Cumulative Mass Distribution Research Articles

The Crushing Distribution Morphology of a Single Particle Subjected to Rotary Impact.

In a vertical shaft impact crusher, the particle crushing process is extraordinarily complex, and the particle shape significantly influences the size distribution of the crushed product. To quantify the crushing behavior of particles more accurately and thus reveal the crushing mechanism of the crusher, an analytical approach is suggested for characterizing the crushing distribution of particles subjected to rotational impact. First, according to the working principle of vertical shaft impact crusher, a rotary impact tester was designed, and the cumulative damage model of particles under repetitive impact was established based on the theory of fracture mechanics, based on which the simulation model of single-particle rotary impact tester was constructed. Then, seven distinct particle shapes were established based on the particle shapes observed during the crusher's actual production. Finally, an investigation was conducted using the simulation model to examine the impact of various rotor velocities and particle shapes on the macroscopic mechanical properties and crushing distribution attributes of single-particle crushing. In the single-particle rotary impact crushing experiments, the findings indicated that the particle crushing transpired at the site of contact with the anvil. The particle size distribution of subparticles generated through the crushing with distinct particle shapes all exhibit single-peak characteristics as rotor speed increases. The magnitude of the peak value progressively escalates in tandem with the rotor speed increase. Furthermore, as the rotor speed increases, so do the cumulative mass distribution and the maximum continuous crushing cumulative mass. When the horizontal aspect ratio of the particles is V < 1 and V > 1, the crushing effect of the particles is poor at the same rotational speed; the curve of the maximum continuous crushing degree has an inverted "V″ shape. The crushing effect of the particles improves as their edges become progressively sharper, and the maximum continuous crushing degree of the particles increases as the edge sharpness of the particles advances.

Impact Disruption of Bjurböle Porous Chondritic Projectile

The ∼200 m s−1 impact of a single 400 kg Bjurböle L/LL ordinary chondrite meteorite onto sea ice resulted in the catastrophic disruption of the projectile. This resulted in a significant fraction of decimeter-sized fragments that exhibit power-law cumulative size and mass distributions. This size range is underrepresented in impact experiments and asteroid boulder studies. The Bjurböle projectile fragments share similarities in shape (sphericity and roughness at small and large scales) with asteroid boulders. However, the mean aspect ratio (3D measurement) and apparent aspect ratio (2D measurement) of the Bjurböle fragments is 0.83 and 0.77, respectively, indicating that Bjurböle fragments are more equidimensional compared to both fragments produced in smaller-scale impact experiments and asteroid boulders. These differences may be attributed either to the fragment source (projectile versus target), to the high porosity and low strength of Bjurböle, to the lower impact velocity compared with typical asteroid collision velocities, or potentially to fragment erosion during sea sediment penetration or cleaning.

Primary and secondary breakup of molten Ti64 in an EIGA atomizer for metal powder production

Electrode Induction melting Gas Atomization (EIGA) is a free-fall gas atomization process used to produce metal powders, where a swirling supersonic gas jet hits a molten metal stream atomizing it into droplets through various fragmentation mechanisms. Fragmentation mechanisms of molten Ti64 are investigated by high-speed video visualization. The role of gas pressure and melting chamber overpressure on the fragmentation mechanisms and on the particle size distribution is determined. The mechanisms observed are fiber breakup, bag breakup and Rayleigh breakup for primary fragmentation and bag breakup and shear breakup for secondary fragmentation. Increasing the gas pressure promotes shear breakup and creates finer droplets. A model based on log-stable law is proposed to fit the mass distribution according to the dominant fragmentation regime. A good agreement is observed between the different analysis (dominant atomization regime, mass cumulative distribution evolution, parameters of log-stable law). A criterion for prediction of nozzle clogging is devised.

