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.     

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.     

Estimation of particle size distributions from focused beam reflectance measurements based on an optical model

A popular in situ particle characterization technique, which can be applied without dilution, is the focused beam reflectance measurement (FBRM^®). The FBRM probe measures a chord length distribution (CLD) which is different from a particle size distribution (PSD). In order to compare results obtained by an FBRM probe with other measurement technologies such as laser diffraction, it is necessary to reconstruct the PSD from a measured CLD. For this reconstruction a measurement model and an inversion procedure are required. Most FBRM models presented in the literature assume that an FBRM records a geometric chord which can be deduced from a two-dimensional projection of the particle silhouette. In previous work [Kail, N., Briesen, H., Marquardt, W., 2008. Analysis of FBRM measurements by means of a 3D optical model. Powder Technology 185 (3), 211-222] it has been demonstrated that FBRM data show significant deviations from this geometric model. Consequently, an estimation of a PSD using such a geometric FBRM model will fail. A novel FBRM model is developed in this work. This model imitates the chord discrimination algorithm used in a Lasentec D600L FBRM system and takes the intensity profile of the laser beam and the optical aperture of the probe into account. The model is ideally suited for the estimation of a PSD from a measured CLD using a sequential, linear inversion routine, as proposed in this work. The novel FBRM model and the inversion procedure are evaluated using small, mono-disperse polystyrene beads, large ion-exchanger beads, and α-lactose-monohydrate particles. The applicability of the FBRM for PSD measurements is discussed on the basis of these results.     

Variation of particle size and its distribution during the synthesis of silicalite-1 nanocrystals

Recent studies imply that the external surface area of the nanozeolite product may, at least in some cases, be related to the average size of the particle population participating in aggregative nucleation, a population which itself is a product of aggregation of even smaller primary nanoparticles. This possibility puts more importance on our understanding of the variation of particle size and its distribution during the crystallization of zeolite nanoparticles. Variation of the particle size and PSD during nanoparticle silicalite-1 crystallization was followed with respect to time by a laser light scattering device with a scattering angle of 173°, for several starting synthesis compositions. Effects of varying TPAOH and water contents in the starting synthesis mixtures on the variation with time of the particle sizes and PSDs, especially across the two distinct aggregation events, were investigated. The products were also analyzed by XRD and AFM. Parallel to the decrease in the average particle size of the final product population with increasing alkalinity and organic template content, its PSD was observed to become narrower too. A reversal in the dependence on TPAOH content, of the average size of the population formed by aggregation, with respect to that of the population participating in aggregation, was observed across both aggregation events, implying that smaller particles aggregated to form larger particles, while larger particles aggregated to form smaller particles during these processes, and this was also seen from the AFM images, to be reflected to the surface features of the final product particles.     

乙氧基镁催化剂粉末粒度及粒度分布测定的研究

用乙醇做分散介质,用激光粒度测定仪测定四个乙氧基镁催化剂粉末试样的粒度及粒度分布,测试快速、准确。试验结果显示乙氧基镁（德国）催化剂粉末粒度最小,粒度分布集中,在四个样品中质量最好,试验结果令人满意。     

Particle size analysis by transmission fluctuation spectrometry with band-pass filters

The transmission fluctuation spectrometry (TFS) is a recently-developed method for real-time, online/inline particle analysis in two-phase flows, whereby the particle size distribution (PSD) and particle concentration can be measured simultaneously. This study presents a new technique of data processing to the fluctuating transmission signal. Instead of low-pass filters, band-pass filters are employed to improve the resolution of the measurement on particle size distribution. Based on the layer model, an analytical expression of the spectrum of the fluctuating transmission through a monolayer is derived and hence the spectrum of the fluctuating transmission through a 3-dimensional suspension is formulated. The comparison between simulation and theory at low concentrations shows a satisfactory match. Measurements on a mono-modal suspension are presented. It is found that the measurements using band-pass filters are of better resolution in the PSD than those with low-pass filters.     

焦油渣含量及其粒度分布测定方法的研究

采用离心———抽提相结合的方法测定焦油渣含量,并运用激光粒度分析技术测定焦油渣粒度分布。结果表明,焦油中焦油渣以<10μm微粒组成为主,占总渣量88%～97%。     

白云石粒度级配对平板玻璃熔制的影响

白云石是平板玻璃生产中的主要原料,它的颗粒度级配对本合料的质量存在明显的影响。应用高温熔制,澄清,均化实验以及Ｘ－射线衍射分析等手段研究具有不同白云石颗粒级配的配合料的熔制过程,从中找出优化的白云石颗粒级配方案,并从理论上加以探讨。     

Effect of quantity and size distribution of calcite filler on the quality of water borne paints

