Continuous Particle Size Distribution Research Articles

Effects of Different Particle Size Distributions on Aluminum Particle–Air Detonation

Due to the involvement of powder materials in dust explosion hazards and detonation experiments, it is imperative to analyze the heterogeneous detonation in a polydisperse suspension with a continuous particle size distribution. Notably, most current studies are limited to monodisperse suspensions with only one particle size. In this study, the rich aluminum particle–air detonation with two particle size distributions (namely, the monodisperse and the polydisperse with log-normal particle size distribution) is numerically studied by using the Eulerian–Lagrangian method along with a new hybrid aluminum combustion model. Significant discrepancies of the one-dimensional detonation front structures are observed between the monodisperse detonation and the polydisperse counterpart. And, the physical mechanisms of these discrepancies have been revealed by decoupling the gas–particles interactions with the one-dimensional flow theory. It is mainly caused by the different timings of the particle phase transition processes and the consequently different heat transfer characteristics, which are the effects of multiple timescales and length scales in the polydisperse detonation. Furthermore, owing to the wider reaction zones of polydisperse detonations than that of the monodisperse counterpart, discrepancies of two-dimensional detonation cell sizes are observed as well. This study reveals the great importance of considering particle size distribution in heterogeneous detonation simulations.

Particle Packing Application for Improvement in the Properties of Compressed Stabilized Earth Blocks with Reduced Clay and Silt

Soil as a building material has been used in different forms such as mud, adobe, rammed earth and bricks. The present study focuses on producing Compressed Stabilized Earth Blocks (CSEBs) giving attention to the particle size distribution in the soil mixture. The literature established that compressive strength significantly depends on clay and silt content and 25% of clay and silt produce optimum results while no attention has been given to the amount of other, larger particles. Soil grading refers to the combination of different-size particles in a soil mixture. The correct selection of sizes in the correct proportion may cause improvements in CSEB properties. This paper explains the application of particle packing technology for the improvement of CSEB properties. The theoretical concepts provide a continuous particle size distribution, and the soil used for the experiments also has a continuous particle size distribution. The soil used in the experiments was subjected to washing to reduce the clay and silt content. Separated clay and silt and large particles of different sizes were added to the mixture to match particle size distribution to the optimization curves as explained in particle packing theories. The experimental results show that the CSEB properties can be significantly improved by modifying particle size distribution to fit the suggested optimization curves. According to the results, the compressive strength improved by more than 50% with different amounts of cement stabilization. Significant improvements in the dry densities and water absorption ratios of blocks were observed with this particle size modification.

Influence of size-induced segregation on the biomass gasification in bubbling fluidized bed with continuous lognormal particle size distribution

Via the multiphase particle-in-cell approach, the biomass gasification in a three-dimensional bubbling fluidized bed with sand material of wide particle size distribution (PSD) is numerically simulated. The gas and solid motion are solved by treating the gas as the continuum medium in the Eulerian framework and numerical parcel in the Lagrangian framework, respectively. After validating the numerical results with experimental data, the radial and axial segregation induced by the wide PSD and chemical reactions, combined with the particle-scale information of both particle type (e.g., temperature, heat transfer coefficient, constituent mass fraction, and solid residence time) are discussed. The results demonstrate that obvious radial and axial segregation impact the spatial distribution of temperature and heat transfer of both particle types. The skewed distribution of the residence time of biomass particles is obtained. Biomass particles exiting the bed behave with large carbon content. PSD width exerts an evident influence on the spatial distribution of heat transfer coefficient, mass, and constituent content of biomass particles. Enlarging the PSD width enhances the gasification performance of biomass particles with the reduced mass and increased residence time for biomass particles in the bed, and the reduced char residual in the biomass particles lost. The results obtained in this work provide new insights regarding the presence of the radial and axial segregation induced by the wide size distribution and chemical reactions, which can be beneficial for the scale-up and the in-depth understanding of the fundamental mechanisms for the gasification process in this kind of reactor.

Continuous gap-graded particle packing designs

Continuous gap-graded systems (packings with a shortage of medium-sized particles) often show excellent application properties in practice. In this study, existing empirical models were reviewed and modified to include a minimum grain size. In the newly proposed modified model with the highest freedom of design, a continuous gap-graded particle size distribution can be fully described by a minimum particle size, a gap particle size, a maximum particle size and two distribution moduli by which the amount of fines as well as the amount of coarses in relation to medium-sized particles (the extent of the gap-grading) can be adjusted.

