Cumulative Particle Size Distribution Research Articles

Exploring the effect of the geological texture at meso and micro scale on grinding performance

Comminution indices are used to represent the grindability of a combination of minerals treated by specific processes. If two rock samples with similar values for an index are treated in the same comminution process, they are expected to have a similar behavior during grinding. However, indices are obtained assuming the breakage of homogeneous and continuous materials without considering minor scale mineral and geological textural characteristics. Eventual differences in the process could be related to those properties and may not be explained by comminution indices by itself. In the present study, two different copper ores samples with similar Bond Work index were used to evaluate the influence of mineralogy and geological texture at meso and micro scale in a ball grinding process at laboratory scale. Samples were characterized through geological texture analysis at micro-scale using petrographic microscopy, hyperspectral characterization, X-ray diffraction, and X-ray fluorescence. The effect of mineral properties on grinding was assessed through controlled grinding kinetics performed in a Magotteaux Mill®. Results show that the BWi allows to describe the transition between initial and final states at long grinding times, but it cannot reproduce the entire grinding kinetic, while textural properties, such as grain size and matrix-grain mineralogical composition, may be linked to P80 variation over time and the variation of cumulative particle size distributions at different grinding times. Results suggest that geological texture may be considered as a complement to traditional grindability indices to evaluate the grinding performance.

VOLUME BASED CLOSED-CYCLE HARDGROVE GRINDABILITY METHOD

This paper deals with the development of a volume based closed-cycle grindability test method based on the recently introduced Universal Hardgrove mill and procedure. Five model materials with various origin and material characteris- tics (hardness, grindability, heterogeneity) were chosen for the experiments, i.e. limestone, quartz, andesite, basalt and cement clinker. The grindability of the material was characterized simultaneously in four various ways: 1) the standard Hardgrove Grindability test (HGI), 2) Bond work index calculated from HGI, 3) the conventional Bond test and 4) the closed-cycle volume based grindability test in the Universal Hardgrove mill. The grindability coefficient (G), and the cumulative particle size distribution of 80% passing size (x80) of the product of the closed-cycle Hardgrove test were determined. Relative deviation of the above parameters was very good (in most cases lower than 3%) which indicates the new proposed method as a robust procedure for rapid determination of specific grinding energy of closed cycle grinding in ring mills. Therefore, this test is able to ease the optimization of grinding conditions relatively fast and reliably.

Process control and in vitro/in vivo evaluation of aripiprazole sustained-release microcrystals for intramuscular injection

This work describes the preparation of aripiprazole sustained-release microcrystals for intramuscular injection, through recrystallization, drying, wet grinding, and solidification steps, which had a great impact on the product quality. Here, we evaluated the crystal form of the drug in each step by differential scanning calorimetry (DSC), powder X-ray diffraction (PXRD), and fourier transform infrared spectroscopy (FT-IR), demonstrating that there is no change in the crystal form of aripiprazole monohydrate (H1) during grinding and freeze-drying. Microscopy and scanning electron microscopy (SEM) data showed that freeze-drying had no effect on the morphology of milled H1, and thermal gravimetric analysis (TGA) results showed that the freeze-dried formulation had acceptable water content. In particular, in this study, a similarity factor fitting was applied to determine the similarity of the particle size cumulative distribution curve, and the similarity factor value (99.00) showed that there was no change in the particle size distribution before and after freeze-drying. A two-chamber transmembrane method was used to investigate the in vitro release of the aripiprazole sustained-release microcrystal (ALSI) and commercial preparations (Abilify Maintena®). The similarity factor fitting of in vitro release profiles and drug cumulative release curves in vivo yielded similarity factor values of 98.00 and 95.43, respectively, indicating similar in vitro release and in vivo bioavailability of rats between the ALSI and Abilify Maintena®. A single-dose administration could produce long-term effects for a month. For a microcrystalline suspension, in addition to the conventional quality control indicators, the similarity of the cumulative particle size distribution, the in vitro release profile, and the similarity of the drug release percentage in vivo can be used to reflect product quality and process control.

