Detailed Particle Size Distribution Research Articles

Fitting Performance of Particle‐size Distribution Models on Data Derived by Conventional and Laser Diffraction Techniques

Mathematical description of most classical particle size distribution (PSD) data is often used for estimating soil hydraulic properties. Fast laser diffraction (LD) techniques now provide more detailed PSDs, but deriving a function to characterize the entire range of sizes is a major challenge. The aim of this study was to compare the fitting performance of seven PSD functions with one to four parameters on sieve‐pipette and LD data sets of fine‐textured soils. The fits were evaluated by the adjusted R2, MSE, and Akaike's information criterion. The fractal and exponential functions performed poorly while the performance of the Gompertz model increased with clay content for the LD data sets. The Fredlund function provided very good fits with sieve‐pipette PSDs but not the corresponding LD data sets, probably due to underestimation of the clay fraction in the latter. The two‐parameter lognormal function showed better overall performance and provided very good fits with both sieve‐pipette and LD data sets.

Application of bag sampling technique for particle size distribution measurements

Bag sampling techniques can be used to temporarily store the aerosol and therefore provide sufficient time to utilize sensitive but slow instrumental techniques for recording detailed particle size distributions. Laboratory based assessment of the method was conducted to examine size dependant deposition loss coefficients for aerosols held in Velostat bags conforming to a horizontal cylindrical geometry. Deposition losses of NaCl particles in the range of 10 nm to 160 nm were analysed in relation to the bag size, storage time, and sampling flow rate. Results of this study suggest that the bag sampling method is most useful for moderately short sampling periods of about 5 minutes.

Textural averages of saturated soil hydraulic conductivity predicted from water retention data

Abstract Modeling of transport processes in soils relies on predicted values of saturated hydraulic conductivity, Ks. The objective of this work was to derive the parameters of a Ks power-law model from water retention (WR) properties defined at the inflection point of s-shaped WR functions. The proposed model uses water content, θinf, pressure potential, ψinf, and the slope, S, at the inflection point to derive an effective porosity, Φinf, (air filled porosity at θinf) and a pore distribution index, λ⁎, (estimated from WR data between pressure potential at air-entry and ψinf or as S/θinf). The Φinf is raised to 3 − λ⁎ or 3 − S/θinf and multiplied by Cinf Dinf where Cinf is a constant and pore diameter is defined as Dinf ∝ ψinf− 1. The model was developed from: A) a dataset containing 374 measurements of Ks together with detailed WR and particle size distribution information, B) a subset of the HYPRES dataset containing 1827 values of Ks and their corresponding sand, silt and clay percentages and parameter values from an s-shaped WR model; and tested for consistency with C) a published dataset containing textural averages of parameters of an s-shape WR model and Ks values developed from 2134 and 1036 samples, respectively. Linear regression between 16 (A), 10 (B) and 12 (C) textural averages of logKs and their predicted values with Cinf = 20 resulted in R2 values of 0.95, 0.82 and 0.82, respectively. The proposed model is physically sound and except for Cinf all its parameters are derived from one point in the WR curve.

FIT Method for Calculating Soil Particle Size Distribution from Particle Density and Settling Time Data

