Particle Size Analysis: A comparative study of various methods

The particle size distribution of component materials can be important parameter governing the proper function of many industrial products. At present, accurate determination of particle size by currently available methods is difficult for both theoretical and practical reasons. In this paper, some elementary notions regarding particle sizing are reviewed as is the relative performance of commercially available particle sizing instrumentation which could be used for particle size analysis of dry powders. Our results indicate that various particle size instruments yield significantly (even vastly) different particle size distributions for the same material. Without great care on the part of the investigator, the results obtained from any given instrument may not accurately describe the powder in question and thus may cause incorrect technical recommendations. The use of Fraunhofer diffraction instruments on samples containing irregularly shaped small ( < 10 μm) particles of low refractive index requires considerable caution.     

Determination of Particle Size Distribution by Laser Diffraction of Doped‐CeO2 Powder Suspensions: Effect of Suspension Stability and Sonication

The particle size distributions (PSDs) of metal oxide powders are often determined by analyzing suspensions of powders using laser diffraction (e.g. Malvern MasterSizer 2000). Particle agglomeration can effectively bias the resulting distribution towards “unrealistic” particle sizes. Solutions to avoid this problem must be found if a particle distribution based on the elemental or primary particle sizes is desired. In this work, the particle size distribution of doped‐CeO₂ powders was studied. These powders show a crystalline single phase structure of controlled stoichiometry as determined by X‐ray diffraction and ICP analysis. The apparent size distribution was found to be a strong function of suspension stability. Dispersant agents (PBTCA and phosphonoacetic acid) and suspension pH affected stability as characterized by zeta potential measurements. Sonication of the suspensions further enhanced particle de‐agglomeration. Finally, only the combined effect of a dispersant agent, pH adjustment of the suspension and sonication provided a primary particle size distribution. The results presented in this work can be used in the analysis of similar ceramic powders in which strong particle agglomeration is present.     

Shape Estimation of Anisometric Particles Using Size Measurement Techniques

This study was conducted to establish a simple method for evaluating the morphology of fine anisometric particles using size measurement techniques. The size distributions of mica particles and carbon fibers classified into narrower size ranges were measured by gravitational sedimentation and laser diffraction techniques. The ratio of mean diameters determined for flaky particles strongly depended on the aspect ratio, i.e. flatness. The relationship between particle shape and diameter is discussed theoretically. The experimental results were similar to those predicted. The flatness of fine particles can be evaluated by the ratio of the median diameter determined by laser diffraction to that determined by sedimentation.     

Improving the accuracy of laser particle sizer with Mie scattering theory

Using the classical Mie scattering theory and Fraunhofer diffraction theory,adetailed analysis of the differences of the light energy distribution falling on the multi-elementconcentric photo-detector of a diffraction based laser particle sizer is given.Numerical calcula-tions and computer simulation are carried out. Experimental studies are also made with latexspheres as Standard Reference Material.Our research shows that when the classical Mie scat-tering theory is used,the accuracy of the particle sizer can be essentially improved not only inthe small size range,but also for large paticles.At the same time the time needed for data re-duction in both cases is almost the same.     

Modeling of Multiple Scattering Effects in Fraunhofer Diffraction Particle Size Analysis

A model for the direct problem of calculating the forward scattering signature of a multiple scattering medium is presented. The new formulation is optimized for integration into schemes for reconstructing the particle size distribution from laser diffraction (forward scattering) signatures obtained from optically thick media. The analysis is valid for media where the particle sizes and interparticle spacings are large (relative to the wavelength and the particle size, respectively) such that Fraunhofer diffraction theory adequately describes the properties of the forward scattered light from individual scattering events. The simulated performance of laser diffraction particle sizing instruments was then studied using predictions of the scattered light signatures which would be measured by laser diffraction instrument under multiple scattering conditions. The results were compared with experimental data and theoretical calculations based on other models.     

Simultaneous Measurement of Particle Size and Particle Velocity by the Spatial Filtering Technique

The objective of this study was to compare the measuring results of a fiber‐optical probe based on a modified spatial filtering technique with given size distributions of different test powders and also with particle velocity values of laser Doppler measurements. Fiber‐optical spatial filtering velocimetry was modified by fiber‐optical spot scanning in order to determine simultaneously the size and the velocity of particles. The fiber‐optical probe system can be used as an in‐line measuring device for sizing of particles in different technical applications. Spherical test particles were narrow‐sized glass beads in the range 30–100 μm and irregularly shaped test particles were limestone particles in the range 10–600 μm. Particles were dispersed by a brush disperser and the measurements were carried out at a fixed position in a free particle‐laden air stream. Owing to the measurement of chord lengths and to the influence of diffraction and divergent angle, the probe results show differences from the given test particle sizes. Owing to the particle‐probe collisions, the mean velocity determined by the probe is smaller than the laser Doppler mean velocity.     