Particle size effects on soil reflectance explained by an analytical radiative transfer model

Experimental evidence points to an intimate link between soil reflectance, R, and particle/aggregate diameter, D. Based on this strong correlation, various statistical methods for remote and proximal sensing of soil texture and hydraulic properties have been developed. In this paper, we derive a more fundamental and physically-based analytical radiative transfer model that yields a closed-form functional R(D) relationship for dry soils. Despite several simplifying assumptions, the proposed model shows good agreement with measured spectral reflectance (350–2500 nm) data of six soils covering a broad range of textures, colors, and mineralogies. The proposed S-shaped R(D) function resembles cumulative particle and pore size distributions as well as the soil water characteristic function. These analogies may potentially lead to new avenues for developing novel physical models for extracting important soil properties from remotely sensed reflectance data.

On soil textural classifications and soil-texture-based estimations

Abstract. The soil texture representation with the standard textural fraction triplet sand–silt–clay is commonly used to estimate soil properties. The objective of this work was to test the hypothesis that other fraction sizes in the triplets may provide a better representation of soil texture for estimating some soil parameters. We estimated the cumulative particle size distribution and bulk density from an entropy-based representation of the textural triplet with experimental data for 6240 soil samples. The results supported the hypothesis. For example, simulated distributions were not significantly different from the original ones in 25 and 85 % of cases when the sand–silt–clay and very coarse+coarse + medium sand − fine + very fine sand − silt+clay were used, respectively. When the same standard and modified triplets were used to estimate the average bulk density, the coefficients of determination were 0.001 and 0.967, respectively. Overall, the textural triplet selection appears to be application and data specific.

Efficient cumulative breakage distribution and breakage rate computation with minimal experiment intervention incorporating optimal time determination for fine grinding simulation

Comminution involves the reduction of materials to the required sizes, from coarser to finer. The population balance method (PBM) is the most frequently used approach to obtain the particle size distribution (PSD) of materials. To numerically obtain the PSD, a semi-empirical approach known as the size-mass balance equation is commonly employed. The existing technique to determine the parameters in the size-mass balance equation is cumbersome as PSD for early grinding times of different feed sizes must be obtained experimentally. Therefore, a new technique using only a limited data to determine the parameters is introduced and examined. In general, the strong capability of the presently proposed technique is evidenced through successfully capturing of the existing experimental PSD. The advantages of using this technique are that only two experimental PSD of any grinding time are needed to predict the PSD using the size-mass balance equation and without the restriction of input from an early grinding time. This study also proposes to use the cumulative PSD rates as an indicator for the limit of particle size reduction of the materials. It is suggested that the grinding of materials should stop before there is a pivotal change in the initial slopes, i.e., before the difference of the cumulative PSD rates between each initial slopes is found to change sign, or when the difference of the cumulative PSD rates is close to 0% in order to prevent agglomeration or over-grinding. The grinding time fulfilling this criterion is considered as optimal.

Mix Design and Flexural Response of Ultra High Performance Fiber Reinforced Concrete (UHPFRC)

The research article addresses on the mix design and investigation of flexural strength development at an increased age of the material is explored through experimental program with addition of hooked end steel fiber, super plasticizer with special densified materials 53 grade cement, micro silica, quartz sand and fine sand. The UHPFRC mix differs from conventional concrete material constitutients by UHPFRC, an Advanced technology Cement based Super plasticized concrete with high workability, improved homogeneity resulting increased compressive strength of the material, the research study is conducted to achieve target flexural strength 25 N/mm2.the material response exhibits improved strain hardening capacity based on the particle packing theory cumulative particle size distribution equations to improve flexural strength cured under elevated temperature accelerates flexural strength yields efficacy of the concrete is highlighted.

