Particle and droplet size analysis from chord distributions (original) (raw)
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Particle and droplet size analysis from chord measurements using Bayes' theorem
Powder Technology, 2001
A method of predicting sphere diameter distributions from chord size data is presented and evaluated. This is the probability Ž . apportioning method PAM2 and is significantly improved on a previous presentation. It assumes that the particles or droplets are near spherical and cut randomly by a sensor. For an assumed particle diameter distribution, Bayes' theorem is used to calculate hit probabilities for each particle diameter. The diameter distribution is then recalculated and the process is repeated until there is no significant further change. Using numerical simulations, PAM2 is shown to be quite accurate and robust for a number of different types of size distribution. q
Obtaining Particle Size Distribution from Chord Length Measurements
Particle & Particle Systems Characterization, 2006
The Lasentec focused-beam reflectance measurement (FBRM) is becoming a more popular technique to measure particle size on-line in different applications. The FBRM uses a focused beam of laser light that scans across particles passing in front of the probe window to measure a chord length distribution (CLD). Compared with CLD information, the particle size distribution (PSD) is more useful because it is directly related to product quality and process productivity. However, it is not straightforward to convert a measured CLD into its corresponding PSD accurately due to the lack of a theoretical analysis for non-spherical particle systems. In this paper, firstly a general model to translate a PSD into its corresponding CLD is given for different shapes including spherical, ellipsoidal and more general non-spherical particles. Then an iterative inversion method is developed to obtain the PSD from a measured CLD. Finally, effectiveness of the proposed PSD-CLD model and iterative inversion method has been extensively validated by experiments.
Chord length distribution to particle size distribution
AIChE Journal, 2016
A simple model is presented to extract the Particle Size Distribution (PSD) from the Chord Length Distribution (CLD) measured using a Focused Beam Reflectance Measurement (FBRM) probe. The model can be implemented using simple spread sheeting tools and does not require the description of additional parameters as opposed to previous models. The model was validated for two systems consisting of spherical ceramic beads by comparing model predicted PSD against the PSD obtained through image analysis (IA). Then, the model was evaluated by considering various systems consisting of irregularly shaped particles (sand/zinc dust/plasma alumina). Model predictions accurately predicted the mean but over-predicted the variance of the PSD in comparison with the PSD obtained from IA. However, overall, a reasonable agreement was observed. Finally, the model was shown to be accurate in predicting PSD in comparison with the measured PSD for systems of practical relevance such as for paracetamol and p-aminophenol crystals.
Chemical Engineering Science, 2015
Information about size and shape of particles produced in various manufacturing processes is very important for process and product development because design of downstream processes as well as final product properties strongly depend on these geometrical particle attributes. However, recovery of particle size and shape information in situ during crystallisation processes has been a major challenge. The focused beam reflectance measurement (FBRM) provides the chord length distribution (CLD) of a population of particles in a suspension flowing close to the sensor window. Recovery of size and shape information from the CLD requires a model relating particle size and shape to its CLD as well as solving the corresponding inverse problem. This paper presents a comprehensive algorithm which produces estimates of particle size distribution and particle aspect ratio from measured CLD
Chemical Engineering Science, 2016
Efficient processing of particulate products across various manufacturing steps requires that particles possess desired attributes such as size and shape. Controlling the particle production process to obtain required attributes will be greatly facilitated using robust algorithms providing the size and shape information of the particles from in situ measurements. However, obtaining particle size and shape information in situ during manufacturing has been a big challenge. This is because the problem of estimating particle size and shape (aspect ratio) from signals provided by in-line measuring tools is often ill posed, and therefore it calls for appropriate constraints to be imposed on the problem. One way to constrain uncertainty in estimation of particle size and shape from in-line measurements is to combine data from different measurements such as chord length distribution (CLD) and imaging. This paper presents two different methods for combining imaging and CLD data obtained with in-line tools in order to get reliable estimates of particle size distribution and aspect ratio, where the imaging data is used to constrain the search space for an aspect ratio from the CLD data.
arXiv (Cornell University), 2018
The in situ measurement of the particle size distribution (PSD) of a suspension of particles presents huge challenges. Various effects from the process could introduce noise to the data from which the PSD is estimated. This in turn could lead to the occurrence of artificial peaks in the estimated PSD. Limitations in the models used in the PSD estimation could also lead to the occurrence of these artificial peaks. This could pose a significant challenge to in situ monitoring of particulate processes, as there will be no independent estimate of the PSD to allow a discrimination of the artificial peaks to be carried out.
Estimation of particle size distribution from cross-sectional particle diameter on the cutting plane
Advanced Powder Technology, 2010
A particle size distribution (PSD) estimation method based on light-scattering properties was validated on experimental visible/near-infrared scattering spectra of polystyrene suspensions, with a nominal particle size ranging from 0.1 to 12 μm in diameter. On the basis of μ s and g spectra extracted from double integrating sphere measurements, good PSD estimates were obtained for particles ≥1 μm. The particle volume fraction estimates in the case of μ s were close to the target concentrations, although influenced by small baseline fluctuations on the spectra. For submicrometer particles, on the other hand, the non-oscillating μ s spectra lack discriminating power, resulting in erroneous PSD estimates. The reduced scattering coefficient spectra (μ s ′) were found less useful for particle size estimation as they lack a characteristic shape, causing an over-or underestimation of the distribution width. In summary, the estimation routine proved to deliver PSD estimates in line with the reference measurements for micrometer-sized or larger particles based on their μ s and g scattering spectra. Additional validation on more polydisperse samples forms the next step before going to bimodal PSD estimates.
Determination of Particle Size Distribution by Par-Tec® 100: Modeling and Experimental Results
Particle & Particle Systems Characterization, 1998
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.
Comparison of Particle Size Distributions Measured Using Different Techniques
Particulate Science and Technology, 2005
In this article, particle size distributions (PSDs) measured by different techniques, including image analysis (IA), laser diffraction (LD), ultrasonic attenuation spectroscopy (UAS), and focused-beam reflectance measurement (FBRM), are compared for spherical glass beads and nonspherical silica flakes. It is shown that particle shape strongly affects the results obtained by different techniques. For spheres, the PSDs obtained by IA, LD, and UAS agree well. There is no consistent result among different particle measurement techniques for nonspherical particles. The conversion between PSDs obtained by IA, LD, and UAS has been based on particle shape factors. Caution must be exercised when a measured chord length distribution (CLD) is used to indicate the PSD during a process because the CLD result obtained by FBRM is complex, depending not only on the PSD, but also on particle optical properties and shape. Keywords Particle size distribution (PSD), image analysis (IA), laser diffraction (LD), ultrasonic attenuation spectroscopy (UAS), focused-beam reflectance measurement (FBRM), chord length distribution (CLD)