Theoretical calculation of uncertainty region for spherical particles based on a picket fence,quasi-monodisperse particles

In order to confirm the reliability of particle size measurement technique and to prepare standard reference particles for calibrating particle size measurement devices, experimental and theoretical studies have been conducted about the uncertainty region of particle size measurement for the picket fence and quasi mono-disperse particles. The vertical and horizontal uncertainty regions based on Tschebyscheff theory are calculated to the picket fence distribution composed of two kinds of nearly mono-disperse particles. The uncertainty region increases around the intermediate particle diameters between the two kinds of particles.Because the original particle size distribution is nearly mono-disperse, the uncertainty regions around the minimum and maximum particle diameter are small compared to the intermediate particle diameters between the two kinds of particles.The uncertainty region in vertical and horizontal direction changes to decrease with the increase of sample size. For the picket fence distribution composed of two kinds of nearly mono-disperse particles, the sample size about more than 10,000 is necessary to obtain the reliable results in particle size counting process.     

Particle size measurement of standard reference particle candidates and theoretical estimation of uncertainty region

In order to confirm reliable particle size measurement technique and to prepare standard reference particles for calibrating particle size measurement devices, experimental and theoretical studies have been conducted about particle size measurement of 0.1–1 μm silica particles. The microscopic method with sample size greater than 90,000 particles was conducted for the size measurement.Theoretical equation of uncertainty region over all particle diameter range is newly proposed and compared with computer simulation. Previous paper [H. Masuda, K. Iinoya, Theoretical study of the scatter of experimental data due to particle size distribution, J. Chem. Eng. 4(1) (1971) 60–67] reported the uncertainty region only for mass median diameter, but this paper presents the uncertainty region for all particle size range. The uncertainty region increases with the increase in particle diameter and also increases as the sample size decreases. Theoretical uncertainty region agreed with the results of computer simulation.     

Particle size measurement of standard reference particle candidates with improved size measurement devices

In order to prepare standard reference particles, experimental and theoretical studies have been conducted on particle size measurement of two kinds of spherical glass beads. The sheath flow- type electrical sensing zone method and the revised sedimentation balance method were used for the measurement. The data were compared with those obtained by the microscopic method with a sample size greater than 10 000. The particle size distributions obtained by use of the sheath flow- type electrical sensing zone method and microscopic method are nearly equal for the two kinds of glass beads. However, deviations of less than 5% were observed between the improved sedimentation balance and microscopic methods. The experimental data of the microscopic method are within the 95% reliability region of the sheath flow-type electrical sensing zone method.     

由 Mie 散射光强反演颗粒粒度分布的一种改进正则化法

基于Mie散射的激光粒度仪广泛地应用在颗粒粒度测量中,其中由光强分布演算出粒度分布的计算方法一直是关注的热点。此反演问题属于第一类Fredholm算子方程,具有不适定性,难以得出准确的稳定解,需要用高效的数值算法。本文提出一种应用于该类仪器颗粒粒度分布反演问题的改进正则化法,采用广义交叉验证法(GCV)来选择正则参数,并引入松弛技术,将迭代值加工成一种松弛值以改善精度,得出了稳定的正则拟解(近似解)。经标准颗粒的验证和计算机模拟证实,此算法是可行和有效的。     

An application of bootstrap method for analysis of particle size distribution

The Bootstrap method, which is used widely in statistics, is a very powerful method that can be applied to the analysis of particle size distribution. For a number based measurement, this method can estimate the statistic uncertainty or confidence interval for any statistical quantities of interest from the distribution, with very simple protocol and without any parametric assumptions. This paper gives a demonstration to introduce the method to the community of particle size analysis.     

Estimation of uncertainty of percentile values in particle size distribution analysis as a function of number of particles

In the analysis of particle size distribution (PSD), evaluation of the uncertainty of the percentile values is often required. Both theoretical and data processing methods are applicable to estimate standard deviations of percentile values. In this paper, a theory, applicable both in paramedic and non-parametric ways, is introduced. As a practical example, theoretical results based on a lognormal distribution are compared to those obtained by bootstrap method. Excellent agreement is demonstrated between the theory and the direct data processing method.     

