New measurement of particle size distribution by a buoyancy weighing-bar method

The rates which particles from JIS Test Powders 1, Class 2 (silica sand), Class 3 (silica sand), Class 16 (calcium carbonate, heavy), and JIS Test Powder 2, Class GBM-20 (barium titanate glass) settled out of homogenous suspensions were determined using the principles of the buoyancy weighing-bar method as well as a sedimentation balance. Samples were standardized by Japanese Industrial Standard, and the dispersing agent was NaPP or NaHMP, while the viscosity improver was a starch syrup solution. Although constructing a handmade sedimentation balance is difficult, developing a handmade weighing tool capable of measuring particle size distribution is easy. Herein three weighing-bars, which were composed of aluminum, stainless steel, and copper, were used to measure the particle size distribution. However, an aluminum slit-cylinder occasionally replaced the weighing-bars. The weighing data obtained via an analytical balance were controlled by connecting the balance to a personal computer with an RS-232C interface, and the determined particle size agreed well with the data obtained by Andreasen analyses and the sedimentation balance.     

Modeling of sedimentation of polydisperse spherical beads with a broad size distribution

This article deals with experimental and theoretical studies of the sedimentation of polydisperse agarose beads with broad particle size distributions. A light-extinction principle was used to measure the variation of solid concentration in the suspension with time and settling distance. Different experimental conditions have been used to show the influence of solid concentration and liquid density and viscosity on the settling behavior of the beads. The sedimentation process was described mathematically by a system of conservation law using Masliyah's hindered settling function. The physical properties of the beads and the optical properties of the suspension were carefully examined to enable a reliable comparison between experimental and simulation results. The model gives good predictions under all the conditions studied, showing its soundness in formulating the hindered settling process of polydisperse particles in a suspension.     

重力沉降原理在微粉和超细粉粒度分析中的应用

探讨了利用重力沉降原理对粉体颗粒粒度分布进行测试时 ,颗粒的布朗运动对测定精度的影响。并推导出常见的耐火材料粉体最小的测试颗粒粒径范围应为 0 .6～ 0 .95 μm。同时介绍了采用国产KCT - 1型沉降天平进行微粉与超细粉的粒度分布测定时的操作要点与技巧。并对测试过程中出现的异常现象和解决的方法进行了阐述     

A new method of processing the time-concentration data of reaction kinetics

Experimental data of reaction kinetics are usually in the form of concentration versus time. For kinetics investigation it is more convenient to have the data in the form of reaction rate versus concentration. Converting time-concentration data into concentration-reaction rate data is an ill-posed problem in the sense that if inappropriate methods are used the noise in the original data will be amplified leading to unreliable results. This paper describes a conversion procedure, independent of reaction rate model or mechanism, that manages to keep noise amplification under control. The performance of this procedure is demonstrated by applying it to several sets of published kinetic data. Since these data are accompanied by their rate equations, the computed rates are used to obtain the unknown parameters in these equations. Comparison of these parameters with published figures and the ease with which they are obtained highlights the advantages of the new procedure.     

A method for computing the partial derivatives of experimental data

This article describes a procedure for obtaining the partial derivatives of experimental data that depend on two independent variables. The starting equation is an ill‐posed integral equation of the first kind. Tikhonov regularization is used to keep noise amplification under control. Implementation of the computation steps is described and the performance of the procedure is demonstrated by four practical examples. © 2010 American Institute of Chemical Engineers AIChE J, 2010     

A new method to synthesize high solid content waterborne polyurethanes by strict control of bimodal particle size distribution

A new method named two-step emulsification process was developed to synthesize high solid content waterborne polyurethanes by strict control of the bimodal particle size distribution. In the first step, a series of 40% solid content polyester-based (WPU-1) with low content of hydrophilic group and large particle size were firstly synthesized. In the second step, polyether-based prepolymers (WPU-2 prepolymers) with high content of hydrophilic group were firstly prepared and WPU-1 emulsions were used to emulsify WPU-2 prepolymers to obtain the final emulsions with high solid content (WPU-3). The particle size of WPU-3 present bimodal distribution and the diameter ratio and volume percentage of large particles to small particles in WPU-3 were able to be strictly controlled by this method. The viscosity of WPU-3 with 55% solid content was only 489.1 mPa s⁻¹ when the diameter ratio of large particles to small particles was 9.2 and the volume percentage of large particles was 74%.     