Application of Three-Parameter Distribution to Approximate the Particle Size Distribution Function of Comminution Products of Dolomitic Type of Copper Ore

AbstractThe paper presents the results of analyze the particle size distribution function of comminution products of dolomitic type of copper ore. The breakage tests for single irregular particles were performed with using a hydraulic press device. The authors prepared five particle size fractions of each material, within ranges: 16-18 mm, 18-20 mm, 20-25 mm, 25-31,5 mm and 31-45 mm. The particle size distribution function of single-particle breakage test was calculated separately for each size fraction. In addition, the cumulative particle size distribution function for five particle size fractions was presented. In theoretical part the study of applied functions of particle size distribution for comminution a set of particles and models of crushing single particles was performed. In that paper the curves of the particle size distribution were approximated by the three-parameter function, which parameters depend on the particle strength and material type. For conformity assessment the model distribution function to the empirical distribution function a residual deviation and non-linear correlation coefficient were calculated. The three-parameter function approximating agrees well with the particle size distribution obtained from experimental data. The dependence of the parameters of a particle size distribution function on the dolomite particle strength was presented. The results indicate the identity of single particle grinding mechanism by slow compression of irregular particles of dolomitic type of copper ore, regardless of the initial particle size.

Geophysical and geochemical alteration of rocks in granitic profiles during intense weathering in southern Purulia district, West Bengal, India

Purulia district of West Bengal is geologically dominated mostly by Proterozic hard granite gneiss rocks including soft phyllite and mica schist of Singhbhum group as part of Chotanagpur plateau. Present study aims to understand the nature of geophysical and geochemical weathering processes for characterization of granitic crust as well as the geochemical ways of this alteration. During the field study 14 rocks and soils samples were collected from three sections of each weathering profile in three different blocks namely, Manbazar-I, Manbazar-II and Banduan. The samples were collected along the roads cuts, natural and other man-made exposures and restricted mostly within the exposed layers of the respective profiles. The samples were analyses in sieve for particle size distribution and in X-ray diffraction for mineralogical alteration. The thin section of selected samples were analysed under polarized optical microscope for understanding the nature of physical and chemical changes in parent rocks. From sieve analysis, the cumulative particle size distribution show that the size of weathered materials gradually reduces from saprolite to overlying soils in every profile. Mineralogical analysis by XRD shows that feldspar, muscovite, quartz and biotite are the primary minerals which are intensely weathered and have undergone some geochemical processes except quartz, to form some secondary clay minerals like montmorillonite, kaolinite and illite in the overlying soil. Optical microscopic analysis reveals that transformation of primary minerals to secondary clay minerals significantly reduced the rocks strength which leads the rocks disintegrate into smaller particles. Finally, the results show that there is an abundance of montmorillonite and altered primary minerals with gravel materials in the profiles are liable for further weathering to develop a mature soil.

Attrition of Victorian brown coal during drying in a fluidized bed

ABSTRACT Analyzing the attrition of Victorian brown coal during air and steam fluidized bed drying, the change in particle size distribution over a range of initial moisture contents (60% to 0%) and residence times (0 to 60 minutes) was determined. Dried at a temperature of 130°C with a fluidization velocity 0.55 m/s and an initial particle size of 0.5–1.2 mm, both fluidization mediums show a shift in the particle size distribution between three and four minutes of fluidization, with a decrease in mean particle size from 665 µm to around 560 µm. Using differential scanning calorimetry (DSC), the change in particle size has been attributed to the transition between bulk and non-freezable water (approximately 55% moisture loss) and can be linked to the removal of adhesion water, but not to fluidization effects. This is proved through the comparison of air fluidized bed drying, steam fluidized bed drying, and fixed bed drying—the fixed bed drying is being used to determine the particle size distribution as a function of drying. The results show the three drying methods produce similar particle size distributions, indicating that both fluidization and fluidization medium have no impact upon the particle size distribution at short residence times around ten minutes. The cumulative particle size distribution for air and steam fluidized bed dried coal has been modeled using the equation P d = A 2 + (A 1 − A 2)/(1 + (d/x 0) p ), with the resultant equations predicting the effects of moisture content on the particle size distribution. Analyzing the effect of longer residence times of 30 and 60 minutes, the particle size distribution for steam fluidized bed dried coal remains the same, while air fluidized bed dried coal has a greater proportion of smaller particles.