Development and experimental study of a scaled model for dust dispersion in fully-mechanized mining face

Model experiment is one of the research methods for the fundamental theory of coal mine dust control. To address the current deficiencies in experiment development for research on dust migration rules, a scaled model for dust dispersion in a fully-mechanized mining face was constructed based on the design prototype of the 25211 mining face at the Hongliulin mine, using a similar theory. The model includes a mining face, a return airway, a haulage roadway, and a subsidiary roadway constructed using aluminum alloy profiles and tempered glass. The model uses U-shaped exhaust ventilation. The shearer, hydraulic support, and reverse loader are equipped with dust sources, and each dust source operates independently with distinct dust generation processes that do not interfere with each other. An experimental plan for dust diffusion during shearer dust generation was designed with a wind speed of 1.0 m/s. Preliminary model experiment was conducted based on this model. The results showed that the farther away from the dust source, the lower the dust concentration. The relative mass distribution and cumulative mass distribution of falling dust particles also showed that the farther away from the dust source, the smaller the particle size of the falling dust particles. The maximum size distribution decreased from 51.4 μm to 27.9 μm, and the average particle size decreased from 34.9 μm to 20.6 μm. The test model results were validated by field tests, indicating that the constructed model has good reliability. Finally, the critical areas for future research based on this model were proposed. The development of the model provides valuable experimental support for the theory of multi-source dust transportation in the airflow on the fully-mechanized mining face.

Application of X-ray computed tomography scanning in describing partition curves of dense medium cyclones

The partition curve is an important tool to evaluate the separation performance of mineral separators like dense medium cyclones (DMCs). This curve is constructed by float-and-sink (FaS) analysis which involves the use of heavy liquids and suspensions. This traditional technique is hazardous to the environment, laborious, and time-consuming. Here, a new technique using X-ray computed tomography (XCT) scanning was successfully developed and applied for describing the partition curve of a DMC at an Australia-based lead–zinc mineral processing plant. The DMC feed, concentrate and reject streams were sampled and sieved into several size classes. The chemical assays and averaged densities according to each class were analysed by X-ray fluorescence spectrometry and gas pycnometry, respectively. The partition behaviour was investigated by XCT analysis. A model was proposed to determine the mass yield value – an important parameter to define partition curves – by mass balance and reconciliation, which is generally unknown during the sampling of continuous separation processes. From the reconstructed XCT images, we obtained detailed information on individual particles such as volume, surface area, mass, and density. Cumulative mass distribution curves and partition curves of the DMC for different size classes were then constructed and agreed with the FaS analysis. Using the XCT technology can help overcome the issues of the traditional FaS analysis. Moreover, this technology would allow for evaluating DMC separation efficiency with continuous, online, and real-time monitoring and control.

Collisional Growth and Fragmentation of Dust Aggregates. II. Mass Distribution of Icy Fragments

By performing N-body simulations, we investigated the fundamental processes of collisions between dust aggregates composed of submicron-sized icy dust monomers. We examined the mass distribution of fragments in the collisional outcomes in a wide range of the mass ratio and the collision velocity between colliding dust aggregates. We derived analytic expressions of the mass distribution of large remnants and small fragments by numerical fitting to the simulation results. Our analytic formulae for masses of the large remnants can reproduce the contribution of mass transfer from a large target to a small projectile, which occurs for a mass ratio of ≳3 and is shown in a previous study. We found that the power-law index of the cumulative mass distribution of the small fragments is independent of the mass ratio and only weakly dependent on the collision velocity. On the other hand, the mass fraction of fragments of individual dust monomers decreases with an increasing total mass of colliding aggregates for a fixed mass ratio. This tendency implies that multiple hierarchical disruptive collisions (i.e., collisions between fragments, and collisions between fragments of fragments) are required for producing a large number of individual dust monomers via collisional fragmentation. Our fragment model suggests that the total geometric cross section integrated over the fragments is estimated to be about the same order as the geometric cross section of the target.

