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.     

Nanoparticle Tracking Analysis: Enhanced Detection of Transparent Materials

This study proposes a novel and simple in-house design of a nanoparticle tracking analysis (NTA) device for the online characterization of nanoparticles in an aqueous solution. The particle size distribution of two sets of model nanoparticles, for example, transparent (SiO₂) and opaque (TiO₂) materials with respect to water as a dispersion medium could be successfully analyzed. Experiments are conducted using two different laser wavelengths of 632.8 (red) and 510 nm (green) and a range of concentrations. The accuracy of the green laser is larger compared to the red laser for all particle concentrations used. The measured average diameter using the presented in-house NTA setup is in the acceptable range compared to the electron microscopy data. The average diameter of the transparent (SiO₂) and opaque (TiO₂) samples is calculated as 36.29 and 27.26 nm using NTA, 36.44 and 27.8 nm analyzing field emission scanning electron microscopy images, and 23.97 and 19.7 nm analyzing transmission electron microscopy images. In the new viewing sample holder, nanoparticles undergo mere Brownian motion with no bulk drift velocity. The effect of solid concentration and wavelength of the laser light on the performance of the NTA sensor is investigated, and the optimal concentration range for model particles is reported.     

Particle Size Distribution Retrieval from Elastic Light Scattering Measurements by a Modified Regularization Method

Retrieval of polymeric emulsions Particle Size Distribution (PSD) from Elastic Light Scattering (ELS) measurements requires the solution of an ill conditioned inverse problem. In this paper we compare the performance of classical regularization methods such as Truncated Singular Value Decomposition and Tikhonov's, to a regularization technique due to Pike that includes positivity constraints on the PSD. We also propose a new method that combines Tikhonov's approach with Pike's method. Simulated ELS measurements for two polymeric materials were generated under different experimental noise assumptions. Uncertainties on the polymer refractive index value were also considered. The PSD estimations obtained show that the implementation of the proposed more sophisticated algorithm is convenient for this very ill‐conditioned problem.     

Improving the Robustness of Particle Size Analysis by Multivariate Statistical Process Control

The robustness of online particle size analysis in wet processes is improved by applying data based modeling methods to the control of the sample preparation and measurement sequence of the particle size analyzer. The aim is to find a more accurate and reliable method of determining the end of the particle size integration period using multivariate statistical process control (MSPC). The studied approach is tested on analyzers installed at two mineral processing plant sites and validated using two validation tests. Research shows that the proposed method works with two very different slurry types. The main advantage of the adapted approach is that there are no adjustable parameters that have to be set by the user.     

The Fundamentals of Particle Size Analysis by Transmission Fluctuation Spectrometry.

A transmission signal measured on a flowing suspension of particles with a high spatial and temporal resolution shows significant fluctuations, which contain the complete information on particle size distribution and particle concentration. In Parts 1 and 2, the basic properties of signal fluctuations were studied for temporal averaging by a gliding time window and for spatial averaging by a circular beam of uniform intensity. However, the experimental implementation of such conditions is difficult. Now, the theory is extended for Gaussian beams of variable diameter and averaging by signal filtering in the frequency domain. This provides the basis for an experimental implementation by transmission of a laser beam and analog signal processing by an array of low pass filters.     

Calculation of Particle Size Distributions from Ultrasonic Measurements: A Mineral Slurry Case Study

Ultrasonic transmission measurements have been used extensively to determine the particle size of solids in slurries. This case study examines the application of mathematical inversion techniques to the determination of the particle size distribution of a mineral slurry from data collected at a minerals processing plant. A new mathematical inversion technique, based on an extension of modified Chahine iteration combined with the principle of maximum entropy has been developed. Four algorithms were constructed and used to calculate particle size distributions from synthetic and raw plant data. These incorporated modified Chahine iteration and its extension, together with two different approaches to applying a density measurement constraint on the particle size distribution. In general the algorithms performed well with regression errors below 3 %. The correlation coefficients and slopes for this technique were 0.86 and 1.35 for the weight fraction of particles less than 75 microns when compared with the laser diffraction analysis. A better match was obtained for the plant data by using the new inversion technique, into which the principle of maximum entropy has been incorporated whereas this was not the case with the synthetic data, illustrating the need to match the inversion technique to the problem.     