Particle size distribution (PSD) is one of the most important fundamental physical properties of soils, as it determines their physical, chemical, mechanical, geotechnical, moreover environmental behaviour. Although the measurement of PSD with different techniques is commonly performed in soil laboratories, their automation and continuous PSD curve generation have not been solved yet. However, there are some physical principles, various sensors and different data storing methods for measuring the density-time function. In the present paper a possible solution is introduced for the measurement of the soil particle density database as a function of settling time. The equipment used for this purpose is an areometer that is widely used e.g. for determining the sugar content of must, or the alcohol content of distilled spirits, etc. The device is equipped with patent pending capacitive sensors on the neck of the areometer. It measures the changes in the water levels nearby the neck of the areometer in 1 μm units with <10 μm accuracy. The typical water level changes are 3-5 cm, which makes possible a very accurate determination of particle density changes due to settling in particle size analysis. The measured signals are stored in the equipment's memory and can be downloaded to the controller computer via a modified USB port. Data evaluation can be carried out online or later. The large number of measured data points led to the introduction of a new evaluation method, the Method of FInite Tangents or shortly the “FIT Method”. The dispersed soil particle system is considered as the aggregation of many mono-disperse systems. From this it follows that the measured density-time function can be divided into grain size fractions with tangent lines drawn to finite, but optional points. These tangent lines are suitable for calculating the settling speed of a given fraction, as the changing speed of density is equal to the multiplication of settling speed and mass of the given grain size fraction. The settling speed of all fractions is calculable by using the Stokes law, so the mass of all of the floating fraction can be calculated. Because the soil suspension is a poly-disperse system, the measured density decrease can be considered as an integration of finite mono-disperse systems. From this, it follows that it can be interpreted as the sum of linear density vs. time functions. If the mass of each grain size fraction is known, the particle size distribution is calculable. The method is relatively easily programmed and the intervals of grain size fractions are freely adjustable, so with this program almost all types of particle size distribution are calculable, not only those being uniform. Using the appropriate controller and evaluation program, soil particle size distribution can be calculated immediately after downloading the measured data. This technique does not need more sample preparation than past methods. The automated reading lessens the manpower required for performing the measurement - which also reduces human error sources - and provides very detailed PSD data that has advantages, among others, like revealing multi-modality in the particle-size distribution.

Numerical simulation and sensitivity analysis of detailed soot particle size distribution in laminar premixed ethylene flames

Abstract In this paper, the prediction of a soot model [J. Appel, H. Bockhorn, M. Frenklach, Combust. Flame 121 (2000) 122–136] is compared to a recently published set of highly detailed soot particle size distributions [B. Zhao, Z. Yang, Z. Li, M.V. Johnston, H. Wang, Proc. Combust. Inst. 30 (2005)]. A stochastic approach is used to obtain soot particle size distributions (PSDs). The key features of the measured and simulated particle size distributions are identified and used as a simple way of comparing PSDs. The sensitivity of the soot PSDs to the parameters defining parts of the soot model, such as soot inception, particle and PAH collision efficiency and enhancement, and surface activity is investigated. Incepting soot particle size is found to have a very significant effect on the small-size end of the PSDs, especially the position of the trough for a bimodal soot PSDs. A new model for the decay in the surface activity is proposed in which the activity of the soot particle depends only on the history of that particle and the local temperature in the flame. This is a first attempt to use local flame variables to define the surface aging which has major impact on the prediction of the large-size end of the PSDs. Using these modifications to the soot model it is possible to improve the agreement between some of the points of interest in the simulated and measured PSDs. The paper achieves the task to help advance the soot models to predict soot PSD in addition to soot volume fraction and number density, which has been the focus of the literature.

Evaluation of different representations of the particle-size distribution to predict soil water retention

Abstract Detailed particle-size distribution (PSD) data or parameters derived from it are used in almost all pedotransfer functions (PTFs) to estimate soil hydraulic properties. Most commonly, the PSD is represented by the sand, silt and clay content of a soil. However, a number of standards exist and are in use internationally to describe PSD and particle-size classes. Additionally, some authors use derived particle-size information, such as the geometric mean diameter and its standard deviation as input to their predictive equations. We compared the usefulness of some of the most common representations of the PSD in estimating water retention at − 33 and − 1500 kPa, using Group Method of Data Handling and data of three databases. The cutoff limit between silt and sand content has been simulated to be at 20, 50 and at 63 μm, as used in various countries. We also used the geometric mean diameter and its standard deviation as predictors. We examined the effect of using the wrong cutoff limit in the PSD curve while applying a PTF. Overall, we could not point out one particular representation of the PSD that would clearly provide better results in estimating the selected soil hydraulic properties. Using geometric mean diameter and its standard deviation to represent the entire PSD curve with two parameters did not result in significantly different estimates of the examined soil hydraulic properties, than models that use distinct particle-size classes as input. We found no evidence suggesting that using interpolated data would reduce the accuracy of the estimation of these soil hydraulic properties. It is not straightforward to pre-determine if using the wrong definition of the silt/sand boundary in the PSD data will result in significant loss of estimation accuracy or not; therefore, using such data should be avoided. Our study suggests that using interpolated data–which of course carries a certain magnitude of interpolation error–poses fewer risks while using a PTF than using measured data with the wrong silt/sand boundary.

