In‐line Particle Size Measurement for Control of Jet Milling

Jet milling is suitable for the production of very fine powders with a well‐defined particle size distribution (PSD). The major disadvantage of the process is the poor energy efficiency. In practice jet mills have to be operated below their maximum capacity in order to avoid the production of off‐specification material, due to operation disturbances. Therefore, it is important to automate operation with a real‐time PSD instrument for quality control. In this paper, a study for in‐line particle size measurement using laser diffraction is presented to improve operation control. This measurement system uses a novel CMOS pixel array, which has a robust and flexible feature for the application. It also includes an in‐line cell system, where direct measurement is implemented in the product particle stream coming from the mill and an air purge for the cell window allows continued operation. Experiments were conducted on a 10‐inch spiral jet mill pilot plant with alpha‐Al₂O₃ as test material. The milling process is investigated by varying the operational conditions. The measurement results are useful to build a grinding model for control purpose.     

Laser Diffraction – Unlimited?

Within the past 20 years, particle size analysis with laser diffraction (LD) has been subject to rapid development, extending the size range stepwise from 1–200 μm to about 0.1–3500 μm. The limits of LD are discussed in terms of light sources, the influence of the beam diameter, special Fourier optics and a new detector design. It is shown that the size range is not only restricted by the wavelength of the laser and the transmission limits of the medium. Its extension is mainly related to improvements in the measurement of the angular intensity distribution. Influences from stability and flow dominate on the coarse side of the measuring range. On the fine side, the spatial extension of aerosols and the resulting demand for extended working distances can be covered only in a parallel laser beam. Extended Fourier optics in combination with an adapatable beam expansion technique and a detector with virtual borders between semicircular elements overcome the existing limits and extend the size range to a lower limit of about 0.05 μm and an upper limit above 10 mm. The sensititivity limit of LD is approaching that of single particle counting techniques. For medical spray and inhaler applications, a 0.1% optical concentration can be converted to particle size distributions even for time-resolved analyses with sample intervals of a few milliseconds. The reproducibility of the sensor, with a standard deviation typically much less than 0.5%, is no longer the limiting factor. The reproducibility of the results is mainly dominated by the reproducibility of sampling, sample splitting, dispersion and the contamination of the optical path. The latter can be improved by the control of flow, especially for in-line and inhaler applications.     

消光起伏光谱的时间相关处理

消光起伏光谱法(TFS)是一种新的颗粒测量方法,可同时测量两相流中颗粒的粒径分布和体积浓度。由于在测量原理和结构上非常简单,这种方法可用来实现在线、实时测量。然而在实际测量中,消光起伏光谱法对颗粒粒径分布的分辨率还比较低且对高浓度颗粒系的测量须考虑颗粒相互作用效应。本文提出一种新的数据处理方法-消光起伏相关光谱法(TFCS),通过对消光起伏信号在不同相关时间参数下进行相关计算来得到消光起伏光谱以提高消光起伏法对颗粒粒径分布的分辨率。     

Determination of Particle Size Distribution by Par-Tec® 100: Modeling and Experimental Results

Some particle size analyzers, such as the Par-Tec® 100 (Laser Sensor Technology, Redmond, WA, USA), measure the so-called cord length distribution (CLD) as the laser beam emitted from the sensor randomly crosses two edges of a particle (a cord length). The objectives of this study were to develop a model that can predict the response of the Par-Tec® 100 in measuring the CLD of a suspension for spherical and ellipsoidal particles and to infer the actual particle size distribution (PSD) using the measured CLD output. The model showed that the measured CLD is reasonably accurate for the spherical particles. However, this measurement progressively deteriorates as the shape of particles changes from spherical to ellipsoidal with large ratios of major to minor diameters. Experimental results obtained with spherical particles having a normal and a non-normal PSD indicated that the Par-Tec® 100 measurements deteriorate as the PSD deviates from a normal distribution. The information obtained from these experiments also showed that the model can reasonably predict the Par-Tec® response. Use of the inferred PSD rather than the measured CLD made a major improvement in estimating the actual PSD. Mean particle size analysis revealed that the Par-Tec® 100 volume-weighted mean particle size is closest to the unweighted mean particle size measured by sieve analysis.     