Particle shape effects on particle size measurement for crushed waste glass

Recently, narrow particle size distributions, as measured by sieve analysis, of crushed waste glass were used as a replacement for Portland cement in concrete. Their chemical reactivity was successfully studied as a function of this measure of particle size. Differences between sieve analysis and laser diffraction measures of particle size prompted this current re-analysis. Extremely careful sieving was used to divide the crushed waste glass particles into 0–25 μm, 25–38 μm, and 63–75 μm sieve size ranges, but laser diffraction did not agree with these particle size cutoffs. We use these same materials to try and understand the discrepancies between particle size as measured by laser diffraction and sieve analysis by using X-ray computed tomography followed by spherical harmonic analysis to measure the three-dimensional particle shape and size, as well as the length (L), width (W), and thickness (T) of each particle. We show how laser diffraction and X-ray CT results, along with sieve analyses, can be quantitatively related for these crushed waste glass particles in the approximate size ranges considered. In contrast to previous speculation, the particle width W does not have to correspond closely to the sieve opening – the correspondence depends on overall particle shape. In addition, we demonstrate how many particles are needed to analyze in order to achieve stable averages and distributions of the L/W, W/T, and L/T aspect ratios, which approximately define particle shape. These results have implications for how particle size is measured and interpreted in the cement and concrete and other industries.     

Theoretical calculation of uncertainty region based on the general size distribution in the preparation of standard reference particles for particle size measurement

In order to confirm the reliability of particle size measurement technique and to prepare standard reference particles for calibrating particle size measurement devices, experimental and theoretical studies have been conducted about the uncertainty region of particle size measurement for the general particle size distribution. A new theoretical equation to calculate fundamental uncertainty region in the case that the maximum and minimum particle sizes are known, is derived based on Tschebyscheff theory. The uncertainty regions calculated based on the proposed method are applied to poly-disperse particles and a picket-fence distribution composed of two kinds of nearly mono-disperse particles.For the poly-disperse particles, the uncertainty region increases with the increase in particle diameter. For the picket-fence distribution composed of two kinds of nearly mono-disperse particles, the uncertainty region increases around the intermediate particle diameters between the two kinds of particles.Numerical simulation of uncertainty region for the picket-fence distribution has also been carried out. The uncertainty region decreases with the increase in sample size or the decrease in geometric standard deviation.     

Effect of particle size distribution on flowability of granulated lactose

The flowability of powders used in tableting significantly affects tablet weight and content uniformity of active pharmaceutical ingredients. Use of granulated materials instead of powdered materials can improve flowability. In this study, the effect of particle size distribution on flowability of granulated lactose was quantitatively analyzed. Three types of granulated lactose were classified into progressively narrower size fractions, and nine samples were systematically prepared. The mass median diameters were nearly constant (i.e., 130.5 ± 13.5 μm) and the geometric standard deviations ranged from 1.29 to 2.04. Two flow properties (angle of repose and compressibility) were measured. The correlations between flow properties and the particle size distributions were analyzed, and the coefficients of determination were obtained for different particle diameters and cumulative mass fractions. The optimal conditions to maximize the coefficients of determination were defined. Furthermore, static and dynamic friction properties were evaluated, and their correlations with particle size distribution were calculated.     

Inline method of droplet and particle size distribution analysis in dilute disperse systems

In the present article a measurement method of particle size distributions (PSD) in industrial installations which use a dispersed phase of low concentration (like spray dryers or spray scrubbers) is introduced. A new type of inline-measurement system has been developed and designed to work in spray drying conditions. A standard digital camera is used to record shadows of flowing particles inside the spray drying chamber. Collected images were analyzed by a newly developed software which recognizes particles only in the focus area and eliminates several types of artifacts. The constructed prototype of the PSD inline-analyzer was installed and used to monitor large laboratory scale spray dryer. All data collected by the designed system during the spray drying experiments were compared with data measured with an offline reference system to show accuracy of the new measurement technique.     

