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.     

Measuring the particle size of a known distribution using the focused beam reflectance measurement technique

The accuracy of the focused beam reflectance measurement (FBRM) probe, which measures a chord length distribution, from Mettler-Toledo Lasentec^® has been explored. A particle video microscope (PVM) probe, which provides in situ digital images, was used as a direct visual method to test the reliability of the FBRM results. These probes can provide in situ particle characterization at high pressures. The FBRM has been used to study emulsions and ice and clathrate hydrate formation. The ability of the FBRM to accurately characterize unimodal and bimodal distributions of particles and droplets and to measure agglomeration events was investigated. It was found that while the FBRM can successfully identify system changes, certain inaccuracies exist in the chord length distributions. Particularly, the FBRM was found to oversize unimodal distributions of glass beads, but undersize droplets in an emulsion and was unable to measure full agglomerate sizes. The onset of ice and hydrate nucleation and growth were successfully detected by the FBRM, but quantitative analysis of the particle and agglomerate sizes required simultaneous PVM measurements to be performed.     

Determination of non-spherical particle size distribution from chord length measurements. Part 1: Theoretical analysis

In this paper, extensive theoretical studies are described on two important issues in translating a chord length distribution (CLD) measured by FBRM instrument into its particle size distribution (PSD) including PSD-CLD and CLD-PSD translation models for general non-spherical particles. Analytical solutions to calculate the PSD-CLD models for spherical and ellipsoidal particles are developed. For non-spherical particles, a numerical method is given to calculate the PSD-CLD model. The iterative non-negative least squares (NNLS) method is proposed in the CLD-PSD model, because of its many advantages converting measured CLD into its PSD, such as insensitivity to measurement noise and particle shape. The effectiveness of the proposed methods is validated by extensive simulations.     

Determination of non-spherical particle size distribution from chord length measurements. Part 2: Experimental validation

In this paper, the theory on the translation of a measured chord length distribution (CLD) into its particle size distribution (PSD), which was developed in the first part of this study [Li and Wilkinson, 2005. Determination of non-spherical particle size distribution from chord length measurements. Part 1: theoretical analysis. Chemical Engineering Science 60, 3251-3265], has been validated using experimental results. CLDs were measured using the Lasentec focused beam reflectance measurement (FBRM) with three different materials, spherical ceramic beads and non-spherical plasma aluminium and zinc dust particles. Meanwhile, the particle shape and PSD of each material were also investigated by image analysis (IA). Comparison of the retrieved PSDs with the measured PSDs by IA shows that the PSD can be retrieved from a measured CLD successfully using the proposed iterative nonnegative least squares (NNLS) method based on the PSD-CLD model.     

Modelling particle disruption of an organic fine chemical compound using Lasentec focussed beam reflectance monitoring (FBRM) in agitated suspensions

The focussed beam reflectance monitoring (FBRM) instrument developed by Lasentec is a ‘powerful’ tool used as an ‘in-situ’ particle monitoring technique for in-line real-time measurement of particle size. This technique was successfully used to monitor particulate attrition and breakage of an organic fine chemical in a turbulently agitated suspension. The great advantage of using the FBRM technique is that the change in the crystal size distribution (CSD) for different particle size classes (fine, intermediate and coarse) can be monitored as a function of time. The attrition rates can be calculated to produce a model for the disruption kernel for the organic compound. The shift in the CSD that was observed with an increase in the specific power input was found to be largely due to micro-attrition effects rather than particle breakage (splitting).     

Comparison of dielectric constant meter with turbidity meter and focused beam reflectance measurement for metastable zone width determination

This work demonstrates a detailed process analytical technology (PAT) comparison study of dielectric constant measurement with turbidity measurement and focused beam reflectance measurement (FBRM) in detecting phase transitions during crystallization of three model solutions, namely stearic acid–ethyl acetate, paracetamol–ethanol and carbamazepine–methanol. The cloud and clear points determined by the dielectric constant measurement are found to be in close agreement with those obtained from the other two well-established PAT tools. A calibration technique can be further applied on the dielectric constant to improve the accuracy of the cloud point detection. The results have shown that the dielectric constant meter can be reliably used for metastable zone width (MZW) determination. This study opens new opportunities for the use of the dielectric constant meter as a simple and inexpensive alternative PAT tool for process monitoring of solution crystallization.     

Focused beam reflectance measurement for monitoring the extent and efficiency of flocculation in mineral systems

Focused beam reflectance measurement (FBRM), where a scanning laser focused through a sapphire window measures real‐time reflected chord distributions without solids dilution, is attractive for characterizing flocculation performance. An enhanced measurement principle in new FBRM instruments has implications for flocculation studies, demonstrated using hematite in synthetic Bayer liquor. Comparisons of previous (M500) and new (G400) instruments were complicated by the impact of their different physical dimensions upon flocculation hydrodynamics, but the G400 clearly measured larger chords. The original measurement principle based on a reflected intensity threshold counts large low‐density aggregates as multiple chords; in contrast, the change to “edge detection” (very low threshold) is more likely to see a single chord, an advantage for studying mineral systems (aggregates often >500 µm). The G400 also captures bimodal character in unweighted chord distributions, producing distinct peaks for aggregates and fines after suboptimal flocculation; such peaks are rarely well resolved in older FBRM. © 2013 American Institute of Chemical Engineers AIChE J, 60: 251–265, 2014     

Effect of particle concentration and turbidity on particle characterization using digital holography

In this paper, the effect of particle concentration and turbidity on the performance of inline transmission based digital holography (DH) for particle characterization is studied. The results are analyzed based on the two metrics, i.e., detection efficiency and mean size of the particle population. Two sample depths are analyzed to quantify the effect of particle concentration. Considering 50% detection efficiency as a threshold, it is concluded that DH works well up to 0.1% (v/v) and 0.2% (v/v) particle concentrations for 10 mm and 5 mm sample depths, respectively. From the turbidity tests, it is found that DH works well up to 150 nephelometric turbidity unit (NTU) turbidity level for 10 mm sample depth.     

Comparison of external bulk video imaging with focused beam reflectance measurement and ultra-violet visible spectroscopy for metastable zone identification in food and pharmaceutical crystallization processes

The purpose of the paper is twofold: it describes the proof of concept of the newly introduced bulk video imaging (BVI) method and it presents the comparison with existing process analytical technologies (PAT) such as focused beam reflectance measurement (FBRM) and ultra-violet visible (UV/vis) spectroscopy. While the latter two sample the system in small volumes closely to the probe, the BVI approach monitors the entire or large parts of the crystallizer volume. The BVI method is proposed as a complementary noninvasive PAT tool and it is shown that it is able to detect the boundaries of the metastable zone with comparable or better performance than the FBRM and UV/vis probes.