Measurement of size and shape distributions of particles through image analysis

The size and shape of particles can be described using a 2D particle size distribution (PSD) where two characteristic lengths define each particle in the population. The determination of 2D PSDs based on microscopic pictures of particles in suspension is studied. The experimental data are represented as an axis length distribution (ALD) that can be extracted from a series of microscopic pictures by a fully automated image analysis. The problem of finding the underlying bi-dimensional PSD is stated as an optimization problem. For the solution a genetic algorithm is used. The approach is tested on simulated ALDs, as well as on an experimentally measured ALD obtained from carbon fiber particles.     

Measurement of size-dependent dynamic shape factors of quartz particles in two flow regimes

Understanding and modeling the behavior of quartz dust particles, commonly found in the atmosphere, requires knowledge of many relevant particle properties, including particle shape. This study uses a single particle mass spectrometer, a differential mobility analyzer, and an aerosol particle mass analyzer to measure quartz aerosol particles mobility (d_m), vacuum aerodynamic, and volume equivalent diameters, mass, composition, effective density, and dynamic shape factor as a function of particle size, in both the free molecular and transition flow regimes. The results clearly demonstrate that dynamic shape factors can vary significantly as a function of particle size. For the quartz samples studied here, the dynamic shape factors increase with size, indicating that larger particles are significantly more aspherical than smaller particles. In addition, dynamic shape factors measured in the free-molecular (χ_v) and transition (χ_t) flow regimes can be significantly different, and these differences vary with the size of the quartz particles. For quartz, χ_v of small (d_m < 200 nm) particles is 1.25, while χ_v of larger particles (d_m ～ 440 nm) is 1.6, with a continuously increasing trend with particle size. In contrast, χ_t of small particles starts at 1.1 increasing slowly to 1.34 for 550 nm diameter particles. The multidimensional particle characterization approach used here goes beyond determination of average properties for each size, to provide additional information about how the particle dynamic shape factor may vary even for particles with the same mass and volume equivalent diameter.

© 2016 American Association for Aerosol Research     

Radial mixing of particles in a dry batch ball mill

Poor mixing in dry ball mills can lead to insufficient presentation of fine particles to the classifying air, overgrinding of particles and wastage of energy in a ball mill. A video capture method has been used to study radial mixing kinetics in a dry batch ball mill. Experiments were conducted in a ball mill with PVC plastic powders being used as particles so that the effect of size reduction could be neglected. Radial mixing in ball mills was studied at typical industrial speeds of 75%, 80% and 90% of critical. The rate of particle mixing was observed to increase with increasing mill speed. A simplified mathematical model is presented that can be used to predict the radial mixing of particles in a ball mill. A parameter, k, was used to quantify the kinetics of mixing as affected by the mill's speed.     

Size analysis of particles of irregular shape from their acoustic emissions

A method developed by the authors for determining average size and for characterizing the size distribution of spherical particles from their acoustic emissions has been extended to include particles of irregular shape. The method seems to be applicable to a large variety of materials over a wide range of sizes from several cm down to approximately 50 μm. It is thought that this method should be especially useful in continuous monitoring of crushing and blending processes.     

The shape of particles produced by comminution. A review

In this paper the literature on the shape of particles produced by comminution is reviewed. There is some agreement amongst workers as to the shapes which are produced by comminution machinery. However, the subject does not have a sound scientific foundation and authors disagree as to the importance of different factors. This ought to be remedied in view of the growing realisation of the importance of particle shape in controlling powder behaviour.     

Measurement of particle size and shape by FBRM and in situ microscopy

In this work a model is defined allowing for a rapid calculation of chord length distributions as well as the prediction of in situ microscopy data. Both calculations are done using the same underlying algorithm. The model assumes convex polyhedral particles that are defined by their vertices only, connected by straight lines, but imposes no further restrictions on particle geometry. Due to its speed, the model can easily be used for the prediction of experimental data from in situ monitoring tools based on whole particle populations, also with non-constant shape. The model has been verified using in situ microscopy to characterize a population of disc shaped particles.The applications of the model are focused on crystallization processes, but are not limited to these. Several relations between data measured by in situ instruments and the underlying multidimensional particle size distribution have been derived. The model is used extensively in a method that is presented allowing for the calculation of bidimensional growth rates from Focused Beam Reflectance Measurement or in situ microscopy measurements.     