米氏理论的近似及在粒度测量中的应用

将夫琅禾费衍射理论与几何散射 (包括折射和反射 )相结合 ,给出平行光入射下圆形颗粒在前向大角度范围内的散射光强分布近似算法。由于考虑了衍射、折射和反射相互间的干涉效应和颗粒对光的吸收性 ,对于正常或非正常衍射状态下无因次参量α≥ 40的耗散颗粒 ,在前向 0°～ 60°散射之内 ,该方法对散射光强计算结果与米氏理论结果是吻合的。由于计算速度比米氏理论快 ,有效角度范围比夫琅禾费衍射理论宽 ,因而适合于大颗粒的前向光强计算。将这一计算方法应用到大角度采光时的激光粒度测量实验中 ,收到了良好的效果     

In-Line Particle Size Determination for Jet Agglomeration Processes

In jet agglomeration plants, powders are agglomerated to obtain good instant properties. The free-falling initial material is wetted in a spray cone by droplets or in a steam jet by condensation at the particle surface. In a subsequent region of high particle concentration, collision between particles occurs and agglomerates form, if the forces of adhesion are strong enough. A commercial measurement device, working according to the principle of Fraunhofer diffraction, was modified for in-line application. It was used to measure particle size distributions and concentrations of solid particles and droplets in jets. A model is presented to calculate local particle sizes by means of mass balances from integral measurements over large volumes. The results of in-line particle size and agglomerate size analyses show the practical importance of dry agglomeration during transport and lead to a better understanding of the subsequent wet agglomeration process.     

Effect of Particle Size and Specific Surface Area on the Determination of the Density of Nanocrystalline Silver Sulfide Ag<Subscript>2</Subscript>S Powders

The effect of the particle size and specific surface area of silver sulfide powders on their density measured by the helium pycnometry method has been studied. Powders with different average particle sizes have been synthesized by hydrochemical deposition. The particle size of the silver sulfide powders has been determined by the Brunauer–Emmett–Teller method according to molecular nitrogen adsorption isotherms and, in the case of fine powders, by X-ray diffraction analysis according to diffraction reflection broadening. It has been shown that the density of the fine powders measured by helium pycnometry is underestimated compared with the true density, owing to the adsorption of helium by the highly developed surface of these powders.     

Determination of the Refractive Index of Water‐dispersible Granules for Use in Laser Diffraction Experiments

Modern laser light scattering equipment can cover a very broad particle size range by using complex algorithms, such as the Mie theory. A disadvantage of this theory, however, is that it requires the knowledge of the refractive index of the particles, which is not straightforward for powdered organic substances. In this study, thiram, a common dithiocarbamate fungicide, was used as a model compound. In a first part, a method was elaborated to determine the refractive index, based on refractive index measurements of solutions of the compound of interest in a range of solvents. Two different extrapolation techniques were compared. Both techniques were validated by applying them to the determination of the refractive indices of poly(vinyl acetate) and poly(methyl methacrylate). Secondly, the influence of the refractive index value on the generated particle size distribution in the laser diffraction software was investigated. It was observed that widely different particle size distributions can be generated by the laser diffraction software for a single experimental data‐set. Therefore, accurate refractive index information is required to obtain reliable particle size distribution results.     

Integral light-scattering indicatrix of optically soft spherical particles

The dependences of the angular distribution of the scattered energy on the particle size and refractive index and on the phase shift (Δ) were studied. It was shown, in particular, that in the hypsometric plane for Δ≥3, the light-scattering indicatrix F calculated by the Mie theory is determined by two factors: the Fraunhofer diffraction and geometrical optics. The possibility of measuring the refractive index from the experimental values of the aperture angle of a photodetector at fixed values of F was also considered.     

Determination of Particle Size Distribution and Electrokinetic Properties with the AcoustoSizer in Comparison with Other Methods

The characterization of suspensions in process concentration is an important task for the optimization of handling and product properties. Only very few instruments are available. The AcoustoSizer (ACS) (Colloidal Dynamics PTY Ltd.) uses the so-called electrokinetic sonic amplitude (ESA) for particle size and zeta potential determination. In this work, the results obtained at moderate concentrations were compared with results of other instruments mostly working with dilute suspensions. For the electrokinetic investigations three methods (beside the ACS) were used: electroacoustics (ESA8000, Matec Applied Sciences), microelectrophoresis (Zetamaster, Malvern Instruments) and streaming current measurements (Particle Charge Detector PCD 03-pH, Miitek). For particle size determination different measuring techniques were applied: laser diffraction spectroscopy (Mastersizer S, Malvern Instruments), dynamic light scattering (Ultra Fine Particle Analyser, Leeds and Northrup), sedimentation analysis (Sedigraph 5000 D, Micromeritics) and scanning electron microscopy. Mainly three powders were used in the investigations: Monospher M1200 silica (Merck), Selectipur titania (Merck) and Aluminiumoxid C alumina (Degussa). The agreement between the different methods for both particle size and zeta potential measurements was excellent. Especially for the electrokinetic investigations, careful sample preparation is needed. The procedure must not change the equilibria determining the physical and chemical state of the suspension.     