Size Fractionation in a Phase-Separated Colloidal Fluid

Phase separation of a polydisperse colloidal dispersion implies size fractionation. An application of this effect is given by size-selective purification procedures associated with the colloidal synthesis of so-called monodisperse nanoparticles. We used electron microscopy to determine detailed particle size distributions of coexisting colloidal fluid phases containing highly polydisperse iron oxide nanoparticles with a log-normal distribution (sigma = 0.54 for the total system). Analysis of N approximately 10000 particles per phase yields the first five statistical moments of the distributions. Within experimental error, the interdependence of the statistical moments is in quantitative agreement with the "universal law of fractionation" proposed by Evans, Fairhurst, and Poon [Phys. Rev. Lett. 1998, 81, 1326], even though the theory was derived in the limit of slight polydispersity.

Mechanistic prediction of ash deposition in a pilot-scale test facility

A mechanistic approach has been used for assessing the ash deposition tendency and has been used for predicting the ash deposition behavior of Australian bituminous coals in a pilot-scale test furnace. The detailed analysis of mineral matter in coal determined by QemSCAN analytical technique was incorporated into an ash formation model to estimate the character of ash particles. The detailed chemical composition and particle size distribution data of ash particles from the ash formation model were incorporated into a computational fluid dynamics (CFD) code to get the arrival rate and retention ability of each ash particle onto the heat transfer surfaces. The CFD code along with the ash character from the ash formation model was able to simulate trends in ash deposition along the furnace length similar to those in the test furnace. The approach was also able to distinguish coals with high ash deposition potential from low ash deposition problems and the results agreed with those in test furnace.

ARIES AIR QUALITY MEASUREMENTS: OVERVIEW, 5-YEAR TRENDS AND SPATIAL VARIABILITY ASSESSMENT

ISEE-71 Introduction: The Aerosol Research Inhalation Epidemiological Study (ARIES) is a long-term investigation of relationships between air quality and human health. Underpinning the study is a comprehensive set of air quality measurements at a central site, with supporting measurements at three satellite sites in and around Atlanta. This paper will describe measurement techniques and summarize data for the period 1999 through 2003. Temporal trends and spatial variability will be analyzed and presented. Methods: Air quality measurements at four monitoring sites began in 1998 and will continue through at least 2004. The central site for this study is Jefferson Street (JST), located in a residential-industrial area about 4 kilometers (km) NW of downtown Atlanta. Satellite sites include Fort McPherson (6 km SW of downtown); Tucker (20 km ENE of downtown) and South DeKalb (11 km SE of downtown). At JST, daily 24-hour integrated filter samples were collected for PM2.5/PMcoarse/PM10 mass and composition analysis. Continuous (i.e., hourly average) particle, gas and meteorological measurements included: PM2.5, black carbon (BC), total carbon (TC), NO, NO2, NOx, NOy, HNO3, O3, CO, SO2, wind speed, wind direction, relative humidity, barometric pressure, precipitation and solar radiation. Detailed particle size distributions (number, surface area, and volume), pollen/spore counts, acidity and NH3 were also measured at JST during the first 25 months of ARIES. Daily PM2.5 mass/composition and continuous PM2.5 mass and BC were measured at the three satellite sites. Extensive quality control checks were performed to assess and document data quality. Results: JST data show that PM2.5 mass averaged 16.9 μg/m3 over the 5-year period and declined significantly from 1999 (18.9 μg/m3) to 2003 (15.6 μg/m3). The observed decline had step function features, with average values above 18 μg/m3 in 1999/2000, but below 16 μg/m3 in 2002/2003. Major components of PM2.5 also declined from 1999 to 2003: sulfate (18%), EC (28%), OC (15%), ammonium (26%). Day of week analyses show a clear pattern for PM2.5 mass and components, with maxima and minima on Wednesday or Thursday and Sunday, respectively (min/max ratios 0.6-0.8). Intersite correlations were significant for all species, but higher for 24-hour samples then 1-hour mass and BC. In general, Jefferson Street correlated more strongly with satellite sites than satellite sites correlated with each other, and sulfate correlated more strongly than BC or TC. PM coarse mass/composition and trace gases also showed appreciable year to year variability, with species-dependent declines over the 5-year period. Discussion: An extensive 5-year record of air quality measurements has been produced under the auspices of ARIES. Inspection of annual statistics shows interesting variability, and possibly indication of downward trends in a broad array of air quality indicators. Intersite comparisons and correlations show that Jefferson Street is a representative central site for such measurements.