Particle shape and orientation in laser diffraction and static image analysis size distribution analysis of micrometer sized rectangular particles

Laser diffraction (LD) and static image analysis (SIA) of rectangular particles [United States Pharmacopeia, USP30-NF25, General Chapter <776>, Optical Miroscopy.] have been systematically studied. To rule out sample dispersion and particle orientation as the root cause of differences in size distribution profiles, we immobilize powder samples on a glass plate by means of a dry disperser. For a defined region of the glass plate, we measure the diffraction pattern as induced by the dispersed particles, and the 2D dimensions of the individual particles using LD and optical microscopy, respectively. We demonstrate a correlation between LD and SIA, with the scattering intensity of the individual particles as the dominant factor. In theory, the scattering intensity is related to the square of the projected area of both spherical and rectangular particles. In traditional LD the size distribution profile is dominated by the maximum projected area of the particles (A). The diffraction diameters of a rectangular particle with length L and breadth B as measured by the LD instrument approximately correspond to spheres of diameter Ø_L and Ø_B respectively. Differences in the scattering intensity between spherical and rectangular particles suggest that the contribution made to the overall LD volume probability distribution by each rectangular particle is proportional to A²/L and A²/B. Accordingly, for rectangular particles the scattering intensity weighted diffraction diameter (SIWDD) explains an overestimation of their shortest dimension and an underestimation of their longest dimension. This study analyzes various samples of particles whose length ranges from approximately 10 to 1000 μm. The correlation we demonstrate between LD and SIA can be used to improve validation of LD methods based on SIA data for a variety of pharmaceutical powders all with a different rectangular particle size and shape.     

Application of grinding kinetics analysis of inorganic powders by a stirred ball mill

The need for ultra fine particles has been increasing in the preparation field of raw powders such as fine ceramics and high functional products. A series of wet grinding experiments were carried out on inorganic powders such as calcite, pyrophyllite and talc by a stirred ball mill. The grinding rate constant K’ in the equation of grinding kinetics was examined based on the grinding kinetics analysis as the same type of function of a previous paper on a vertical type planetary ball mill. The experimental particle size distribution of the ground products was obtained in various grinding conditions. The grinding rate constants K and K’ were expressed by empirical equation involving experimental conditions by a stirred ball mill. The empirical equation on the grinding rate constant was expressed in terms of a function involving the ball diameter of grinding balls, the median diameter of feed material, and Bond’s work index of material, in the experimental conditions. The values of empirical constants C1 and C₂ were 21.13 and 0.0109 on K, while C₁ and C₂ were 120.99 and 0.0192 on K′, respectively. And the particle size distribution of ground products of each test material for a given grinding time was found to be expressing the selection function (the specific rate of breakage) which was obtained from the grinding kinetics analysis. In this study, the grinding rate change on calcite and pyrophyllite was similar at the same experimental operation condition. However, in the case of talc, it was observed that the grinding rate was not increased compared with other samples.     

Experimental and numerical analysis of a lab-scale fluid energy mill

This study investigates the grinding performance of Fluid Energy Mill (FEM) through experimental studying and numerical simulation. The experimental parametric study shows that the mean product particle size decreases with grinding pressure (GP) and increases with the solid feed rate (SFR). In comparison, the influence of the feed pressure (FP) on the product size is much less significant. Visualization study indicates the existence of a particle-concentrated layer near the peripheral wall region, named the grinding region in this article since most of the collision-induced size reduction occurred in this region. The grinding air streams re-orient the particles, facilitating particle-particle and particle-wall collisions downstream in the grinding region. To understand the influence of the particle-wall collision, the peripheral wall of FEM was coated with a foam film in some experiments. The particle-wall collision was found to play a significant role in size reduction, especially under low air pressure.The gas flow inside the grinding chamber was simulated as the initial step to the ongoing 2-phase flow simulation of the milling process in the FEM. The simulation results show that eddies are formed at the feed air entrance, which explains the tendency of fine particle deposition in this region. The simulation results also suggest a strong relationship between the GP and the mean gas velocity in the grinding region.     