Fractal Characteristics of the Seepage Erosion Process in Porous Soil

Seepage-induced erosion in porous soil has always been a major concern in the field of geofluids. Various fractal models have been built to theoretically investigate the porosity and permeability coefficient. However, the seepage erosion process (i.e., incubation, formation, evolution, and destruction) in porous soil is not clearly demonstrated to clarify the seepage fractal characteristics. In this paper, a series of hydraulic tests were performed to reveal the mass fractal characteristics of sandy gravels, coarse-grained sands, and fine-grained sands in the seepage erosion process. The results show that the mass fractal dimension was appropriate to describe the cumulative mass distribution of particles, the complexity of pore networks, and the dynamic changes of the seepage erosion process. Moreover, the scale-invariant interval, as an essential precondition for the accurate calculation of the mass fractal dimension, was to some extent affected by the average grain size and the fine content of porous soil. In particular, the changing trend of porosity and permeability coefficient with the mass fractal dimension was demonstrated in the seepage erosion process. Both porosity and permeability coefficients indicated an increasing trend as the development of seepage erosion. However, the mass fractal dimension gradually decreased due to the removal of fine particles induced by seepage flow water. Research findings will not only provide a new perspective on the seepage erosion mechanism but also predict the development of the seepage erosion process in engineering practice.

New Insights into the Drill Cutting Characteristics and Fault Distribution in Gas-Containing Coal Seams

This study is aimed at detecting small faults in coal seams. With coal seams of different buried depths in Luling Coal Mine, Yuenan Coal Mine, and Sihe Coal Mine with obvious difference in hardness and outburst hazards selected as the research objects, the morphological characteristics of a sample particle size such as the Rosin-Rammler distribution function, average particle size, cumulative mass distribution, and mechanical parameters such as particle strength and F value were statistically analyzed through drill cuttings related to sampling points at different positions of faults already known. The results show that the effect of tectonic stress reduces the strength and permeability of the coal after the borehole enters the fault damage zone, resulting in abnormal fluctuations in the morphological characteristics of the drill cuttings. Correspondingly, large-size particles account for a high percentage. The weight analysis discloses that the characteristic particle size of the Rosin-Rammler distribution function has the greatest influence on the determination of fault existence. The analysis of drill cutting characteristics conduces to detecting the distribution of small faults, helps to improve the utilization of mine information, and is of great significance for accident prevention and control.

Dynamic fragmentation in steel cylindrical shells

The paper describes an experimental study of the influence of the composition and mechanical properties (ultimate and yield strength, reduction of area, impact toughness, and the fraction of fibrous fracture) of brittle, quasi-brittle, and ductile steels on the parameters of dynamic fragmentation and fracture mechanisms. The experiment showed that simple exponential functions could be used to describe cumulative mass distributions of shell fragments from the materials under study. The exponent of these functions is the reciprocal characteristic mass (1/μ) and it decreases as the fraction of fibrous fracture of shell fragments increases. It serves as a dynamic fracture criterion that is sensitive to changes in the composition and mechanical properties of the material. The relations between the fragmentation parameter 1/μ and mechanical properties and composition of shell materials were obtained. Reaching the critical value of the fragmentation criterion (1/μc) leads to changing the fracture mechanism from “ductile” to “brittle” mode which arises in a material with ∼40% of fibrous fracture at the fracture surface of impact specimens and ∼50% of shear fracture of fragments.The authors studied the structure and features of ductile and brittle fracture surfaces of shell fragments, compared the statistical distributions widely used to describe the fragmentation process (Mott, Weibull, and Grady-Odintsov) and the dependencies of their parameters on material properties. The study did not reveal any advantages of the parameters of these distributions over the 1/μ parameter of the exponential function. The analysis of the literature data on the fragmentation of shells of different steels showed that they did not contradict the obtained results, and the usage of simple exponential distributions makes it possible to reveal the physical meaning of parameters of statistical distributions. Several common patterns of fragmentation of solids are discussed.

β2-adrenergic stimulation potentiates spontaneous calcium release by increasing signal mass and co-activation of ryanodine receptor clusters.