An improved estimation of size distribution from particle profile measurements

Several methods are available to measure particle size. The majority of them, such as sieving, are off-stream techniques where samples must first be separated from the main stream for analysis.Therefore, the search for on-line particle size analysis systems has provided the impetus for the introduction of image-based particle size analysers to the mineral industry in the past three decades. Generally, the estimation of particle size distribution on the basis of image analysis depends on measuring a single parameter of particle profile. For example the equivalent area diameter (d_A) or mean Feret's diameter (d_F) distributions, then transforming this data to the equivalent size distribution. However, due to the irregularity of particles being analysed, it is believed that this kind of analysis may increase the error in estimation of particle size distribution since profiles of irregular particles carry more information than can be represented by a single parameter.In this paper, a proposed technique which measures two parameters, equivalent area diameter (d_A) and mean Feret's diameter (d_F), for each particle profile has been developed. The accuracy of the technique has then been investigated in the laboratory by successfully estimating (unfolding) the size distribution, where size refers to sieve size, of three samples of different particle shapes with known size distribution.     

A new method for the control of dilute suspension sedimentation by horizontal movement

This research addresses some factors that control the stability of dilute suspensions in sedimentation processes under a dynamic environment. Experimental and numerical studies were conducted about the sedimentation velocity control of dilute suspensions by horizontal movement for particle concentrations up to 8 wt.%. Nearly monodispersed particles were used as test particles. The effects of horizontal movement speed and amplitude on particle sedimentation process were investigated. Under stationary conditions, particles settle in only one vertical direction because of gravitational force. However, complicated particle motions arise under moving conditions due to circulation flow in horizontal moving conditions. The results show that horizontal movement can reduce the particle settling velocity or maintain the stability of the suspension.     

A particle analyser for measuring particle size distribution and shape,on-line or in the laboratory

Norsk Hydro has developed a Particle Analyser for on-line or laboratory use, which measures particle size, size distribution and the deviation from sphericity (called nonspherical).The principle for this system is that the particles fall in a monolayer curtain in front of a high resolution CCD camera. The computer unit in the analyser measures and calculates the particle size and a sphericity factor for each particle. The data are presented as four real time trend curves, shown simultaneously for the on-line version. These curves show % oversize and fines, d₅₀ and the percentage nonspherical particles. For the laboratory version the data are presented in table and cumulative form.The on-line particle analyser has been installed in two of Norsk Hydro's prilling plants in Norway. The analyser has in both plants improved the product quality during the two years of installation.     

Influence of particle size distribution on rheology and particle packing of silica-based suspensions

The effect of particle size, particle size distribution and milling time on the rheological behaviour and particle packing of silica suspensions was investigated using slurries containing total solids loading of 46 vol.%. Three silica powders with different average particle sizes (2.2, 6.5 and 19 μm), derived from dry milling of sand, and a colloidal fumed silica powder with 0.07 μm were used. Different proportions of colloidal fumed silica powder were added to each of the coarser silica powders and the mixtures were ball-milled for different time periods. The influence of these factors and of the particle size ratio on the rheological behaviour of the suspensions and densities of green slip cast bodies was studied.The results show that the flow properties of slips are strongly influenced by the particle size distribution. The viscosity of suspensions increases with the addition of fine particles, imposing some practical limitations in terms of volume fraction of fines that can be added. On the other hand, increasing the size ratio enhanced the shear thinning character of the suspensions, while decreasing the size ratio led to an accentuation of the shear thickening behaviour. For all mixed suspensions, green densities increased with increasing milling time, due to size reduction of silica powders and a more efficient deagglomeration of fumed silica. Increasing amounts of fumed silica led to a first increase of particle packing up to a maximum, followed by a decreasing trend for further additions. Good relationships could be observed between rheological results and packing densities.     