Effects of particle size and distribution on the mechanical properties of SiC reinforced Al-Cu alloy composites

This paper studied the combined effects of particle size and distribution on the mechanical properties of the SiC particle reinforced Al-Cu alloy composites. It has been shown that small ratio between matrix/reinforcement particle sizes resulted in more uniform distribution of the SiC particles in the matrix. The SiC particles distributed more uniformly in the matrix with increasing in mixing time. It has also been shown that homogenous distribution of the SiC particles resulted in higher yield strength, ultimate tensile strength and elongation. Yield strength and ultimate tensile strength of the composite reinforced by 4.7 μm sized SiC particles are higher than those of composite reinforced by 77 μm sized SiC particles, while the elongation shows opposite trend with yield strength and ultimate tensile strength. Fracture surface observations showed that the dominant fracture mechanism of the composites with small SiC particle size (4.7 μm) is ductile fracture of the matrix, accompanied by the “pull-out” of the particles from the matrix, while the dominant fracture mechanism of the composites with large SiC particle size (77 μm) is ductile fracture of the matrix, accompanied by the SiC particle fracture.     

高分子量PAN的粒径分布与均匀度关系的考察

对高性能碳纤维原丝性能有重要影响的聚合物粒径均匀度问题目前尚未有人研究过。本研究率先采用沉淀聚合合成高分子量PAN,根据其微观形貌,应用第四统计力学群子统计参数理论研究了聚合物的粒径分布与粒径均匀度的关系,表明粒径均匀度与混合溶剂无关,而与混合溶剂的配比有关,DMSO含量越少,粒径分布越均匀。     

颗粒粒度分布对树脂基磁致伸缩复合材料性能的影响

已有研究在Terfenol-D颗粒粒径及粒度分布对树脂基磁致伸缩复合材料性能的影响规律上存在分歧。本文中以Terfenol-D为磁致伸缩颗粒,以不饱和聚酯树脂为基体,采用5 种窄分布颗粒(30～53μm、53～150μm、150～300μm、300～450μm、450～500μm)和1种宽分布颗粒(30～500μm)制备颗粒体积分数为20 %的磁致伸缩复合材料,并测试其动静态磁致伸缩系数、磁机械耦合系数、弹性模量及抗压强度等性能参数。在窄分布颗粒制备的试样中,以53～150μm制备的复合材料的磁致伸缩性能最佳;而采用宽分布颗粒制备的试样其性能优于窄分布颗粒制备的试样。该结果表明,增大颗粒粒径同时具有积极作用与消极作用, 其对复合材料磁致伸缩性能的影响取决于哪一个居主导地位。      

Influence of controlled particle size on pore size distribution and mechanical resistance of agarose beads for bioadsorption application

ABSTRACT

In this work the influence of fabrication conditions (ion strength, surfactant utilization) on the macro- (particle size distribution, PSD) and microscopic [pore size distribution (PoSD), specific surface area] structure of agarose beads was investigated. The main purpose was achieving uniform sized and porous beads with improved mechanical strength for bioseparation and chromatography applications. Therefore, PSD, PoSD, mechanical resistance, and flux through packed bed of the fabricated beads (4, 6, and 8% wt/wt) were analyzed. Based on porosimetry results, it was found that increasing ion concentration or presence of surfactant (the key variable for narrowing PSD) decreases the span value of PSD (p-value <0.05); thus, leading to a more uniform distribution. Moreover, as a result of controlling PSD, the PoSD changes from micro- to meso- and macropores in higher ion charged solutions. Furthermore, the obtained PoSD affects mechanical resistance of the prepared microspheres either as single beads or packed in a column. Mesoporous 6%-agarose beads showed the highest flux due to elevated mechanical resistance and elastic characteristic. Mesoporous 4%-beads showed the highest elasticity, and thus lower flux through column. These results demonstrate that manipulation of both macro- and microscopic characteristics of the beads should be commensurate with the intended application i.e., bioadsorption chromatography.     

Combining kernel matrix optimization and regularization to improve particle size distribution retrieval

A new method combining Tikhonov regularization and kernel matrix optimization by multi-wavelength incidence is proposed for retrieving particle size distribution (PSD) in an independent model with improved accuracy and stability. In comparison to individual regularization or multi-wavelength least squares, the proposed method exhibited better anti-noise capability, higher accuracy and stability. While standard regularization typically makes use of the unit matrix, it is not universal for different PSDs, particularly for Junge distributions. Thus, a suitable regularization matrix was chosen by numerical simulation, with the second-order differential matrix found to be appropriate for most PSD types.     