Particle size distributions and viscosity of suspensions undergoing shear-induced coagulation and fragmentation

The dynamic behavior of concentrated suspensions (up to a solids volume fraction of 20%) of non-spherical particles is investigated theoretically by coupling a rheological law to a population balance model accounting for coagulation and fragmentation of the detailed particle size distribution. In these suspensions, the immobilization of matrix liquid renders the viscosity dependent on the particle aggregation state. The effect of initial solids volume concentration and shear rate on the transient behavior of particle size distribution and suspension viscosity is examined. Power law correlations for the equilibrium flow curves of aggregating suspensions are deduced and compared to experimental data. Steady-state or equilibrium particle size distributions are found to be self-preserving with respect to solids volume fraction and shear rate.

A decision support system for wet soil cleaning

Newly developed software can predict the essential characteristics of the sand product resulting from the ex-situ washing of contaminated soil, dredging sludge or breaker sand. The system was designed for the Dutch situation and it works on the basis of readily available information. The primary output of the system is an assessment of the reusability of the sand product, which is obtained by comparing the prediction of the residual contamination and engineering quality with accepted levels and standards for building materials. The system also provides a ranking of potential applications for the sand with respect to treatment cost, the amount of recycled material or the environmental quality of the product. The software integrates soil cleaning expertise and unit process modelling in a way that allows varying levels of refinement of input data, ranging from a simple identification of the pollution source to a detailed particle size distribution of the contaminated soil. Tests on a database containing information on 117 processed batches of soil, dredging sludge and breaker sand show an 80% success rate in predicting cleanability, even though the input contamination levels were predominantly taken from (relatively inaccurate) in-situ data.

Titania formation by TiCl 4 gas phase oxidation, surface growth and coagulation

Abstract Titania particle formation by TiCl 4 gas phase oxidation, surface growth and coagulation is investigated by a moving sectional population balance model. The dynamic evolution of the detailed particle size distribution is studied accounting for and neglecting the effect of surface growth. The effects of process temperature, T , and precursor volume fraction, φ , on the average diameter, d p , and geometric standard deviation of the particle size distribution are highlighted. Accounting for surface reaction accelerates particle growth for φ >0.01 and gives a size distribution narrower than the self-preserving one as long as the precursor conversion is less than 99%. At higher conversions, the particle size distribution reaches the self-preserving limit corresponding to aerosols made by coagulation. A monodisperse model represents well aerosol dynamics at high process temperatures. A design diagram summarizing the significance of surface reaction in terms of φ and d p at various process temperatures is presented.

Applying Eulerian and Lagrangian Approaches to the Modeling of Dry Desulfurization Process in Pulverized Coal Furnaces