离心沉降法粒度分析──固液分离设备选型依据之一

应用离心沉降粒度分析仪进行粒度分析时，准确、合理地选择沉降介质及圆盘转速等测试条件是获得正确测试结果的关键。粒度分析结果为固液分离设备及分离介质的选型提供了依据。     

Challenges in particle size distribution measurement past, present and for the 21st century

The field of particle size distribution (PSD) characterization and measurement has experienced a renaissance over the past ten years. This revitalization has been driven by advances in electronics, computer technology and sensor technology in conjunction with the market pull for PSD methods embodied in cost effective user friendly instrumentation. The renaissance can be characterized by at least four activities. (1) End user innovation exemplified by techniques such as hydrodynamic chromatography (HDC), capillary hydrodynamic fractionation (CHDF) and field flow fractionation methods (SdFFF, FlFFF, and ThFFF). (2) Revitalization of older instrumental methods such as gravitational and centrifugal sedimentation; (3) Evolution of research grade instrumentation into low cost, routine, user friendly instrumentation exemplified by dynamic light scattering (DLS). (4) The attempt to meet extremely difficult technical challenges such as: (a) providing a single hybrid instrument with high resolution over a very broad dynamic range (4+ decades in size; e.g., Fraunhofer/Mie; photozone sensing/DLS); (b) PSD measurement of concentrated dispersions (acoustophoretic, dielectric measurements, fiber optic DLS (FOQELS)); (c) in-situ process particle size sensors (in-line or at line, e.g., FOQELS); (d) routine measurement of particle shape and structure (e.g., image analysis). Instrumental methods resulting from these activities are discussed in terms of measurement principles and the strengths and weaknesses of these methods for characterizing PSDs. Business and societal driving forces will impact customer perceived instrumentation and knowledge needs for the 21st century and the ability to meet the specific difficult technical challenges in particle size distribution characterization mentioned above. Anticipated progress toward meeting these technical challenges is discussed in conjunction with the associated anticipated advances in required technologies.     

基于带约束TSVD方法的粒径分布反演

利用光全散射法,在独立模式下通过测量可见光不同波段下的光谱消光值反演几种常见粒径分布,其中正问题利用反常衍射近似（ADA）计算得到估计值,测量值通过Mie理论计算得到,反问题利用截断奇异值分解（TSVD）的正则化方法,并结合粒径分布非负和粒径分布积分和为1两个约束条件优化反演结果,通过数值模拟证明了带约束的TSVD方法在粒径分布的反演中具有更高的反演精度、稳定性和抗噪性。     

Measurement of the floating particle size distribution by a buoyancy weighing-bar method

The particle size distribution of cylinder-shaped solid particles was measured using a buoyancy weighing-bar method where the liquid phase density was adjusted to settle or float the particles. The particle size distribution obtained in our experiment agrees with the particle size measured by other method. The present study demonstrates that a buoyancy weighing-bar method, a novel method for measuring the particle size distribution, is suitable for measuring the particle size distribution of a floating solid. The precision of the resulting particle size distribution is comparable to that of a laser diffraction/scattering method as well as a direct measurement with a micrometer. Moreover, this buoyancy weighing-bar method can measure the particle size distribution even in a mixture of two particles with different sizes.     

Control of particle size distribution for the synthesis of small particle size high solids content latexes

A polymerization process to synthesize bimodal latexes with maximum particle diameters below 350 nm and solids content above 65 wt% has been developed.The process is based on an iterative strategy to determine the optimal particle size distribution that gives the maximum packing factor for a given range of particle sizes and at a given solids content. The calculated optimal bimodal PSD was experimentally obtained in a seeded semi-continuous emulsion polymerization reaction as follows: in the first step, a polymer seed latex was loaded in the reactor and grown, under monomer starved conditions, until a given particle size. At this point a fraction of the same seed was added to the reactor and the feed was continued until the desired particle size distribution and solids content were achieved. The point at which the seed was added again to the reactor and the amount of seed required were determined by the iterative strategy and depended on the competitive growth rate ratio of large and small particles that is an input for the iterative strategy.Implementation of the solution obtained from the iterative strategy, and for the first time in the open literature, led to the production of a coagulum free and stable bimodal latex with 70 wt% of solids content and particle sizes below 350 nm.     

