of TPP ash-and-slag waste separation in closed flotation circuit when applying recleaning operations of enriched product. Methodology. The methods for calculating separation indices using the separation characteristics of separation processes and calculating the indices of the release of valuable mineral using statistical relationships between the particle size of the inclusion, ash content and particle size distribution function were used. Findings. Separation characteristics of rough and recleaning flotation operations were preliminarily determined experimentally, relations that allow calculating the indices of the release of coal particles in ash-and-slag dumps were defined, based on which the functions of particle distribution by their content of valuable mineral fractional composition were found. The separation characteristics of the connections of the separation blocks, including several operations of cleaning of the enriched froth product, were determined. Calculations to determine the quantitative and qualitative separation indices were performed. Originality. Analytical relationships to determine the indices of the release of coal inclusions in the process of material from ash-and-slag dumps grinding were obtained. Practical value. The established dependencies make it possible to justify the required grinding coarseness to achieve the specified parameters of the enrichment process based on the values of the beneficiation properties of ash-and-slag dumps.

Settling of copper-rich suspended particles from acid drainage neutralization as a function of chemical composition and particle size distribution

The attenuation of total and dissolved metals from acid drainage (AD) results from the interaction of physical and chemical processes occurring during and after AD neutralization in impacted rivers. Chemical removal occurs when dissolved metals are transferred into fine particles or flocs, while physical removal occurs when metal-rich suspended particles are deposited from the water column onto the riverbed. Most works studying metal attenuation in rivers focus on characterizing chemical and physical removal processes separately, yet these processes often interact and take place concurrently. The fate of copper (Cu) in particle suspensions formed from partial neutralization of AD was studied using a settling column coupled to a device that measured particles size distribution in situ, with minimal floc disruption. Chemical composition, particles size distribution, and total suspended solids (TSS) were measured as particles settled. The physical removal of freshly formed particles was enhanced by aluminum (Al), promoting the formation of larger particles and higher rates of TSS removal. However, Fe promoted higher partition of Cu onto particles, controlling its chemical removal. While the rate of Cu association to particles increased over time, TSS settled out from solution within the initial hour, regardless of the chemical composition within the range of tested conditions. Therefore, different remediation strategies may be applied depending on the goal for removal (e.g., removal of TSS, removal of Cu) and water composition. These strategies must consider chemical conditions (i.e., pH and concentrations of Al and Fe), settling times, and mixing conditions during particles formation for an optimal removal.