Effect of Composition on Basic Properties of Engineered Media for Living Roofs and Bioretention

AbstractEngineered media used in living roofs and bioretention plays a crucial role in determining stormwater mitigation performance. Engineered media with compositions varying in four aggregates, volumetric ratio of compost (0, 10, and 20%) and three amendments (zeolite, paving sand, and topsoil) were prepared in the laboratory. Media basic properties including particle-size distribution (PSD), dry bulk density, particle density, porosity, and saturated hydraulic conductivity (Ks), were characterized and investigated as a function of the varying composition. All media are classified as poorly-graded sand (SP), exhibiting porosity greater than 0.51, with magnitudes of Ks ranging from 10−2 to 10−1 cm/s. Media with pumice-based aggregates have particle densities between 2.21 and 2.48 g/cm3. The Ks of a pure aggregate classified as SP is positively related to the particle size corresponding to 50% fines on the cumulative PSD curve. Ks values of four aggregates either remain unchanged or decrease by 73% at ...

Content of respirable and inhalable fractions in dust created at sawing beech wood and its modifications

This paper presents the results of the granulometric analysis of sawdust, created during the sawing of modified and unmodified beech wood with a circular saw. The aim of this work was to analyze the effect of the treatment of beech wood (Fagus sylvatica L.) on the content of respirable and inhalable particles in sawdust generated during the sawing process using a modern circular saw. Different methods of particle-size determination were used. The results obtained from the sieve analysis prove that the sawdust created during the cutting of DMDHEU was finer than the sawdust from native beech and other modified materials. It was also discovered that the dust created during the cutting of Bendywood was finer than when machining native beech and Lignamon. There was an increase in the share of fine fraction in the range of granularity x < 100 μm at the expense of the fraction x = 0.25–1 mm. The properties of Lignamon are primarily based on the properties of raw wood material, therefore this modified material had a similar cumulative particle-size distribution to the native beech dust.

Population balance model for biomass milling

The aim of this work is to develop a model of the milling process of biomass. For this purpose, a classic approach is selected. The breakage probability, characterized by a material mastercurve, and breakage function are used to determine the breakage matrix. A classification function is also proposed, based on physics of the process itself and the calculation of the impact number for a particle. Knowing all these, the milling product characteristic in the steady state can be reproduced. The model has been tested for the milling of two biomasses: an herbaceous one (corn stalk/leaves) and a woody biomass (poplar) in a commercial laboratory mill. The model will reproduce quite reasonably to both cumulative and discrete particle size distributions for the two biomasses tested and for several operating conditions of the mill (rotor speed, sieve openings and feed rate), as shown validating the model results with experimental work. Other parameters as input size of the material show to be less important for the sizes essayed. The main novelty of this work is to present this milling model for biomass material, introducing also the classification system modeling and the calculation of the number of impact.

Algorithm to calculate limiting cumulative particle size distribution functions from turbidimetric data

An algorithm is offered for finding the range within which cumulative particle size distribution functions can be located in consistency with experimental turbidimetric data at a number of wavelengths. It is based on linear programming and minimization techniques. Several tests were performed. The lower right-hand branch of the corridor was found to locate near the initial distribution function.