A new experimental method for determining particle capture efficiency in flotation

A single bubble experiment has been developed for the determination of the capture efficiency of particles by bubbles in flotation under well-controlled hydrodynamics and physico-chemical conditions. In a glass column, small single bubbles (d_b=0.22−1.16 mm) are produced in pure water and then rise at their terminal velocity through a suspension consisting of spherical glass particles where bubble–particle capture takes place. The capture efficiency E_capt is calculated as the ratio of the number of particles captured by one bubble to the number of particles present in the volume swept out by this bubble. Images recorded at high optical magnification show that particles slip on the interface, then adhere to air bubbles individually or as aggregates and cover the rear part of bubble surface. The bubble's effective density and interface contamination level are increased by captured particles. As a result, bubble's rising velocity U_b is reduced along the experimental device. By establishing the relationship between capture efficiency E_capt, bubble rise velocity U_b and bubble clean angle θ_clean, a new approach to measure particle–bubble capture efficiency is proposed. This new experimental technique is applied to provide a new set of data for capture efficiency in the case of bubbles with a clean interface. E_capt is found to grow as d_b decreases and d_p increases, within the range between 0.02 and 0.20, which is in the order of magnitude of experimental results of Ralston and Dukhin (1999) as well as of numerical results of Sarrot et al. (2005). These data are favorably compared to numerical modeling of collision efficiency.     

试论沉降法测定颗粒粒度及其分布

颗粒的粒度及其分布显著影响粉末的性质和用途，为了掌握生产中产品的质量，必须对粉末进行粒度分布的检测。详细介绍了沉降法的基本原理，实验方法、步骤和结果处理。试验和生产应用表明，粒度测定的方法多种多样，沉降法以其原理简单、易于操作而被广泛采用。     

On-line automatic optical inspection system for coarse particle size distribution

A new online automatic optical inspection system (OAOIS) using digital image processing has been developed to measure the coarse particle size distribution. The OAOIS is composed of particle separation module, image acquisition module, image processing and analysis module and PC/PLC-based electric control module. Experiments were performed with non-uniform particles (1-100 mm). The particle size distribution, number of the particles, and accumulated weight percentages of particles are obtained by using the developed system. The experimental results show that the repeated precision of accumulated weight percentages is around ± 1%. To improve the reliability and accuracy of the OAOIS measuring results, the linear regression equation is applied to mapping the result of OAOIS to that of traditional net sieving system (TNSS). It has been shown that the developed system has a high accuracy and precision for coarse particle sizing distribution.     

Part I: Dynamic evolution of the particle size distribution in particulate processes undergoing combined particle growth and aggregation

The present study provides a comprehensive investigation on the numerical problems arising in the solution of dynamic population balance equations (PBEs) for particulate processes undergoing simultaneous particle growth and aggregation. The general PBE was numerically solved in both the continuous and its equivalent discrete form using the orthogonal collocation on finite elements (OCFE) and the discretized PBE method (DPBE), respectively. A detailed investigation on the effect of different particle growth rate functions on the calculated PSD was carried out over a wide range of variation of dimensionless aggregation and growth times. The performance (i.e., accuracy and stability) of the employed numerical methods was assessed by a direct comparison of predicted PSDs or/and their respective moments to available analytical solutions. It was found that the OCFE method was in general more accurate than the discretized PBE method but was susceptible to numerical instabilities. On the other hand, for growth dominated systems, the discretized PBE method was very robust but suffered from poor accuracy. For both methods, discretization of the volume domain was found to affect significantly the performance of the numerical solution. The optimal discretization of the volume domain was closely related with the satisfactory resolution of the time-varying PSD. Finally, it was shown that, in specific cases, further improvement of the numerical results could be obtained with the addition of an artificial diffusion term or the use of a moment-weighting method to correct the calculated PSD.