The dry additive desulfurization process (DAP) is an appropriate approach for SO X -reduction in power plants with small and medium capacity and for the retrofit of existing boilers with spatial limitations. In engineering practice, it can be optimized by means of numerical modeling. In the present work, a comprehensive model for simulating the DAP in pulverized coal furnaces is established. A pore model (PM)3069 is suggested to describe the gas-solid reaction between the sorbent and SO X . The overall DAP model is implemented into a coal combustion simulation CFD program AIOLOS, because of the feature of two-phase-flow of DAP, in both Eulerian and Lagrangian (particle tracking) schemes. DAP-desulfurization in engineering processes can be simulated. Numerical studies were performed through various calculations with both Eulerian and Lagrangian approaches for a small-scale furnace. The behaviors and results of the two approaches were compared. The present DAP model offers reasonable results. In addition, it was found: (a) For sorbent particles finer than 60-70 μm, quite similar desulfurization results can be obtained from the two modeling schemes. Above this size range the slip between phases shows significant influence. (b) The CPU-time of the Lagrangian approach increases rapidly with decreasing particle size below about 30 μm. In the present study with 400 tracing particles, the Lagrangian approach requires less computing time than Eulerian above particle size of 60-70 μm. (c) The Lagrangian approach is more suitable for handling two-phase flow with detailed particle size distributions. The Eulerian approach has advantages for treating flows with finer particle suspensions. (d) The Eulerian scheme has less convergence problems, whereas the Lagrangian approach is more sensitive to the computation procedure and requires small relaxation factors.

Mapping of Soot Particles in a Weakly Sooting Diffusion Flame by Aerosol Techniques

The evolution of detailed particle size distributions has been measured along the centerline of an axisymmetric diffusion flame of CH4 + Ar burning in air at 1 atm. Soot particles with mean diameters of 3–18 nm were observed. Changes in the size distribution exhibited zones where either nucleation, coagulation, or destruction of soot particles dominated. These highly sensitive measurements were made by microprobe sampling with an immediate dilution of 1:400, to quench the aerosol, and by subsequent application of aerosol measurement techniques. In parallel, the yield of photoemitted electrons from size-selected particles was determined. The yield shows a characteristic dependence on location in the flame, indicating changes of the particle’s surface. Multiphoton, time-of-flight mass spectrometry was used to investigate the correlation between polycyclic aromatic hydrocarbons in the flame and enhanced photoemission yield from the soot particles.

Simulation and system identification of dynamic models for flocculation control

Instrumentation to support advances in particle-fluid separation control have recently become commercially available; however process models, system identification and automatic control laws are still required. This article first describes the derivation and simulation of a dynamic model for the flocculation process based on a population balance approach. This process model contains a poorly modeled function of the coagulant, mixing power, and average particle size. Accurate on-line identification of this function will be critical for the implementation of high performance flocculation control. As an initial step in this direction, this article describes experimental work involving identification of this unknown function across independent controlled experiments. Consistent results partially validate the proposed system model. The ultimate objective is to use detailed particle size distribution measurements and the dynamic models of particle flocculation to analyze and develop control laws for the flocculation process.

Simulation and system identification of dynamic models for flocculation control

Instrumentation to support advances in particle-fluid separation control have recently become commercially available; however process models, system identification and automatic control laws are still required. This article first describes the derivation and simulation of a dynamic model for the flocculation process based on a population balance approach. This process model contains a poorly modeled function of the coagulant, mixing power, and average particle size. Accurate on-line identification of this function will be critical for the implementation of high performance flocculation control. As an initial step in this direction, this article describes experimental work involving identification of this unknown function across independent controlled experiments. Consistent results partially validate the proposed system model. The ultimate objective is to use detailed particle size distribution measurements and the dynamic models of particle flocculation to analyze and develop control laws for the flocculation process.

Experimental and theoretical values of the ultrasonic properties of dispersions: effect of particle state and size distribution

Abstract Experimental and theoretical data are presented on the ultrasonic properties of polydisperse oil-in-water dispersions. Both emulsions (containing liquid oil droplets) and suspensions (containing crystallized oil particles) have been studied. The suspensions were prepared by crystallizing octadecane droplets in the emulsion. Then, by using a supercooling effect, measurements were obtained at 20°C with either liquid or solid particles. The particle concentrations were 5 and 4.3% v/v for the emulsions and suspensions, respectively, and the particles had diameters in the range 0.2–30 μm. Measurements were made of ultrasonic velocity and attenuation in the frequency range 5–96 MHz. The results are compared with theoretical predictions using a first-order multiple scattering formalism, including polydispersity in particle size. There are dramatic effects, both theoretically and experimentally, upon freezing the particles, mainly due to the presence of resonances in the suspension. In this system the largest particles in the distribution are those most likely to be undergoing resonance. Thus the ultrasonic properties are highly dependent on the detailed particle size distribution.