灭蚊窗涂剂的毛细管柱气相色谱分析

介绍了用AT-101毛细管柱，以邻苯二甲酸二正戊酯为内标，对灭蚊窗涂剂中3种有效成分残杀威、氯菊酯、氯氰菊酯同柱同条件下定量分析的方法。该方法的分析时间短，准确度、精密度高，重现性好。     

影响聚氯乙烯树脂颗粒形态的因素

介绍了搅拌、分散剂、转化率、聚合温度水油比对聚氯乙烯树脂颗粒形态的影响,提出了保证合适的树脂质量及形态的控制工艺条件和参数。     

Drag of non-spherical solid particles of regular and irregular shape

The drag of a non-spherical particle was reviewed and investigated for a variety of shapes (regular and irregular) and particle Reynolds numbers (Re_p). Point-force models for the trajectory-averaged drag were discussed for both the Stokes regime (Re_p ? 1) and Newton regime (Re_p ? 1 and sub-critical with approximately constant drag coefficient) for a particular particle shape. While exact solutions were often available for the Stokes regime, the Newton regime depended on: aspect ratio for spheroidal particles, surface area ratio for other regularly-shaped particles, and min-med-max area for irregularly shaped particles. The combination of the Stokes and Newton regimes were well integrated using a general method by Ganser (developed for isometric shapes and disks). In particular, a modified Clift-Gauvin expression was developed for particles with approximately cylindrical cross-sections relative to the flow, e.g. rods, prolate spheroids, and oblate spheroids with near-unity aspect ratios. However, particles with non-circular cross-sections exhibited a weaker dependence on Reynolds number, which is attributed to the more rapid transition to flow separation and turbulent boundary layer conditions. Their drag coefficient behavior was better represented by a modified Dallavalle drag model, by again integrating the Stokes and Newton regimes. This paper first discusses spherical particle drag and classification of particle shapes, followed by the main body which discusses drag in Stokes and Newton regimes and then combines these results for the intermediate regimes.     

不同熟料对筛分磨产量的影响及配球措施

我公司有１台Φ３m×１１m筛分磨，一仓长２．７５m，二仓长２．００m，三仓长５．５０m。在生产过程中发现不同的熟料对筛分磨产量影响很大，最高时达４０t／h，最低仅２０t／h。本文根据我公司对不同熟料的特点进行分析，找出规律，采用不同的研磨体级配来消除熟料对磨机产量的影响，以供参考。１熟料的特点我公司有１０００t／d窑外分解窑生产线１条和机立窑５台，熟料品种多，优劣程度有一定的波动，根据熟料外观、理化性能及对筛分磨产量的影响程度，可分成４种：A类表示优质回转窑熟料，B类表示较差的回转窑熟料，C和D类分别表示优…     

Drag coefficient and settling velocity for particles of cylindrical shape

Solid particles of cylindrical shape play a significant role in many separations processes. Explicit equations for the drag coefficient and the terminal velocity of free-falling cylindrical particles have been developed in this work. The developed equations are based on available experimental data for falling cylindrical particles in all flow regimes. The aspect ratio (i.e., length-over-diameter ratio) has been used to account for the particle shape. Comparisons with correlations proposed by other researchers using different parameters to account for the geometry are presented. Good agreement is found for small aspect ratios, and increasing differences appear when the aspect ratio increases. The aspect ratio of cylindrical particles satisfactorily accounts for the geometrical influence on fluid flow of settling particles.     

The identification of particles using diagrams and distributions of shape indices

Using five kinds of real powder paricles, we obtained their shape indices from their pictures, attempted to identify the powder particles morphologically and studied the distribution functions of particle shapes and their relationships. The results were indicated as the follwing.It is possible to identify powder particles on the diagrams of the shape indices. The distributions of the shape indices are expressed by some distribution functions. The sample material and the particle size of sample particles affect the distribution of the shape indices in a different way. The distributions of two characteristic diameters and the distribution of shape index defined by ratio of these diameters are accurately connected by an equation.