The effect of gelation on statically and dynamically freeze‐cast structures

AbstractFreeze‐casting is a technique used to produce structures with anisotropic porosity in the form of well‐defined microchannels throughout a sample. Here, this technique is used on the magnetocaloric ceramic La0.66Ca0.26Sr0.07 Mn1.05O3. We show that a dynamic freezing profile, where the temperature is decreased continuously at −10 K/min, results in homogeneous, lamellar channels with widths of ∼15 µm, while static freezing, where the temperature is kept constant at 177 K, results in channels of increasing size away from the initial ice crystal nucleation site. The effect of gelation before freeze‐casting is also investigated. Gelation inhibits ice crystal growth, which significantly changes the morphology by making channel cross sections less elongated, while additionally introducing more dendrites and ceramic bridges in the structure. The latter significantly dominates the flow path through the gelated structures, affecting the calculated tortuosity, which increases to τ ≈ 4 when compared to non‐gelated samples where calculated tortuosities are in the range of ∼1.3 to ∼3. Finally, we present a systematic and automatic approach for evaluating channel and wall sizes and calculating tortuosities. This is based on analysis of images obtained by scanning electron microscopy using a continuous particle size distribution method and the TauFactor application in MATLAB®.

A moment-based kinetic theory model for polydisperse gas–particle flows

Starting from a generalized population balance equation and the Boltzmann–Enskog collision model for hard spheres, a kinetic theory model for polydisperse gas–particle flows is presented. Here, polydispersity results from spherical particles with the same material density but different diameters. The particle size distribution (PSD) of the particles is allowed to evolve in space and time due to physical processes such as mixing. In order to treat a continuous PSD, the particle-phase model is formulated in terms of the moments of the PSD, and velocity moments conditioned on the particle size. Velocity moments up to second order are included, resulting in transport equations for the mass, momentum and granular temperature, all conditioned on the particle size. In the numerical implementation, the PSD is represented using quadrature-based moment methods (QBMM). With QBMM, a continuous PSD can be treated using a relatively small number of moments as compared to class or sectional methods. Here, a realizable numerical algorithm for solving the moment system in a finite-volume code is proposed, valid for dilute systems wherein frictional forces are negligible. The ability of the proposed model to describe polydisperse gas–particle systems is demonstrated using cluster-induced turbulence and riser flow.

Is the Laser Diffraction Method Reliable for Soil Particle Size Distribution Analysis?

Core Ideas LDM was evaluated by SPM and SEM for soil PSD determination. LDM significantly overestimated sand and silt but underestimated clay contents compared to SPM. LDM resulted in soil texture class shifts in nearly half of the soil samples in contrast to SPM. Linear conversions were significant for sand and silt but not for clay contents from LDM to SPM. LDM held statistically similar median particle sizes with SEM for PSDs within the clay fraction. The laser diffraction method (LDM) has been increasingly applied for quantifying soil particle size distribution (PSD), owing to its advantages of rapid analysis, high reproducibility, and continuous PSD measurement for a wide range of size fractions. However, some ambiguities exist regarding the comparability of results with those obtained using other classical methods. The objective of the current study was to evaluate LDM‐derived PSDs via comparisons with PSDs obtained with the standard sieve–pipette method (SPM) and from the absolute method of microscopy. A total of 277 soil samples were collected at different soil depths in a typical cropland in the northeast mountainous region of Beijing and analyzed with both SPM and LDM. Due to time and labor constraints, scanning electron microscopy (SEM) was performed on 100 samples randomly selected for the PSDs within the clay fraction withdrawn by SPM. The results manifested on the average 18.9% underestimation of clay content and 25.3% overestimation of silt content by LDM compared to SPM. These disagreements directly caused the shifts of soil texture class in 44.8% of the soil samples. Significant linear regression equations were generated to convert LDM–derived sand and silt contents to SPM–derived ones (p < 0.01). The linear conversions for the clay content were only significant for the calibration samples, but possessed negative coefficients of determination for the validation set. According to SEM, silt‐sized particles were wrongly included in the clay fraction identified by SPM. Eliminating such particles, the clay contents corrected by SEM were significantly lower when assuming the shape of clay particles < 2 µm as plates or discs with constant thickness–diameter ratio of 1/10, and higher when considering the clay particles as spheres for volume calculation, in contrast to those measured by LDM (P < 0.01). Detailed volume‐based PSDs within the clay fraction were further compared between SEM and LDM, revealing dissimilar PSD patterns but statistically similar median particle diameters. These findings suggest the effectiveness of LDM in soil PSD determination. Future work is needed to systematically quantify the impact of other possible factors such as clay mineralogy and refractive index on LDM‐derived PSDs.