It is unknown how β-adrenergic stimulation affects calcium dynamics in individual RyR2 clusters and leads to the induction of spontaneous calcium waves. To address this, we analysed spontaneous calcium release events in green fluorescent protein (GFP)-tagged RyR2 clusters. Cardiomyocytes from mice with GFP-tagged RyR2 or human right atrial tissue were subjected to immunofluorescent labelling or confocal calcium imaging. Spontaneous calcium release from single RyR2 clusters induced 91.4%±2.0% of all calcium sparks while 8.0%±1.6% were caused by release from two neighbouring clusters. Sparks with two RyR2 clusters had 40% bigger amplitude, were 26% wider, and lasted 35% longer at half maximum. Consequently, the spark mass was larger in two- than one-cluster sparks with a median and interquartile range for the cumulative distribution of 15.7±20.1 vs 7.6±5.7 a.u. (P<.01). β2-adrenergic stimulation increased RyR2 phosphorylation at s2809 and s2815, tripled the fraction of two- and three-cluster sparks, and significantly increased the spark mass. Interestingly, the amplitude and mass of the calcium released from a RyR2 cluster were proportional to the SR calcium load, but the firing rate was not. The spark mass was also higher in 33 patients with atrial fibrillation than in 36 without (22.9±23.4 a.u. vs 10.7±10.9; P=.015). Most sparks are caused by activation of a single RyR2 cluster at baseline while β-adrenergic stimulation doubles the mass and the number of clusters per spark. This mimics the shift in the cumulative spark mass distribution observed in myocytes from patients with atrial fibrillation.

CFD simulation of tailings slurry thickening in a gravity thickener

In the present study, the thickening process of tailings slurry in a gravity thickener is modelled using Computational Fluid Dynamics (CFD), with a focus on the effects of particle size and feed velocity. A Two-Fluid Model (TFM) is employed to describe the particle-fluid and particle-particle interactions while turbulence is described by the ω-based Reynolds Stress Model (RSM). The validity of the model is demonstrated by close agreement between experimental measurement and simulation predictions of total solid mass of underflow, and particle cumulative mass distribution as a function of particle size in the underflow. The feedwell performance is evaluated in terms of kinetic energy dissipation and mixing performance. Particle size has a significant influence on the distribution of solid concentration. The increase of particle size leads to a higher critical settling height. For a given underflow discharging rate, solid concentration in the underflow increases with feed velocity only in a certain range, whereas increases continuously in the overflow. Large particle size corresponds to a higher critical feed velocity. Modelling the granular flow with a wide particle size distribution in a thickener helps explore the particle dynamic behaviors, thereby improving the thickening process.

Scaling laws in fragmentation dynamics of rock materials

Dynamic and quasi-static tests for uniaxial compression of cylinders made of quartzite were carried out. The failure of the specimens was accompanied by fractoluminescence. The fractoluminescence was recorded by a photomultiplier tube (PMT) and a high-speed camera. The high-speed camera allowed us to visualize fracture process accompanied with fractoluminescence and PMT provided high temporal resolution for statistical analysis of fracture. A statistical analysis of the mass distribution of quartzite fragments and a statistical analysis of the time intervals between pulses on the signals from the PMT are carried out. The cumulative fragments mass distributions for all samples had two slopes, which were described by power functions. The cumulative time distribution between pulses was also described by a power function, which corresponds to brittle fracture of the material.

Dynamic fragmentation of a Zr-based metallic glass under various impact velocities

The dynamic fragmentation of ZrCuNiAl bulk metallic glass (BMG) subjected to various impact velocities was investigated in argon atmosphere. The results demonstrated that the ZrCuNiAl metallic glass generated debris after impact. The cumulative mass distribution curves of ZrCuNiAl BMG samples after impact under various velocities were obtained; the results showed that the cumulative mass of BMG samples conforms to the Schuhmann power function distribution. The characteristic fragment size λ governing the fragment distributions was determined by fracture toughness and expansion strain rate. The results demonstrated that characteristic fragment size decreases with an increase in impact velocity, which was well described by the model. A relationship between the cumulative mass distribution and the impact velocity of Zr55Cu30Ni5Al10 alloy was obtained based on energy principles. This formula is feasible to predict the cumulative mass distribution of Zr55Cu30Ni5Al10 alloy after impact under a wide velocity range.