The interpretation of polymerization kinetics with radical initiation. Solution and emulsion polymerization

Abstract Australian studies have contributed very greatly to recent gains in understanding of the processes involved in polymer formation from solution and from emulsions. The greatest part of the work was done by the Sydney University School but it has relied heavily on measurements made at AINSE and also the directions in which future work appears to us to be heading. We wish to discuss the chemistry of the processes before and after the formation of “latex” particles for the formation of polyacrylonitrile. We shall use data obtained from studies of the evolution of the detailed particle size distribution during polymerization and accurate measurements of the rates of monomer use which have only become possible in the very recent past.

Textural differentiation in chronosequences from eastern australia, II. evidence from particle-size distributions

Abstract Data from particle-size analyses were used to determine the relative importance of the four mechanisms proposed to explain the development of strong textural contrast in the end members of four chronosequences. The mechanisms proposed were sedimentary layering, in-situ chemical weathering, clay illuviation and physical breakdown. Depth functions of fine clay: total clay ratios and detailed particle-size distributions at o intervals from 0.6 μm to 2000 μm indicated that there had been a marked increase in fine clay in the B horizons of the older soils of each sequence, a result consistent with, but not proving, a clay illuviation hypothesis. Cumulative particle-size distribution indices showed that most profiles had texturally uniform parent materials. Changes in the ratio fine silt : total silt with depth were slight for all but one profile, indicating no significant contribution to the clay fraction by in-situ chemical weathering of the silt fraction. From changes in the depth functions of gravel with time, it was concluded that physical breakdown had occurred but that it had not been responsible for the development of the textural B horizon. The rate of disintegration was particularly high early in pedogenesis, preceding the development of texture-contrast. Breakdown contributed fines to the whole solum and was not generally any more intense in one horizon than another. Grain counts of rock fragments in the medium sand range lent support to this conclusion. Changes in the particle-size distribution of quartz from 0.2 μm to 2000 μm indicated that the contribution to the clay fraction from physical disintegration was only slight.

Variation of elemental composition with particle size in the St. Louis aerosol

Detailed particle size distribution of elemental constituents have been determined in the St. Louis aerosol by sampling with cascade impactors for particles >0.25 μm aerodynamic diameter and by analyzing using proton-induced X-ray emission, PIXE, for S, Cl, K, Ca, Ti, Mn, Fe, Zn, Br, and Pb. Two rooftop sites were selected for intensive sampling in industrial and residential locations in St. Louis during February 1974, every 12 h for a 7 d period which included clear, rainy, and snowy weather regimes. The data could be compared with the results of a similar study of the St. Louis aerosol during August 1973 when the weather was generally warm and without rain. Both data sets could also be compared with results of studies of Tallahassee, situated in coastal north Florida, and the north Atlantic marine atmosphere of Bermuda. Although variation in elemental concentrations and their size distributions were observed which could be associated with local weather conditions during the February sampling period, the data set was sufficiently large for meaningful average characteristics to be computed. As examples, two elements of pollution importance, sulfur and iron, show the following comparison between St. Louis and the Florida and Atlantic locations: Sulfur in all data sets was most abundant in the smallest particle size classes. Winter and summer concentration in St. Louis air were the same within a factor of two but generally exceeded north Florida concentrations. Bermuda concentrations were intermediate between St. Louis and north Florida, except for largest particles where sea spray derived material was present. The results reflect the importance of gas phase conversion to particulate forms of sulfur, e.g. sulfate, in all three locations. Iron concentrations in St. Louis generally exceeded those in north Florida for smallest particles and to a lesser extent for larger sizes. Concentrations in Bermuda were about 10-fold lower than in St. Louis for all particle sizes. The results reflect the terrestrial dust origin of iron and also suggest that iron is partially pollution-derived in the St. Louis atmosphere, especially in smaller size ranges.