Agglomeration of turmeric powder and its effect on physico-chemical and microstructural characteristics

Agglomerated foods have gained attention in recent years due to their convenience in use. Turmeric powder has been subjected to agglomeration process at different moisture contents (10–28%) and steaming times (0–60min). Experimental cumulative particle size distribution data of agglomerated samples can be predicted well (0.951⩽r⩽0.999, p⩽0.01) with Rosin–Rammler–Bennett model. The functional properties related to hydration characteristics like wetting time (10–35s) and sinking time (15–115s) of agglomerated samples decrease with an increase in moisture content and/or steaming time. Microstructural observation shows that the non-agglomerated sample possesses spheroids and ellipsoids of different sizes. The size of agglomerates ranges between 50 and 160μm; their shape varies from spheroid to elongated ellipsoids. Image analysis infers that the size related parameters increase with an increase in moisture content/steaming time. A four-layered artificial neural network having a structure of 2–10-8–4 has been developed to predict the agglomeration process of turmeric powder.

Breakage of an artificial crushable material under loading

The mechanical behaviour of granular materials depends on their grading. Crushing of particles under compression or shear modifies the grain size distribution, with a tendency for the percentage of fine material to increase. It follows that the frictional properties of the material and the critical states are modified as a consequence of the changes in grain size distribution and the available range of packing densities. This paper illustrates an extended experimental investigation of the evolution of the grading of an artificial granular material, consisting of crushed expanded clay pellets under different loading conditions. The changes of grading of the material after isotropic, one-dimensional and constant mean effective stress triaxial compression were described using a single parameter based on the ratio of the areas under the current and an ultimate cumulative particle size distribution, which were both assumed to be consistent with self similar grading with varying fractal dimension. Relative breakage was related to the total work input for unit of volume. For poorly graded samples, the observed maximum rate of breakage is practically independent of initial uniformity. Further experiments at higher confining stress are required to investigate the mechanics of breakage of better graded samples.

Caracterização Hidrodinâmica dos Solos da Bacia Experimental do Riacho Guaraíra Utilizando o Método Beerkan

Knowledge of hydraulic properties of soil, such as the water retention and hydraulic conductivity curves, is indispensable for water and sediment transport modeling. Thus, in this work, a methodology used to obtain hydrodynamic soil properties, known as Beerkan, is presented to spatially characterize the main soil hydrodynamic characteristics, i.e., saturated hydraulic conductivity, porosity, and water retention in the soil, for the Guaraira River Experimental Basin, located in the coastal zone of northeastern Brazil. Disturbed soil samples were collected and infiltration tests were accomplished in a regular grid of 196 cells in the basin with 200 m spacing. This method was applied to two soil types (Argisols and Spodosols) with different textural classification (sand, loamy sand, sandy loam). For the hydrodynamic characterization, the shape and the normalization parameters of the θ(h) and of K(θ) curves were determined. The shape parameters depend upon the soil texture and they were obtained from the cumulative particle size distribution curve; the normalization parameters depend on soil structure and they were obtained from the infiltration experiments using the simple ring infiltrometer. The obtained results showed that the values of sorptivity (S) and saturated hydraulic conductivity (Ks) are slightly higher for soils with a lower sand percentage. It was also verified that S and Ks values are higher for the Spodosols, showing that Spodosols are more permeable than Argisols, for any textural class analyzed. Finally, the Beerkan method showed to be a promising method and easily applied to modeling three-dimensional infiltration in the field, as

Effect of Particle Size Distribution on Loose-filled and Tapped Densities of Selected Biomass after Knife Mill Size Reduction