Calcite is the most widely used mineral filler in paint formulations. It provides not only a decrease in the cost of paint but also modifies some physical paint properties. Although some properties of calcite such as particle size distribution and refractive index are not comparable in quality to TiO₂, calcite can improve the distribution of TiO₂ via its interaction with TiO₂ particles. In this study, calcites of different size distributions are used as filler in the architectural waterborne, acrylic based paint recipes. The quality of paints was compared to properties based on both wet and dry paint such as viscosity, density, opacity, gloss, scrub resistance and Buchholz hardness. Examination of the results identified an optimum quantity and size distribution of calcite for the paint recipe. The second series of this study involved substitution possibilities of TiO₂ with calcite using seven different paint formulations. Phase images of the dry paint films obtained using “Atomic Force Microscopy” (AFM) showed the extent of distribution and aggregation of particles for each formulation on the paint surface. The overall experimental results revealed that the use of TiO₂ can be decreased up to 4% by replacement of calcite with an optimum size distribution that was also supported by AFM measurements.     

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.     

How the coarse fraction influences the microstructure and the effective thermal conductivity of alumina castables – An experimental and numerical study

This study investigates the particle size distribution's effect on the microstructure and effective thermal conductivity (ETC) of alumina castables. The ETC was measured by the transient plane source method and predicted numerically based on a two-scale model describing the structure on a fine and coarse scale. The prediction considered particle and pore size distributions, porosity (around 20%) and grain morphology. The microstructure was investigated by scanning electron microscopy. For a constant fines content, increasing the coarse grain fraction while decreasing the medium fraction enhanced sintering of the matrix. Small pores (≤250 nm) increased the sintering activity. The densest castable contained the most small pores. The particles’ and pores’ contributions to the sintering activity led to intensified microcracking and a decreased ETC. The numerical model did not consider constituents ≤500 nm like the small pores and microcracks and the calculated ETC values consequently deviated from the measured values.     

Characterization of heterogeneity in concrete and cement by mechanical spectroscopy

We propose a method to obtain the degree of heterogeneity of samples of cement or concrete due to the presence of cracks, bubbles or simply the native ingredients of the material. A number of samples are prepared in a cylindrical shape, and their transverse vibration resonant frequencies are measured. A given mode of oscillation will correspond to slightly different frequencies in different samples due to the random nature of the system. For example, for a given mixing formula, the ratio of sand to cement may be known, but the precise position of sand grain cannot be determined. We studied the statistical distributions of frequencies for each mode and found that there exists a relationship between the width of the probability functions and the degree of heterogeneity.     

Measurement of number and size distribution of particles emitted from a mid-sized transportation multipoint port fuel injection gasoline engine

This study was carried out to characterize the engine-exhaust particulate emissions from a typical multipoint port fuel injection gasoline engine used in transportation sector. Though gasoline engine showed no visible tail pipe emissions yet its particle concentrations were comparable to mineral diesel, particularly at high engine loads. Average sizes of particles emitted in gasoline exhaust are found to be way smaller than particles emitted in diesel exhaust under similar operating conditions. The peak particle concentrations for mineral diesel never go below 40 nm size however for gasoline engine, it was as low as 20 nm for most engine operating conditions. Within a very limited operating range, gasoline engine performance was superior to its diesel counterparts in terms of particulate size and number distribution however it deteriorates very quickly as soon as the fuel-air mixture becomes closer to stoichiometric ratio, typically under high engine load and speed conditions.     

High‐Solid‐Content Emulsions of PVC: Scale‐Down of an Industrial Process for Enhanced Understanding of Particle Formation Part 2: Preliminary Analysis of Seed Production

A scale‐down study of an industrial reactor for the production of polyvinyl chloride (PVC) via an emulsion polymerization process was performed in order to understand the source of batch‐to‐batch variations in product quality. In Part 2 of this series of three papers, it is demonstrated that a large excess of base is required to control the particle size distribution of the seed process. Although differences exist between the critical micelle concentration and the surface area occupied by a surfactant molecule for linear and branched isomers of the surfactant sodium dodecyl benzene sulfonate, the characteristics of the molecules from different suppliers were reasonably similar.     

High‐Solid‐Content Emulsions of PVC: Scale‐Down of an Industrial Process for Enhanced Understanding of Particle Formation Part 1: Introduction and Scale‐Down

A scale‐down study of an industrial reactor for the production of polyvinyl chloride (PVC) via an emulsion polymerization process was carried out in order to understand the source of batch‐to‐batch variations in product quality. In Part 1, an analysis of the plant is presented and the industrial recipe scaled down to a pilot‐scale reactor. In the following Parts 2 and 3 a systematic analysis of the main process parameters revealed that particle generation and stabilization actually occurred in a manner slightly different from what was thought at the production site.