The molecular mass function of the local Universe

Aims. We construct the molecular mass function using the bivariate K-band-mass function (BMF) of the Herschel Reference Survey (HRS), which is a volume-limited sample that has already been widely studied at the entire electromagnetic spectrum. Methods. The molecular mass function was derived from the K-band and the gas mass cumulative distribution using a copula method, which is described in detail in our previous papers. Results. The H2 mass is relatively strongly correlated with the K-band luminosity because of the tight relation between the stellar mass and the molecular gas mass within the sample with a scatter, which is likely due to those galaxies which have lost their molecular content because of environmental effects or because of a larger gas consumption due to past star formation processes. The derived H2 MF samples the molecular mass range from ∼4 × 106 M⊙ to ∼1010 M⊙, and when compared with theoretical models, it agrees well with the theoretical predictions at the lower end of the mass values; whereas at masses larger than 1010 M⊙, the HRS sample may miss galaxies with a large content of molecular hydrogen and the outcomes are not conclusive. The value of the local density of the molecular gas mass inferred from our analysis is ∼1.5 × 107 M⊙ Mpc−3, and it is compared with the results at larger redshifts, confirming the lack of strong evolution for the molecular mass density between z = 0 and z = 4. Conclusions. This is the first molecular mass function that has been derived on a complete sample in the local Universe, which can be used as a reliable calibration at redshift z = 0 for models aiming to predict the evolution of the molecular mass density.

Structure of polytropic stars in General Relativity

The inner structure of a star or a primordial interstellar cloud is a major topic in classical and relativistic physics. The impact that General Relativistic principles have on this structure has been the subject of many research papers. In this paper we consider within the context of General Relativity a prototype model for this problem by assuming that a star consists of polytropic gas. To justify this assumption we observe that stars undergo thermodynamically irreversible processes and emit heat and radiation to their surroundings. Due to the emission of this energy it is worthwhile to consider an idealized model in which the gas is polytropic. To find interior solutions to the Einstein equations of General Relativity in this setting we derive a single equation for the cumulative mass distribution of the star and use Tolman-Oppenheimer-Volkoff equation to derive formulas for the isentropic index and coefficient. Using these formulas we present analytic and numerical solutions for the polytropic structure of self-gravitating stars and examine their stability. We prove also that when the thermodynamics of a star as represented by the isentropic index and coefficient is known, the corresponding matter density within the star is uniquely determined.

Gaseous Emissions and Particle Microstructure Characteristics of PODE/Diesel Blend Fuel

Polyoxymethylene dimethyl ethers (PODE) has good application prospects as an alternative to diesel fuel with a great potential to achieve clean combustion on diesel engines. In current study, the effects of PODE/diesel blends with PODE volume fraction at 10 %, 20 % and 30 % on performance and emission characteristics are investigated on a common-rail diesel engine under different engine loads. The particle size distribution and microstructure characteristics of the combustion particles are also analized. Results show that the PODE/diesel blends have shorter ignition delay, higher in-cylinder maximum burst pressure and advanced heat release. The brake thermal efficiency increases slightly with the increment of PODE blending ratio. There is a simultaneous improvement in CO, HC and soot emissions when fueling blend fuels. A more obvious shifting tendency toward the direction of small particle size can be found in number concentration, mass density and mass cumulative distribution of particles with increment of PODE. The microstructure of the blend fuels combustion particles is mainly in the form of agglomerates. Compared with diesel fuel, combustion particles of blend fuels have bigger layer spacing and microcrystalline curvature as well as smaller crystallite size, also the box dimension of the particles and the degree of agglomeration increase.