DEM Study on the effect of particle‐size distribution on jamming in a 3D conical hopper

Despite the advancement on the understanding on the unwelcome phenomenon of hopper jamming, the influence of the particle‐size distribution (PSD) width of the ubiquitous continuous PSDs remains unknown. Accordingly, this study investigated using discrete element method a range of PSD widths (10%≤σ/μ≤50%) of lognormal PSDs with a constant mean particle diameter of 10 mm in a three‐dimensional hopper. Results indicate that, although the monodisperse particles of 10 mm diameters do not jam, the wider PSDs (σ/μ≥30%) jam. The flatter arches and higher mass‐averaged force that are linked to the denser packing of wider PSDs underlie the propensity to jam. To reduce the jamming probability, the friction coefficient and initial fill height can be reduced, but not changes in particle density. The results here highlight that the mean particle diameter alone is an insufficient parameter to predict jamming and the impact of PSD width is non‐negligible. © 2018 American Institute of Chemical Engineers AIChE J, 65: 512–519, 2019

Local Fixed Pivot Quadrature Method of Moments for Solution of Population Balance Equation

A local fixed pivot quadrature method of moments (LFPQMOM) is proposed for the solution of the population balance equation (PBE) for the aggregation and breakage process. First, the sectional representation for aggregation and breakage is presented. The continuous summation of the Dirac Delta function is adopted as the discrete form of the continuous particle size distribution in the local section as performed in short time Fourier transformation (STFT) and the moments in local sections are tracked successfully. Numerical simulation of benchmark test cases including aggregation, breakage, and aggregation breakage combined processes demonstrate that the new method could make good predictions for the moments along with particle size distribution without further assumption. The accuracy in the numerical results of the moments is comparable to or higher than the quadrature method of moment (QMOM) in most of the test cases. In theory, any number of moments can be tracked with the new method, but the computational expense can be relatively large due to many scalar equations that may be included.

Expanding particle size distribution and morphology of aluminium-silicon powders for Laser Beam Melting by dry coating with silica nanoparticles

Current requirements for metal powder in Additive Manufacturing via Laser Beam Melting in powder bed (LBM) that ensure repeatably homogeneous thin layers can be spread and LBM products with high relative density ρrel can be built are high sphericity and particle size distributions (PSD) with limited share of fine particles. The most established LBM powder production method today is delicate and costly inert gas atomization. It yields highly spherical particles with continuous particle size distributions, but two thirds of the atomized powder exceed established LBM size ranges. A novel process route to improve flowability of cohesive metal powders is the coating of micro-sized powder particles with small amounts of nanoparticles. In this article, significant improvements in powder layer smoothness and ρrel of LBM samples are shown by statistical analysis of physical experiments on the example of Al-Si powders dry coated with 0.5 wt% nanoparticular fumed silica SiOx. This setup was chosen because Al is most prone to powder flowability issues in LBM and no new chemical elements are added to the alloy from dry coated SiOx. Particle shape is varied from spherical over ovoidal to irregular using powder atomized with Ar, N and air. Effects of variations of PSD and LBM parameters on ρrel, defect types, microstructure and hardness using powders with and without SiOx are investigated. Because ρrel are skewed towards 100%, ANOVA on ranks is the applicable statistical method. Since the principle of using nanoparticles as spacers between microparticles is based on geometry, it is transferrable to other material systems. This may help for example to increase ρrel of LBM metal matrix composites prepared by mechanical alloying as non-spherical particles with considerable amounts of fine particles. The use of larger percentages of atomized powders in LBM can increase resource efficiency.

Chemical potential of a test hard sphere of variable size in hard-sphere fluid mixtures.

A detailed comparison between the Boublík-Mansoori-Carnahan-Starling-Leland (BMCSL) equation of state of hard-sphere mixtures is made with Molecular Dynamics (MD) simulations of the same compositions. The Labík and Smith simulation technique [S. Labík and W. R. Smith, Mol. Simul. 12, 23-31 (1994)] was used to implement the Widom particle insertion method to calculate the excess chemical potential, βμ0ex, of a test particle of variable diameter, σ0, immersed in a hard-sphere fluid mixture with different compositions and values of the packing fraction, η. Use is made of the fact that the only polynomial representation of βμ0ex which is consistent with the limits σ0 → 0 and σ0 → ∞ has to be of the cubic form, i.e., c0(η)+c¯1(η)σ0/M1+c¯2(η)(σ0/M1)2+c¯3(η)(σ0/M1)3, where M1 is the first moment of the distribution. The first two coefficients, c0(η) and c¯1(η), are known analytically, while c¯2(η) and c¯3(η) were obtained by fitting the MD data to this expression. This in turn provides a method to determine the excess free energy per particle, βaex, in terms of c¯2, c¯3, and the compressibility factor, Z. Very good agreement between the BMCSL formulas and the MD data is found for βμ0ex, Z, and βaex for binary mixtures and continuous particle size distributions with the top-hat analytic form. However, the BMCSL theory typically slightly underestimates the simulation values, especially for Z, differences which the Boublík-Carnahan-Starling-Kolafa formulas and an interpolation between two Percus-Yevick routes capture well in different ranges of the system parameter space.