Measurements on Particle Size Distribution and Concentration by Transmission Fluctuation Spectrometry with Temporal Correlation

Transmission fluctuation spectrometry with temporal correlation (TFS‐TC) is a new method for particle analysis. When a narrow light beam irradiates on a particle dispersion flow, the variation of the number of particles in the small measuring zone will cause the transmitted light to fluctuate, which includes the complete information on both particle size distribution (PSD) and particle concentration. The method may be used for real‐time, inline/online applications due to its simplicity of measuring principle and experimental setup. Until recently, the theory has been limited to low particle concentrations. In this work, an experimental study of the TFS‐TC measurement is presented for a very wide range of the particle concentrations. By introducing an empirical correction including the high concentration effects and considering the effect from rheological conditions in the inversion algorithm, the particle size distribution and particle concentration are reconstructed, resulting in the coverage of a broad range of particle size and concentration.     

Exact solution of a coagulation equation with a product kernel in the multicomponent case

In this paper, we obtain the general solution for the continuous Smoluchowski equation in the multicomponent case with a product kernel as a series expansion. The solution of the problem involves the Laplace transform in several dimensions. We obtain a nonlinear partial differential equation (PDE) of the advective kind generalizing the one previously given by other authors for the mono-component case.As in its relative mono-component case, gelation is produced at some point, the conditions for its occurrence being the same as those for the mono-component case, though substituting a sum of derivatives by a derivative in the Laplace transform field. We demonstrate that for a multicomponent particle size distribution (PSD) of multiplicative form, it is sufficient for one of the marginal PSDs to generate instantaneous gelation for the occurrence of instantaneous gelation in the multicomponent PSD.The general solution is applied to several specific cases, a discrete case that recovers a previously known solution, and another two continuous cases which can be used to check numerical methods designed to directly solve the Smoluchowski equation in more general cases.We have compared the solutions for the multicomponent PSD for constant, additive and product kernels and we conjecture about the relation existing between the functional forms for the solutions both in the mono-component and the multicomponent case.Finally, we have analysed the shape of the solutions for multicomponent PSD for constant, additive and product kernels for very small masses of components, obtaining a qualitatively different behaviour for the product kernel. This has effects in the mixing state of the sol phase as time passes.     

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%.     

Modeling and Experimental Analysis of PSD Measurements through FBRM

The Focused Beam Reflectance Measurement (FBRM) technique provides on‐line and in‐situ information about the chord length distribution of a population of particles in dispersion. This is rather promising for applications such as crystal size distribution control in crystallization processes. The objective of this study is to deepen the understanding of the characteristics of the FBRM measurement. On the one hand, a model is presented, which allows in principle to transform particle size distributions (PSD) into chord length distributions (CLD). On the other hand, measurements with particles in suspension show the critical dependence of the measurement on the optical properties of the system. A special technique has been developed to measure CLDs of single particles. These measurements clarify some of the above effects, detect possible over‐ and underestimations of particle size and give indications about how to interpret and exploit on‐line CLD spectra.     

基于颗粒粒度信息分布特征的动态光散射加权反演

宽分布和双峰分布颗粒的准确反演是动态光散射技术至今未能有效解决的难题,尤其峰值位置比小于2:1且含有大粒径颗粒(350 nm)的双峰分布.造成这一难题的主要原因包括:1)单角度测量数据的粒度信息含量不足;2)常规反演方法对测量数据的噪声抑制以及粒度信息利用缺乏针对性.对测量数据(即光强自相关函数)的研究发现,数据噪声主要分布在长延迟时段,而粒度信息集中分布在衰减延迟时段.基于此,本文提出了采用粒度信息分布为底数、调节参数为指数的权重系数对自相关函数进行加权反演的约束正则化方法.由于采用了与粒度信息分布一致的权重系数,该方法既充分利用了衰减延迟时段的粒度信息,又有效地抑制了长延迟时段的数据噪声.不同噪声水平下,宽分布和双峰分布颗粒体系的反演结果表明,与常规反演方法相比,这一方法可以获得更为准确的宽分布和近双峰分布的反演结果.     