A new model to evaluate solar spectrum impacts on the short circuit current of solar photovoltaic modules

Solar spectrum plays an important role on electrical performance of PV modules via affecting their short circuit current. In this study, a new model combining the impacts of both air mass and diffuse solar radiation ratio is developed to evaluate the solar spectrum impacts on the short circuit current of photovoltaic (PV) modules. A new method, named air mass cumulative distribution function method (AMCDF), is introduced to represent the relationship between air mass and solar spectrum effect. The experimental data shows that when air mass is less than 4.5, the relationship between the normalized short-circuit current and the air mass cumulative distribution function can be well represented by a five-order polynomial. However, when air mass is larger than 4.5, the relationship becomes irregular. Further study on the irregular data indicates that the chaotic relationship is caused by the impact of diffuse solar radiation ratio (Rd). Based on these findings, the new model which combines the air mass cumulative distribution function and the diffuse solar radiation ratio is developed to evaluate the spectrum effect. Compared to conventional models, the proposed model has higher prediction accuracy and it also can predict short circuit current even when the air mass is high.

Estimation of Acid-Hydrolyzed Cellulose Fiber Size Distribution with Exponential and Rosin-Rammler (R-R) Laws

A new method was developed to characterize the cellulose fiber (hardwood dissolving pulp) size distribution after 50 wt% sulfuric acid hydrolysis at different hydrolysis temperatures with exponential and Rosin-Rammler (R-R) laws. The results show that the two above laws can be effective to explain the cellulose hydrolysis process. The exponential and the R-R laws were found to be well fitted to the sulfuric acid hydrolyzed cellulose fiber length distribution. The cumulative number distribution from Fiber Tester was shown to fit the exponential distribution well, while the cumulative mass distribution obtained from the acid hydrolysis was found to be suitable to the R-R law via an approximation process. The results from SEM analyses also supported the above conclusions. This approach can be used to characterize the cellulosic fiber properties before a further process of biorefinery, nanocellulose preparation, or other application of lignocellulosic fibers.

Dependence of pea root mass distribution on weather conditions under varying levels of phosphorus application

Abstract The aim of the study was to describe the distribution of pea root mass in the soil, over a three-year period, under varying weather conditions and at different levels of phosphorus application, by means of evaluating and comparing parameters of a mathematical model characterising cumulative root mass distribution. A two-factor experiment was conducted in Prusy, near Krakow: the first factor was the level of phosphorus application (0-70-140 kg P2O5 ha−1) and the second was the cultivars (six cultivars were tested). Experimental data produced using the model indicated that the root distribution was strongly differentiated by water availability in the years of the study. This appeared in some cases to be a more important factor than phosphorus application rates. The estimated soil depth at which 50% of the root mass was accumulated differed significantly for the dry and the wet year. In the wet year, only very high phosphorus application rates contributed to an increase in root mass distribution. The estimation of root mass distribution from the presented data can be used to improve phosphorus application depending on the amount of precipitation.

Experimental and Numerical Modeling of Aerosol Delivery for Preterm Infants

Respiratory distress syndrome (RDS) represents one of the major causes of mortality among preterm infants, and the best approach to treat it is an open research issue. The use of perfluorocarbons (PFC) along with non-invasive respiratory support techniques has proven the usefulness of PFC as a complementary substance to achieve a more homogeneous surfactant distribution. The aim of this work was to study the inhaled particles generated by means of an intracorporeal inhalation catheter, evaluating the size and mass distribution of different PFC aerosols. In this article, we discuss different experiments with the PFC perfluorodecalin (PFD) and FC75 with a driving pressure of 4–5 bar, evaluating properties such as the aerodynamic diameter (Da), since its value is directly linked to particle deposition in the lung. Furthermore, we develop a numerical model with computational fluid dynamics (CFD) techniques. The computational results showed an accurate prediction of the airflow axial velocity at different downstream positions when compared with the data gathered from the real experiments. The numerical validation of the cumulative mass distribution for PFD particles also confirmed a closer match with the experimental data measured at the optimal distance of 60 mm from the catheter tip. In the case of FC75, the cumulative mass fraction for particles above 10 µm was considerable higher with a driving pressure of 5 bar. These numerical models could be a helpful tool to assist parametric studies of new non-invasive devices for the treatment of RDS in preterm infants.