High shear breakage of compact polyelectrolyte-bridged flocs: A method for obtaining model-independent breakage rate function data

A method of obtaining model-independent breakage rate or fragmentation kinetic function (FKF) data in the population balance (PB) equation (PBE) was proposed for the high shear breakage of compact polyelectrolyte-bridged alumina flocs. The continuous particle size distribution function (PSDF) data were obtained as a function of fragmentation time. The PSDF data at zero fragmentation time was and must be used as the input in the PB modelling. Computed temporal PSDF curves were obtained by solving the dimensionless log-form PBE using a FKF based only on the fragmenting particle and a daughter size. Another important requirement is that the experimental time must be used in the scaling. Using appropriate values for the parameters in the FKF, an excellent match between the temporal experimental and computed PSDF data was achieved. Upon meeting all these conditions, the FKF values used in the computation should truly represent the experimental values for all father-daughter size combinations encountered in the fragmentation process. The fragmentation occurred in the rotor-stator device under the conditions where the Kolmogorov microscale and characteristics velocity gradient of 37 μm and 1600 s−1. The ratio of the largest to smallest length scale turbulent eddies was 2047.

A simple particle-size distribution model for granular materials

Particle-size distribution (PSD) is a fundamental soil property that plays an important role in soil classification and soil hydromechanical behaviour. A continuous mathematical model representing the PSD curve facilitates the quantification of particle breakage, which often takes place when granular soils are compressed or sheared. This paper proposes a simple and continuous PSD model for granular soils involving particle breakage. The model has two parameters and is able to represent different types of continuous PSD curves. It is found that one model parameter is closely related to the coefficient of nonuniformity (Cu) and the coefficient of curvature (Cc), while the other represents a characteristic particle diameter. A database of 53 granular soils with 154 varying PSD curves is analyzed to evaluate the performance of the proposed PSD model, as well as that of three other PSD models in the literature. The results show that the proposed model has improved overall performance and captures the typical trends in PSD evolution during particle breakage. In addition, the proposed model is also used for assessing the internal stability of 27 widely graded soils.

DEM study of the size-induced segregation dynamics of a ternary-size granular mixture in the rolling-regime rotating drum

Segregation induced by size, shape, or density difference of the granular material is inevitable in both natural and industrial processes; unfortunately, the underlying mechanism is still not fully understood. In view of the ubiquitous continuous particle size distributions, this study builds on the considerable knowledge gained so far from binary-size mixtures and extends it to a ternary-size mixture to understand the impact of the presence of a third particle size in the three-dimensional rotating drum operating in the rolling flow regime. The discrete element method is employed. The evolution of segregation, the active-passive interface, and the dynamical response of the particle-scale characteristics of the different particle types in the two regions are investigated. The results reveal that the medium particles are spatially sandwiched in between the large and small particles in both the radial and axial directions and therefore exhibit behaviors intermediate to the other two particle types. Compared to the binary-size mixture, the presence of the medium particles leads to (i) higher purity of small particles in the innermost of the radial core, causing a decrease of the translational velocity of small particles; (ii) decrease and increase of the collision forces exerted on, respectively, the large and small particles in both regions; and (iii) increase in the relative ratio of the active-passive exchange rates of small to large particles. The results obtained in the current study therefore provide valuable insights regarding the size-segregation dynamics of granular mixtures with constituents of different sizes.

Particle size distribution predicts particulate phosphorus removal

Particulate phosphorus (PP) is often the largest component of the total phosphorus (P) load in stormwater. Fine-resolution measurement of particle sizes allows us to investigate the mechanisms behind the removal of PP in stormwater wetlands, since the diameter of particles influences the settling velocity and the amount of sorbed P on a particle. In this paper, we present a novel method to estimate PP, where we measure and count individual particles in stormwater and use the total surface area as a proxy for PP. Our results show a strong relationship between total particle surface area and PP, which we use to put forth a simple mechanistic model of PP removal via gravitational settling of individual mineral particles, based on a continuous particle size distribution. This information can help improve the design of stormwater Best management practices to reduce PP loading in both urban and agricultural watersheds.