Testing a new photocentrifuge for submicron particles with silica spheres

A theory has been developed for spectral photosedimentation in a centrifuge. The use of several wavelengths allows particle size analyses in the submicron range without a knowledge of the optical material properties and is not restricted to spherical particles. As a result of this theory the extinction efficiency and the particle size distribution of the analysed particles can be calculated even for non-spherical particles from an experiment. A photocentrifuge has been built according to the developed theory. The theory has been verified by the measurement of spherical particles for which Mie theory is applicable. The experimentally obtained extinction efficiency agrees well with computations according to Mie theory. The accuracy of measured particle size distributions is comparable to those measured with other sedimentometers.     

海洋悬浮颗粒的光谱模拟:ADA与Mie的比较研究

基于海洋悬浮颗粒的折射率、粒径分布特征,利用异常衍射近似ADA(anomalous diffraction approximation)和米(Mie)散射方法进行衰减、吸收和散射效率的光谱模拟,分析两种方法计算结果相对偏差Δc,Δa,Δb及其影响因素,探讨利用计算速度占优的ADA方法进行海洋悬浮颗粒光谱模拟的可行性,研究发现:Δc,Δa,Δb受颗粒粒径、折射率实部和虚部的共同影响,且影响方式复杂;ADA方法满足计算精度(相对偏差小于5%)要求的最小颗粒半径Rmin随折射率和波长等的变化而变化。考虑到ADA与Mie的计算偏差受到多种因素的影响,而且海洋悬浮颗粒组分复杂多样,建议在进行海洋悬浮颗粒光谱模拟时,采用经典的Mie方法,而不是计算相对快速的ADA方法。     

Anomalous diffraction approximation method for retrieval of spherical and spheroidal particle size distributions in total light scattering

Using total light scattering technique to measure the particle size distribution has advantages of simplicity in measurement principle and convenience in the optical arrangement. However, the calculation of extinction efficiency based on Mie theory for a spherical particle is expensive in both time and resources. Thus, a simple but accurate approximation formula for the exact extinction efficiency may be very desirable. The accuracy and limitations of using the anomalous diffraction approximation (ADA) method for calculating the extinction efficiency of a spherical particle are investigated. Meanwhile, the monomodal and bimodal particle size distributions of spherical particles are retrieved using the genetic algorithm in the dependent model. Furthermore, the spheroidal model in the retrieval of non-spherical particle size distribution is also discussed, which verifies the non-sphericity has a significant effect on the retrieval of particle size distribution compared with the assumed homogeneous isotropic sphere. Both numerical computer simulations and experimental results illustrate that the ADA can be successfully applied to retrieve the particle size distributions for spherical and spheroidal particles with high stability even in the presence of random noise. The method has advantages of simplicity, rapidity, and suitability for in-line particle size measurement.     

Forward Scattering Signature of a Spherical Particle Crossing a Laser Beam out of the Beam Waist

When a particle crosses a laser beam out of the focal plane, the light attenuation signal occuring on the beam axis contains some information regarding the particle size and trajectory. These attenuation signatures are analysed and predicted with a simplified model based on Fraunhofer diffraction. Numerical and experimental results are found to be in good agreement. A modified laser Doppler velocimeter using this sizing method is able to perform simulataneous measurement of size and velocity of spherical particle in the range 10 μm–500 μm.     

基于粒子谱的多波长激光雷达近场大气光学参数校正方法

非同轴激光雷达由于存在发射激光与接收望远镜之间的不完全重叠区, 造成近场回波信号与真实大气信号不一致. 对于多波长激光雷达, 这种不一致更为突出和复杂. 然而, 近场大气是人类活动最集中的区域, 因此对多波长激光雷达近场信号进行校正, 对于了解和探究边界层大气具有十分重要的意义. 提出了一种利用粒子谱仪测量近地层气溶胶尺度谱分布并运用Mie 散射理论和低层大气指数衰减规律, 进而直接校正多波长激光雷达消光系数廓线近场信号的新方法. 通过对晴天、多云天气和雾天多波长气溶胶消光系数廓线近场信号的校正, 证明了该方法的可行性和实用性. 该方法着重考虑了多波长激光雷达比的波长依赖性和气溶胶粒子谱分布的天气相关性, 将该方法用于近地层大气消光系数廓线校正, 减少了由于不考虑这两个因素带来的消光系数廓线反演和校正的不确定性. 该方法对于研究不同天气情况下边界层内的大气气溶胶物理、光学特性具有一定的实用价值和借鉴意义.     

夫琅和费衍射颗粒粒度测量中的改进Chin-Shifrin反演算法

在基于线阵CCD的夫琅和费衍射颗粒粒度测量中,采用Chin-Shifrin积分变换反演算法使得反演的粒度分布出现假峰现象.为解决此问题,提出在该Chin-Shifrin积分变换反演算法中引入矩形窗函数,并在分析颗粒粒径与衍射光强导数最小值之间关系的基础上,确定矩形窗函数中心点位置及左右边界,利用该矩形窗函数对粒度分布进行截断处理,消除虚假峰,提高反演颗粒粒度分布的准确性.分别对两种标准颗粒进行了测量,并对不同算法的反演结果进行了对比.实验结果表明:引入矩形窗函数的改进Chin-Shifrin算法,能够有效排除粒度分布中的多假峰;粒度分布测量相对误差小于3%,重复性小于4%.