Characterization of spherical core–shell particles by static light scattering. Estimation of the core- and particle-size distributions

A numerical method is proposed for the characterization of core–shell spherical particles from static light scattering (SLS) measurements. The method is able to estimate the core size distribution (CSD) and the particle size distribution (PSD), through the following two-step procedure: (i) the estimation of the bivariate core–particle size distribution (C–PSD), by solving a linear ill-conditioned inverse problem through a generalized Tikhonov regularization strategy, and (ii) the calculation of the CSD and the PSD from the estimated C–PSD. First, the method was evaluated on the basis of several simulated examples, with polystyrene–poly(methyl methacrylate) core–shell particles of different CSDs and PSDs. Then, two samples of hematite–Yttrium basic carbonate core–shell particles were successfully characterized. In all analyzed examples, acceptable estimates of the PSD and the average diameter of the CSD were obtained. Based on the single-scattering Mie theory, the proposed method is an effective tool for characterizing core–shell colloidal particles larger than their Rayleigh limits without requiring any a-priori assumption on the shapes of the size distributions. Under such conditions, the PSDs can always be adequately estimated, while acceptable CSD estimates are obtained when the core/shell particles exhibit either a high optical contrast, or a moderate optical contrast but with a high ‘average core diameter’/‘average particle diameter’ ratio.     

Estimation of Particle‐Size Distribution and Classifier Selectivity

A new, practical, and informative technique is presented for the efficient calculation of classifier efficiencies. Kernel density estimation, a well‐developed statistical tool, is applied to particle‐size datasets from classifier flow streams. It is demonstrated that this construction of particle‐size densities is more accurate and appropriate than histograms. The resulting classifier efficiency curves then display the key features of the classifier efficiency without propagating the noise inherent in most particle‐sizing techniques, and without the constraint of any selectivity curve parametrization.     

基于二阶滤波器的消光起伏谱颗粒测量结果

消光起伏频谱法是一种新的测量两相流系统中颗粒粒径分布和浓度的方法,装置简单,操作方便,适合实时、在线测量。采用二阶低通滤波器对起伏的透射率信号分析,得到消光起伏频谱实验数据,并利用改进的Chahine循环方法计算得到颗粒的粒径分布和浓度信息。重点讨论高浓度情况,包括对特征函数频率响应的修正和对其阶高修正两个方面,得到修正参量并运用到反演算法中从而得到正确的测量结果。测量结果表明,通过高浓度修正,消光起伏频谱法可以在很大的颗粒浓度动态范围得到合理的测量结果,其可测颗粒最大体积分数视颗粒的大小而定。     

Progress in unipolar corona discharger designs for airborne particle charging: A literature review

Particle motion induced by electrical forces is the basis for important class of measuring instruments. Charging is important in aerosol size measurement. Unipolar charger is a crucial component in the aerosol particle sizing system by electrical mobility analysis. For an electrical mobility analyzer, the charging is aimed to impose a known net charge distribution on each aerosol size. The charger performance depends on the charging efficiency and stable operation. A well-designed unipolar charger should provide high charging efficiency and stability that can be accurately determined for any given operating conditions. This article presents and discusses progress on the development of existing unipolar aerosol chargers based on corona discharge technique. The operating principles as well as detailed physical characteristics of these chargers, including the corona-wire and corona-needle chargers, are described with extensive list of references.     