DEM analysis of granular crushing during simple shearing

ABSTRACTIn this study, simple shear tests on breakable polydisperse granular materials were simulated using two-dimensional discrete element method (DEM). A new technique of generating polydisperse DEM samples with a smooth and continuous particle size distribution curve was proposed. A modified breakage criterion was introduced to reflect the contact force anisotropy of particles in the numerical sample. The simulation results showed that during the simple shearing, grain crushing in the sample mainly occurred in the contraction process and decreased gradually when the sample began to dilate. As the shearing proceeded to a larger strain, the grain crushing tended to a stable value. This grain crushing trend was in accordance with the evolution of the average normal contact forces of particles in the sample during shearing. The average normal contact forces of potential breakage particles increased in the contraction process and decreased in the dilatancy process. A decrease in the average normal contact forces of potential breakage particles resulted in the decrease in grain crushing during the later stage of shearing.

Using the meter small-angle dispersity in automated systems continuous monitoring particle size distribution of aerosols

We present the results of observations of the particle size distribution of aerosols on a stationary post in the city of Sevastopol in 2015-16 years. The basic patterns of aerosol distribution in individual size groups and their relationship with environmental parameters. The relevance of the proposed monitoring of the various indicators of aerosol was noted.

Annulus flow behavior of Geldart Group B particles in a pilot-scale CFB riser

Solids flow direction near the wall of a CFB riser was studied for three monodisperse, two binary mixtures and one continuous particle size distribution (PSD) of Geldart Group B particles. Measurements were taken at five axial positions along a 0.3m diameter, 18m tall pilot-scale CFB riser at four operating conditions. The data were compared to predictions available from flow regime maps. Results showed that (i) for monodisperse systems, particle diameter was more dominant in dictating upflow annulus behavior; (ii) the binary mixtures exhibited largely upflow annulus behavior, presumably due to the dominant influence of the larger constituent particles in dictating upflow annulus behavior; (iii) for the continuous particle size distribution (PSD), the impact of this type of polydispersity was more pronounced at lower solid loading conditions; and (iv) the applicability of the available regime maps, which were largely developed based on Geldart Group A particles, was found to be limited for the Geldart Group B and non-monodisperse particle systems investigated in this study.

Effect of size distribution of the particulate material on the specific breakage rate of particles in dry ball milling

In the dry ball milling operation, the specific breakage rate of particles has been found to vary significantly with the size distribution of the particulate material. However, due to the lack of suitable experimental data and a clear understanding of the role of inter-particle interactions in determining the specific breakage rate of particles, it has not been possible to develop a general mathematical model that can be used to describe the variation of the specific breakage rate of particles. These limitations were overcome in our investigation by using feed charges for batch grinding experiments that were prepared according to specially designed continuous and discontinuous particle size distributions. A detailed analysis of the experimental results led to several new findings about the nature of the non-linear grinding kinetics. In particular, it was found: (i) for a given size fraction of particles, while the effect of the coarser and immediately finer sizes on its specific breakage rate was negative, the effect of the other finer sizes was positive and it increased as the particle size decreased, (ii) the overall effect varied with the material type and particle size, being more pronounced in the case of the softer material and coarse particles, (iii) the breakage distribution parameters were also significantly affected by the particle size distribution, and (iv) a simple linear relationship in terms of the mass fractions of different sizes described the variation of the specific breakage rate parameters with particle size distribution quite satisfactorily.

Particle Size Distribution for Refractory Castables: A Review

Particle size distribution is important for the development of both shaped and unshaped refractories. But it is more critical for the castables as they need to satisfy two near contradictory properties, flow and compaction (strength). Continuous particle size distribution of ordered particle sizing systems is employed primarily in advanced castables due to the many advantage such as reducing the water demand, imparting desired rheological characteristics (such as vibratory/thixotropic flow or free flow/self-leveling behavior), minimizing porosity, and maximizing particle contact for enhanced bonding and optimum strength development. Casting and placing properties of castables, which are dependent on flow behavior, are the most critical ones as they affect refractory property development in castables. Many researchers have worked on particle size distribution for castables. Primarily the works of Furnas, Andreasen and Dinger & Funk are well accepted in the castable industries mainly because of their simple approach. This paper reviews these distribution models for castables and their suitability in practical castable development.