Particle size induced heterogeneity in compacted powders: Effect of large particles

We investigated the effect of particle size distribution on heterogeneity of compacted powders. We used experiments and discrete particle based simulations to compact powders, test the mechanical strength of the compact, and study the microstructure of the compact. A metallic powder which has a wide particle size distribution was used in the experiments. We found that the compaction profile is not reproducible when particles larger than 1/6 of the die diameter are present in the powder sample. The presence of these large particles generate a highly heterogeneous inter-particle contact and bonding forces. The discrete particle simulations showed that for these heterogeneous compacts the tensile strength exhibits high variability, even for one compact if the diametrical compression force is applied along different axes. Based on these results, it is recommend that the largest particle in a powder compact should not exceed one sixth of the die diameter, which is the same as the recommendation of ASTM International D4767 - 11 for compression test of cohesive soils.     

激光粒度仪颗粒联测的结果与评价

为了解不同激光粒度仪的硬件、软件等方面差异对粒度测量结果的影响,用4种颗粒形状不同的粉末在不同公司生产的激光粒度仪上进行测试。结果表明:激光粒度仪测试结果重复性很好;对于球形粉末和形状较规则的粉末,大部分激光粒度仪测得的中位径值之间可以比较;而粒径范围较宽和不规则形状粉末,个别仪器测量的中位径值有差异。     

Study of particle size distribution of pulverized coals in utility boilers

Particle size distribution (PSD) is a measurement in the energy industry and provides information about the range and width of distribution of particle sizes. PSD function is widely used to characterize dispersed systems like powders and droplets and finds immense applications in coal and related processing. In the present work, pulverized coal samples were analyzed from the perspective of their PSD. Three coal samples were crushed and ground using ball mill, and the obtained pulverized coal samples were then tested for their morphological characteristics and chemical composition using scanning electron microscopy (SEM) and energy dispersive spectroscopy (EDS), respectively. The coal samples were then sieved mechanically to obtain the PSD curves. Two mathematical models, viz Rosin-Rammler (RR) and Gates-Gaudin-Schuhmann (GGS), were used and compared for the estimation of the distribution function F(d) (mass fraction) for the data obtained from the PSD curves. The RR model provided splendid results when it is applied on the data procured from PSD curves of coal samples, leading to more accurate segregation of divergent particle sizes.     

Effect of particle size distribution on hydrodynamics of pneumatic conveying system based on CPFD simulation

The effect of particle size distribution on the hydrodynamics of dilute-phase pneumatic conveying system was analyzed using computational particle fluid dynamics (CPFD) simulation. The influence of a simulation parameter, i.e., correction factor of drag coefficient (k), on the hydrodynamics of pneumatic conveying system was determined via CPFD simulation. When results of simulation were compared with experimental data of previous studies, the average error of pressure drop per length predicted by the CPFD approach with the correction factor was below 4.4%. Saltation velocity and the pressure drop per unit length declined as the drag force coefficient increased. Simulation results also revealed that the pressure drop per length and the saltation velocity were decreased when the fine powder fraction in the particle size distribution was increased, although the width of particle size distribution was widened, and the standard deviation was increased. Finally, the Relative Standard Deviation (RSD) of pressure drop per length was measured and compared with median diameter (d₅₀), Sauter mean diameter, geometric mean diameter, and arithmetic mean diameter. The RSD of the Sauter mean diameter was 5.8%, approximately twice less than the RSD value of d₅₀ commonly used in pneumatic conveying.     

The control of particle size distribution for fabricated alumina nanoparticles using a thermophoretic separator

Control of the particle size distribution of fabricated alumina nanoparticles from general alumina powder with a large geometric standard deviation (GSD) was studied. A thermophoretic separator was used to control the GSD of the nanoparticles, and unevaporated and primary particles were separated to yield a small GSD. The fabricated nanoparticles were characterized by field emission scanning electron microscopy (FESEM) and a scanning mobility particle sizer (SMPS). We confirmed that the GSD of the nanoparticles was controlled by the thermophoretic separator. A temperature difference between 79 K and 151 K was applied to the thermophoretic separator for control of the nanoparticle GSD. The GSD of the fabricated alumina nanoparticles was improved from 1.74 to 1.44.