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.     

Chord length characterization using focused beam reflectance measurement probe - methodologies and pitfalls

The impact of the solid concentration and refractive index of dispersing medium on the FBRM measurement of chord length and particle counts were investigated using the PVC (polyvinylchloride) particle systems. It was found that the chord length increased with the solid concentration in the diluted region, but decreased as the concentration became greater than 1.1%. The total particle counts were found to increase initially with the solid concentration, tapering off at high concentrations. The measured counts of small chords (1 μm-50 μm) were found to increase linearly with the solid concentration, those of the large chords increased with the concentration initially and leveled off (50 μm-200 μm) or decreased (200 μm-500 μm) with further increase of concentration. The impact of the refractive index of the dispersing medium on the FBRM measurement was also investigated, the result of which was corroborated by microscopy studies. Comparison between the FBRM and other sizing techniques revealed that when appropriate weighting factors were applied, good agreement could be achieved between the median average values of the chord length and particle size distributions.     

Kinetics of structure II gas hydrate formation for propane and ethane using an in-situ particle size analyzer and a Raman spectrometer

The kinetics of structure II gas hydrates, formed from pure propane and a mixture of propane and ethane, were investigated and intrinsic rate constants were regressed from the experimental data. The experiments were conducted in a semi-batch stirred tank reactor equipped with an in-situ particle size analyzer and connected to an external Raman spectrometer. Experiments were conducted with pure propane at temperatures ranging from 274 to 276 K and pressures ranging from 0.39 to 0.43 MPa. The intrinsic rate constant for ethane in structure II was subsequently regressed from experimental data on the formation of hydrates formed from an equimolar mixture of propane and ethane at 274 K and 0.35 MPa. Raman spectroscopy was used to verify that ethane was present only in the large sII cavity.     

On the role of an unconventional rigid rodlike cationic surfactant on the styrene emulsion polymerization. Kinetics, particle size and particle size distribution

An unconventional amphiphile (1-[ω-(4′-methoxy-4-biphenylyloxy)octyl]pyridinium bromide, PC8) was used as surfactant in the emulsion polymerization of styrene. At low surfactant concentration (6, 12 or 36 mmol l⁻¹), curves of polymerization rate versus conversion obeyed the typical behavior characterized by intervals I, II and III. However, at high concentration (48 or 72 mmol l⁻¹) the interval II was not observed. The particle size distribution curves showed two families of polymer particles, indicating the participation of at least two mechanisms of particle formation, one being the simple micellar nucleation and the other probably the coagulative nucleation of precursor particles. The latter was considered to occur during the nucleation interval.     

Hydrate formation from high water content-crude oil emulsions

Methane hydrate formation and dissociation studies from high water content ( water) - crude oil emulsions were performed. The hydrate and emulsion system was characterized using two particle size analyzers and conductivity measurements. It was observed that hydrate formation and dissociation from water-in-oil (W/O) emulsions destabilized the emulsion, with the final emulsion formulation favoring a water continuous state following re-emulsification. Hence, following dissociation, the W/O emulsion formed a multiple o/W/O emulsion (60 vol% water) or inverted at even higher water cuts, forming an oil-in-water (O/W) emulsion (68 vol% water). In contrast, hydrate formation and dissociation from O/W emulsions ( water) stabilized the O/W emulsion.     

Measurement methods of particle size distribution in emulsion polymerization

The particle size distribution of polymer always develops in emulsion polymerization systems, and certain key phenomena/mechanisms as well as properties of the final product are significantly affected by this distribution. This review mainly focuses on the measurement methods of particle size distribution rather than average particle size during the emulsion polymerization process, including the existing off-line, on-line, and in-line measurement methods. Moreover, the principle, resolution, performance, advantages, and drawbacks of various methods for evaluating particle size distribution are contrasted and illustrated. Besides, several possible development directions or solutions of the in-line measurement technology are explored     

Numerical study on particle size distribution in the process of preparing ultrafine particles by reactive precipitation

Based on the population balance and mass balance in a reactive precipitation process, a numerical simulation model was developed to predict the particle size distribution (PSD) in the reactive precipitation process. The precipitation system of BaCl₂ with Na₂SO₄ to prepare BaSO₄ in aqueous solution was adopted to obtain ultrafine particles in a stirred precipitation reactor and the particle size distribution and the morphology of the particle were observed under transmission electron microscope. It was illustrated by the experimental observation of the micrographs of BaSO₄ particles obtained that apparent agglomeration occurred between the particles, which phenomenon must be taken into consideration in PSD modeling. The population balance equation was calculated by discretization method to obtain particle number and particle size distribution. By implementing the model, the reactive precipitation process in a batch reactor including reaction, nucleation, growth and agglomeration was simulated. The simulation results were validated by the experimental data of BaSO₄ precipitation. Further analysis was endeavored to explore the effects of some important factors such as the supersaturation degree and agglomeration on the evolution of the volume-based characteristic particle size and the variance of volume-based characteristic size of the particles. It was depicted that particle size and particle size distribution are controlled by the supersaturation degree and agglomeration between the particles. Stemming from the analysis in the context, the disciplinarian of the influences of these factors and the method for controlling particle size distribution were presented for the reactive precipitation process.     