非独立模式算法下粒径分布反演及分类的研究

在光全散射法颗粒粒径测量中,提出一种非独立模式算法下粒径分布反演及分类的方法。对被测颗粒系分别按照不同的粒径分布函数同时进行反演,并依据反演误差大小判断被测颗粒系符合哪种分布函数。仿真实验结果表明,在非独立模式下,完全可以利用已知的不同分布函数的反演误差作为分类依据,从而更准确地确定被测颗粒系的粒径分布。采用的遗传反演算法能够在3个可见光波长下得到较准确的粒径分布,反演结果稳定可靠,最大限度地减少了多个波长的使用,从而对光源有更大的选择余地。对透射消光测量结果加入5%随机噪声时,单峰分布颗粒系的反演误差小于5%,多峰分布颗粒系的反演误差小于10%。整个算法运行时间小于2 s。该方法具有原理简单,计算速度快等优点,能够满足颗粒粒径在线测量的要求。     

Estimation of Nanoparticle Size Distributions by Image Analysis

Knowledge of the nanoparticle size distribution is important for the interpretation of experimental results in many studies of nanoparticle properties. An automated method is needed for accurate and robust estimation of particle size distribution from nanoparticle images with thousands of particles. In this paper, we present an automated image analysis technique based on a deformable ellipse model that can perform this task. Results of using this technique are shown for both nearly spherical particles and more irregularly shaped particles. The technique proves to be a very useful tool for nanoparticle research.     

Particle Size Distribution of Nanospheres by Monte Carlo Fitting of Small Angle X‐Ray Scattering Curves

A method for recovering the size distribution of spherical particles from small angle scattering data by using a Monte Carlo interference function fitting algorithm is presented. The method is based on the direct simulation of the small angle scattering data upon the assumption of non‐interacting hard sphere ensembles (“dilute” solution approximation). The algorithm for retrieving the particle size distribution does not require any additional parameters apart from the input of the scattering data. The fitting strategy necessarily implies positive particle size distributions, while preserving the advantage of the indirect transformation method for data desmearing. Furthermore, the present approach does not use any regularisation procedures of the best fit solution and favours smooth particle size distributions. The Monte Carlo procedure has been tested against several simulated cases with various types of mono‐ and bi‐modal size distributions and different noise levels. In the special case of non‐interacting spheres, the Monte Carlo fitting algorithm had the same retrieving ability as the well assessed indirect transformation, structure interference and maximum entropy methods. Finally, the algorithm was applied to retrieve the distribution of spherical nanopowders produced by gas‐to‐particle conversion both as free powder and as reinforcing second‐phase agent in polymer nanocomposites.     

Estimating Average Particle Size by Focused Beam Reflectance Measurement (FBRM)

The Lasentec focused beam reflectance measurement (FBRM) probe provides in situ particle characterisation over a wide range of suspension concentrations. This is a significant advantage over conventional instruments that require sampling and dilution. However, FBRM gives a chord distribution, rather than a conventional diameter distribution. Both theoretical and empirical methods for converting from chord to diameter data are available, but the empirical method was found to be more successful.     

激光散射法对尿液中纳米微晶粒径及其分布的研究

泌尿系结石已经成为威胁人类健康的一种常见病、多发病,目前对其形成的机制尚不清楚。文章采用激光散射法测定了正常人尿液和尿石症患者尿液中纳米粒子的粒径和粒径分布,该方法快速准确、经济、容易操作。正常人尿液比尿石症患者尿液的稳定性好,归因于正常人尿液中纳米微晶尺寸分布均匀,不容易聚集,而尿石症患者尿液的纳米微晶尺寸分布不均匀,粒子间容易聚集而沉降。通过分析尿样稀释、离心或者用微孔滤膜过滤后体系的光强-自相关函数曲线,得到了制备稳定的尿样悬浮液的方法：尿样先稀释20%,然后离心或用1.2 μm微孔滤膜过滤,可得到稳定的尿液悬浮液。激光散射法结果与TEM检测结果一致。从尿液中存在的范德华力、尿液粘度、酸碱性、离子强度、尿液中纳米微晶的表面电荷和Zeta电位等方面解释了尿液稳定的原因。     

Monte Carlo Simulations of Reflected Spectra Derived from Tissue Phantom with Double-Peak Particle Size Distribution

We made a tissue phantom with double-peak particle size distribution, which has polystyrene particles of cell nuclear size and mitochondrial size, and measured the spectrum from the tissue phantom using a single optical fiber. In this paper we investigate the characterization method for the tissue phantom with double-peak particle size distribution by comparing the measured spectra with the calculated ones using the Monte Carlo (MC) method. It is first shown that the Mie phase function characterizes better than the Henyey-Greenstein (H-G) phase function in MC calculation. Next, we compare the measurement spectra with those obtained by modeling as single-peak, conventional modeling for particle size distribution, and for double-peak particle size distribution. The single-peak modeling is found to cause considerable error for the tissue phantom with double-peak particle size distribution, which seems to simulate a biological tissue. We suggest that if one simulates the particle size distribution of a biological tissue by conventional modeling, the accuracy of estimation will be lower.     