Unique particle size distributions were created with a knife mill using four different classifying screen sizes ranging from 12.7 to 50.8 mm, plus other mill operating conditions. Mathematical descriptors of these distributions were then correlated with loose-filled and tapped densities. A forage size distribution standard (ASABE Standard S424.1) was used to determine the mass fractions on five sizes of sieves and a pan. Weakness of the forage standard was noted for coarse particle distributions that were not normally distributed across sieve sizes. Resulting particle distributions were modeled using both unconstrained and constrained Sigmoid ('S') curves. A wider range of increased sieve sizes for the standard would aide particle distribution modeling. Mass fractions retained on the bottom sieve and pan correlated significantly with biomass densities, likely due to packing of fine particles in void space. Fitting of the cumulative particle size distributions using unconstrained 'S' curves indicated a strong linear correlation between curve fit parameters such as asymptote value and slope factor with densities of biomass. Asymptote values correlated significantly with loose-filled and tapped bulk densities with Pearson correlation coefficients ranging from -0.668 to -0.765 for chopped switchgrass, wheat straw, and corn stover. Slope factors correlated significantly with loose-filled and tapped bulk densities with correlation coefficients ranging from -0.712 to -0.879. Regression models developed using slope factor predicted the loose filled and tapped bulk density with greater accuracy than a regression model using asymptote value. Mean loose-filled bulk densities were 67.5 18.4 kg/m3 for switchgrass, 36.1 8.6 kg/m3 for wheat straw, and 52.1 10.8 kg/m3 for corn stover. Mean tapped bulk densities were 81.8 26.2 kg/m3 for switchgrass, 42.8 11.7 kg/m3 for wheat straw, and 58.9 13.4 kg/m3 for corn stover. On average, tapping increased bulk density by 21.2% for switchgrass, 18.7% for wheat straw, and 13.0% for corn stover. These results can be used to design efficient size reduction, handling, storage, and transportation systems for chopped biomass.

Caracterização hidrodinâmica de solos: aplicação do método Beerkan

O conhecimento das propriedades hidráulicas do solo, tais como as curvas de retenção da água no solo teta(h) e da condutividade hidráulica K(teta), é indispensável para a modelagem do transporte de água e de poluentes em sistemas agrícolas. Várias técnicas experimentais têm sido propostas para determinar essas características do solo diretamente no campo, porém a complexidade, os custos elevados e o tempo de execução dessas medidas, são fatores que limitam bastante a obtenção dessas informações em grande escala. Apresenta-se, no presente trabalho, uma metodologia conhecida como "Beerkan", com a qual se busca minimizar esses fatores utilizando-se dados experimentais de infiltração, da distribuição granulométrica e da massa específica do solo, para então se estimar os parâmetros das curvas de teta(h) e K(teta). O método foi aplicado em dois solos com diferentes classes texturais (três de um Latossolo Amarelo e três de um Neossolo Flúvico). Determinaram-se, com vistas à caracterização hidrodinâmica, os parâmetros de forma das curvas de teta(h) de van Genuchten e de K(teta) de Brooks e Corey, dependentes majoritariamente da textura do solo e obtidos a partir da curva de distribuição dos tamanhos das partículas, além dos parâmetros de normalização dependentes, essencialmente, da estrutura do solo e obtidos a partir dos ensaios de infiltração utilizando-se o infiltrômetro de anel simples. O método Beerkan provou ser robusto e adaptado à caracterização hidrodinâmica dos dois solos.

On the Consequences of Non‐First‐Order Breakage Kinetics in Comminution Processes: Absence of Self‐Similar Size Spectra

AbstractComminution or size reduction is a commonly used unit operation in a variety of industries including pharmaceuticals. In quantitative analysis of comminution at the process length scale, population balance modeling has been used with an assumption that the breakage rate of particles is first‐order and that the population balance model is linear. For certain forms of the specific breakage rate and breakage distribution functions, a similarity solution to the linear population balance exists, and self‐similarity plots have been used to show its validity in batch comminution processes. On the other hand, ample experimental batch milling data in the literature indicate the inadequacy of the linear theory. In this study, a theoretical investigation has been conducted within the framework of a recently proposed non‐linear theory. The non‐linear theory takes into account phenomenologically the non‐first‐order effects resulting from mechanical multi‐particle interactions. Specifically, the cushioning action of small particles on the coarser ones is considered. It is found that self‐similarity does not exist in the presence of the non‐first‐order breakage kinetics. The present study suggests the use of self‐similarity plots for an approximate assessment of the impact of non‐first‐order kinetics on the shape of the cumulative particle size distribution.