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.     

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.     

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.     

Monitoring the particle size and shape in the crystallization of paracetamol from water

In this work, a technique capable of restoring bidimensional particle size distributions from images of the particles in suspension is applied to the seeded cooling crystallization of paracetamol from water. The effects of cooling rate and stirring rate on the final particle size and shape are studied and the average growth rates along different directions of particles are found to be strongly dependend on supersaturation. This observation is in line with previous studies, though in this work it has been established for the first time using populations of particles. The technique was capable of quantifying changes in particle size and shape, indicating particle sizes and shapes that correlated well with observations from electron microscopy images.     

Inferential closed-loop control of particle size distribution for styrene emulsion polymerization

In this work, a new control strategy for controlling the particle size distribution (PSD) in emulsion polymerization has been proposed. It is shown that the desired PSD can be achieved by controlling the free surfactant concentration which in turn can be done by manipulating the surfactant feed rate. Simulation results show that the closed-loop control of free surfactant concentration results in a better control of PSD compared to open-loop control strategy, in presence of model mismatch and disturbances. Since the on-line measuring of ionic free surfactant concentration is difficult, conductivity which is related to it is measured instead and used for control purposes. The closed-loop control of conductivity also results in a better control of PSD compared to open-loop control strategy, but its performance is not as good as controlling free surfactant concentration in presence of model mismatch.     

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.     

A neural network-based soft sensor for particle size distribution using image analysis

Many industrial processes require on-line measurement of particle size and particle size distribution for process monitoring and control. The available techniques for reliable on-line measurement are, however, limited. In this paper, based on the captured surface images of randomly disarranged ore particles, the image uniformity was characterized. Particle size distribution was then investigated by applying a neural network-based modeling with the obtained image uniformity. The proposed soft sensor provides an improved prediction model and can be used for real time measurement of particle size distribution in the industrial operations.     

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.     

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.     

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.     

Alkali-activated waste ceramics: Importance of precursor particle size distribution

The waste ceramics belongs to wide range of aluminosilicate materials which can be alkaline-activated to geopolymer cement – possible “green” alternative to conventional Portland cement. The studied ceramic material is generated during the size adjustment of ceramic building blocks by means of grinding. It means that most of the material is very fine, but it contains also some larger shards. This ceramic powder was used as geopolymer precursor “as received” and after removal of particles retained on 1, 0.5 and 0.125 mm sieves. These four types of precursor were activated by sodium silicate (SiO₂/Na₂O = 1) solution. The prepared mortars were tested for strength, basic physical properties, transport parameters and characterized by help of XRD and thermal analysis. It was found that the best mechanical performance provided the precursor after removal of particles retained on 0.5 mm sieve thanks to the highest geopolymerization rate. The presence of coarser particles in precursor gave rise to porosity, what consequently influenced transport parameter of geopolymers towards the lower thermal conductivity and faster moisture transport.     

Internal particle size distribution of biofuel pellets

Several methods for disintegration of biofuel pellets were tested and compared for their ability to break up the pellets into the original particles of the raw material. Analyses performed on softwood pellets and straw pellets concluded that wet disintegration in water at ambient temperature is insufficient for a determination of the internal particle size distribution of wood- and straw pellets. When the wet disintegration was performed with water heated to the boiling point and coupled with mechanical disintegration in terms of stirring a more complete disintegration of the pellets was obtained. Based on the results obtained in the initial study a round robin was set up including six European laboratories where the selected method was tested. In the round robin test the method combining heated water and stirring of the slurry was tested on solid biofuel pellets produced of comminute straw, deciduous wood and coniferous wood respectively. With the method a satisfactory disintegration was obtained of all three types of pellets.Further wet disintegration of coniferous pellets was compared to a dry disintegration using a hammer mill. The dry disintegration of the coniferous pellets resulted in smaller particle sizes compared to the wet disintegration using heated water and stirring of the slurry indicating a further disintegration of the original particles in the hammer mill process.Overall the wet disintegration combined with mechanical impact was found to be the most suitable method for disintegration of solid biofuel pellets. Combined with sieving analysis the method gives realistic image of the internal particle size distribution of solid biofuel pellets.