Experimental Study on Particle Size Distribution and Concentration Using Transmission Fluctuation Spectrometry with the Autocorrelation Technique

Based on the statistical characteristics of the transmission fluctuations in the particle suspension, transmission fluctuation spectrometry with autocorrelation (TFS‐AC) is described theoretically, with the assumptions of geometric ray propagation and completely absorbent particles in the suspension. The experiments presented here are realized in a focused Gaussian beam with the TFS‐AC technique. The acquisition of transmission fluctuation signals is achieved by using a high‐resolution digital oscilloscope. The transition function of TFS‐AC is obtained by varying the autocorrelation time. With a modified iterative Chahine inversion algorithm, solving a linear equation retrieves information on the particle size distribution and particle concentration. Some experimental results on spherical and non‐spherical particles are presented and discussed. The experiments cover a particle size range from 1μm to 1000 μm and a particle concentration of up to 12 %.     

Combination of the Particle Size Distributions of Some Industrial Minerals Measured by Andreasen Pipette and Sieving Techniques

It is known that size of the individual particles is the predominant factor affecting the behavior of particulate materials, and that the size effects become increasingly important as the particles become finer. In this article, particle size distributions (PSDs) measured by different techniques, i.e. sieving and Andreasen pipette sedimentation, were combined for different mill (ball and rod) products of some industrial (talc and quartz) minerals. The corrected sedimentation data came closer to the sieving data. The apparent mean shape factors, r, determined from the corrected PSDs for the talc mineral ground by ball and rod mill were found to be 1.34, 0.62, whereas it was 1.00, 1.12 for the quartz mineral ground by ball and rod mill, respectively. The results show that the ball milled products of talc mineral have more regular (rounder in shape) particles than those of rod milled, but the rod milled products of quartz mineral studied were not more regular in shape than ball milled products of quartz mineral as confirmed by the SEM pictures and reviewed literature.     

基于MIE散射理论的粒度分布测量系统研究

粒度测量广泛应用于粉体工程,测量结果直接影响粉体产品优劣。在深入研究MIE散射理论的基础上,提出一种基于改进反演算法的粒度测量系统设计方案,利用激光器、傅里叶透镜、光电传感器采集含有待测微粒信息的电信号,通过调理电路进行处理,应用改进反演算法分析得出粒度值及分布。通过实验验证,效的本文提出的设计方案能实现准确高粒度测量。     

A Comparative Study of the Determination of Ferrofluid Particle Size by Means of Rotational Brownian Motion and Translational Brownian Motion

Two methods, the Toroidal Technique and the Forced Rayleigh Scattering (FRS) method, were used in the determination of the size of magnetic particles and their aggregates in magnetic fluids. The toroidal technique was used in the determination of the complex, frequency dependent magnetic susceptibility, x(w)=x'(w) - ix"(w) of magnetic fluids consisting of two colloidal suspensions of cobalt ferrite in hexadecene and a colloidal suspension of magnetite in isopar m with corresponding saturation magnetisation of 45.5 mT, 20 mT and 90 mT, respectively. Plots of the susceptibility components against frequency f over the range 10 Hz to 1 MHz, are shown to have approximate Debye-type profiles with the presence of relaxation components being indicated by the frequency, f _max, of the maximum of the loss-peak in the x"(w) profiles. The FRS method (the interference of two intense laser beams in the thin film of magnetic fluid) was used to create the periodical structure of needle like clusters of magnetic particles. This creation is caused by a thermodiffusion effect known as the Soret effect. The obtained structures are indicative of as a self diffraction effect of the used primary laser beams. The relaxation phenomena arising from the switching off of the laser interference field is discussed in terms of a spectrum of relaxation times. This spectrum is proportional to the hydrodynamic particle size distribution. Corresponding calculations of particle hydrodynamic radius obtained by both mentioned methods indicate the presence of aggregates of magnetic particles.     

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.     

涡场中黏附性颗粒团聚体粒径分布的预测

黏附性颗粒团聚现象在自然界和工业界普遍存在,扰动流场中黏附性颗粒间的碰撞、摩擦和吸附等动力学行为,导致团聚体形态不断演化,准确预测黏附性颗粒团聚体的粒径分布是调控颗粒团聚过程的重要前提。本文通过二维泰勒格林涡场中黏附性颗粒团聚的数值模拟研究,明确了利用Monte Carlo模型预测团聚体粒径分布的可行性及其适用范围,发现当黏附性颗粒间内聚数小于3.5×10^?4时,Monte Carlo模型可较好的预测团聚体粒径分布,且相对误差小于±30%;而当内聚数大于3.5×10^?4后,Monte Carlo模型不再适用。     

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.