消光起伏自相关频谱法颗粒测量技术

消光起伏相关频谱法(TFCS)是一种新的颗粒测量方法。采用一束窄光束照射两相流系统,照射区中颗粒浓度的起伏所导致的透射光起伏信号中包含了颗粒的粒径和浓度信息,对光束的透过率信号作相关处理得到消光起伏相关频谱,可用来同时测量两相流中颗粒的粒径分布和体积浓度。由于在测量原理和结构上非常简单,这种方法可用来实现在线、实时测量。本文介绍消光起伏自相关频谱的测量原理,并给出部分实测结果。     

Modeling Focused Beam Reflectance Measurement and its Application to Sizing of Particles of Variable Shape

A model for particle detection in focused beam reflectance measurement is presented in the general case of particles of any convex shape. Shape dependent convolution relationships between measured chord length distribution (CLD), particle size distribution (PSD) and particle mass distribution (PMD) are derived and an explicit formula for the weighting characteristic length is given in terms of particle shape. Based on the derived convolution relationships, equations relating moments of the CLD, PSD and PMD are obtained. Issues related to the definition of particle size of non spherical objects and its connection to the particle sizing technique are discussed. Based on the moment relationships, particle size is defined for focused beam reflectance measurement measurements in terms of a CLD equivalent sphere. CLD and characteristic length for a thin cylinder are obtained analytically and used as simple model in order to illustrate issues in sizing particles of variable shape. General conclusions regarding the role of the weighting characteristic length on the behavior of the measured CLD are drawn.     

Determining particle size distribution and refractive index in a two-layer tissue phantom by linearly polarized light

We report a new method for measuring particle size distribution (PSD) and refractive index of the top layer in a two-layer tissue phantom simulated epithelium tissue by varying the azimuth angle of incident linearly polarized light. The polarization gating technique is used to decouple the single and multiple scattering components in the returned signal. The theoretical model based on Mie theory is presented and a nonlinear inversion method - floating genetic algorithm - is applied to inverting the azimuth dependence of component of polarization light backscattered. The experiment results demonstrate that the size distribution and refractive index of the scatters of the top layer can be determined by measuring and analyzing the differential signal of the parallel and perpendicular components from a two-layer tissue phantom. The method implies to detect precancerous changes in human epithelial tissue.     

Information Content of Acoustic Attenuation Spectra

In recent years ultrasonic attenuation spectroscopy has gained much attention as a method for the characterisation of concentrated dispersions. Several publications have shown, that this method allows the accurate determination of particle size. In particular for submicron dispersions there is, however, some uncertainty to which degree the details of a size distribution can be resolved by acoustic attenuation measurements. Ideally the inversion of an attenuation spectrum into a size distribution would yield as much distribution parameters as sound frequencies. In practice, however, the measurement errors affect the inversion very strongly and may result in multiple solutions for the size distribution. The maximum number of distribution parameters, for which a unique solution exists, can be therefore regarded as the information content. For a given ultrasonic spectrometer and material system it is possible to quantify the information content. Such an information analysis has been conducted with selected material systems in the submicron range. The investigation shows that the information content of acoustic attenuation spectra with regard to particle size analysis in the submicron range is relatively low. On the other hand, the results imply that the number of frequencies can be reduced significantly without loss of information content or stability of inversion algorithms.     

Transmission Fluctuation Spectrometry in Concentrated Suspensions. Part Three: Measurements

The theory of transmission fluctuation spectrometry (TFS) was developed for particle size analysis in flowing particle suspensions, whereby the statistical transmission fluctuations are used to extract the particle size distribution (PSD) and particle concentration. In the previous parts of this publication high concentration effects on TFS were investigated theoretically and by simulation. This work presents a study on TFS measurements in concentrated suspensions. By introducing an empirical correction to include the high concentration effects from both the monolayer structure and particle overlapping in the inversion algorithm, it is possible to obtain the particle size distribution and particle concentration over broad ranges of particle sizes and concentrations.     

On-line Measurement of Solids Concentration or the Mean Particle Size in a Saturated Slurry Containing Background Particles Using a Turbidity Method

An on-line double-sensor turbidimeter for estimating the solids concentration or the mean particle size in a saturated slurry system in the presence of foreign insoluble particles is proposed. The correlation representing the operation of the double-sensor turbidimeter for on-line implementation is also developed. The technique relies on measuring the transmittance of an infrared light beam through the suspension, once in the presence of soluble particles and a second time when the soluble particles have completely dissolved. The device can be easily implemented on a crystallization system for monitoring and control applications. The maximum errors for solids concentration and mean particle size measurements were 13% and 7%, respectively.