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.     

Determining particle-size distributions from chord length measurements for different particle morphologies

A recently proposed model to determine particle-size distributions (PSDs) from chord length measurements has been applied to different particle morphologies, namely compact, platelet- and rod-shaped particles. To study these systems, chord length distributions (CLDs) were measured at varying particle size and solids concentration for each compound and were subsequently utilized to determine the system-specific parameters. Each model was successfully applied to its respective compound such that the experimental PSDs and model predictions were in good agreement. Moreover, the effect of other variables such as agitation rate and solvent composition was investigated and found to be negligible for the specific systems tested. Finally, potential model optimizations of the general model construct have been studied. Two variants of the CLD compression step, namely principal component analysis and a geometric model have been considered as surrogate models. However, neither of these approaches yielded superior results than the previously proposed approach.     

RADIAL DISPERSION AND BUBBLE CHARACTERISTICS IN THREE-PHASE FLUIDIZED BEDS

The effects of gas and liquid velocities, liquid viscosity and particle size on the radial dispersion coefficient of liquid phase (D_r) and the bubble properties in three-phase fluidized beds have been determined. A new flow regime map based on the drift flux theory in three-phase fluidized beds has been proposed.

In three-phase fluidized beds, D, increases with increasing gas velocity in the bubble coalescing and in the slug flow regimes, but it decreases in the bubble disintegrating regime. The coefficient exhibits a maximum value in the bed of small particles with increasing liquid velocity at lower gas velocities. However, it increases with increasing liquid velocity at higher gas velocities. In two and three-phase fluidized beds of larger particles (6,8 mm), D_r exhibits a maximum value with an increase in liquid viscosity at lower gas velocities, but it increases at higher gas velocities. The mean bubble chord length and its rising velocity increase with increasing gas velocity and liquid viscosity. However, the bubble chord length decreases with an increase in liquid velocity and it exhibits a maximum value with increasing particle size in the bed. The radial dispersion coefficients in the bubble coalescing and disintegrating regimes of three-phase fluidized beds in terms of the Peclet number in the present and previous studies have been well represented by the correlations based on the concept of isotropic turbulence theory.     

Analysis of Filtration Characteristics for Compressible Polycrystalline Particles by Partial Least Squares Regression

Crystal size and morphology have been varied by changing the initial supersaturation ratio and the temperature in reactive crystallization experiments. The influence of the chord length distribution, average cake porosity, and filtration pressure difference on the average cake resistance of polycrystalline particles of an industrially produced aromatic amine has been investigated by means of partial least squares (PLS) regression and sensitivity analysis. Analysis of the results has disclosed that wider chord length distributions as well as lower values of the measured average porosity lead to higher values for the average cake resistance. However, PLS regression and sensitivity analysis have identified the applied pressure difference itself as the most significant parameter influencing the magnitude of the cake resistance. This unexpected behavior is accounted for by compression of the filter cake occurring predominantly in small layers above the filter cloth characteristic for highly compressible cakes.     

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.     

In‐Line Monitoring of Crystallization Processes Using a Laser Reflection Sensor and a Neural Network Model

Laboratory‐scale experiments were carried out for measuring the chord length distribution of different particle systems using a laser reflection sensor. Samples consisted of monodisperse, polydisperse and bimodal FCC catalyst and PVC particles of different sizes, ranging from about 20 to 500 μm. The particles were dispersed in water, forming suspensions with solid‐phase mass fractions ranging from ca. 0.2 % until ca. 30 %. The experimental results, consisting of the particle number counting per chord length class, were used in fitting a neural network model for estimating the mass concentration of particles in the suspension and the volume‐based size distribution, eliminating the effects of suspension concentration and particle shape. The results indicate the feasibility of using such a model as a software sensor in crystallization processes monitoring.     

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.     

低速回转圆筒内磷铵颗粒粒度分布规律研究

利用取样－筛分－称重的实验方法,提出固体颗粒在倾斜回转圆筒内的径向、沿弦长（料面）方向及轴向粒度分布规律,并得出混合粒径固体颗粒在倾斜回转圆筒内发生径向偏析和轴向偏析的结论。研究所用回转圆筒直径为６００ｍｍ,实验物料为不同粒度配比的磷酸一铵。研究结果对内分级内返料喷浆造粒干燥机的设计有指导意义。     

自絮凝酵母颗粒的在线检测与定量表征

引　言固定化细胞可以提高生物反应器的设备生产强度指标, 并且使产物与细胞容易分离, 因此引起人们的极大兴趣[1,2]. 利用细胞的自絮凝功能, 将其作为一种有效的固定化细胞手段, 是近年来提出的新概念, 并在乙醇发酵领域得到了发展[3,4].然而, 细胞自絮凝形成的颗粒一般都具有     

Improved Performance of Nano-Size H-BEA Zeolite Catalysts for the Friedel–Crafts Acetylation of Anisole by Acetic Anhydride

Two 0.1 wt% Pt-porous glass catalysts have been characterized: mesopores formed by finely dispersed colloidal silica inside a macroporous glass, and micropores defined by the porous glass itself. Introducing the so-called range order length parameter L, chord length analysis for L = 5 nm yields specific structure parameters of the metal particles inside both catalyst supports (dispersion, specific metal surface areas, basic arrangement, size distribution and volume fraction). The pore size available basically differs with both pore systems. In the one case an unlimited three-dimensional growth, and, in the other one a limited two-dimensional growth of small Pt-crystallites have been detected. The corresponding particle size distributions f(d) and f(H) have been determined.     

Restoration of particle size distributions from fiber-optical in-line measurements in fluidized bed processes

An in-line probe for the measurement of chord length distributions was employed in fluidized bed granulation processes to investigate the growth behavior and the influence of process parameters. The application of a transformation approach of chord lengths into particles sizes enabled the real-time detection of the evolving particle size distribution, which is a presupposition for the integration into process control systems. Due to the ill-conditioned nature of the transformation algorithm several concepts for noise reduction and stability preservation were investigated and revealed significant synergetic effects for the combination of filtering techniques with discretization parameters. In order to meet the fluctuating, process dependent SNR-levels of the chord length distribution measured by the probe the filtering approaches were required to be self-regulating. Featuring a dynamic noise reduction the power spectral density aided sliding discrete Fourier transform produced the most adequate filtering results.     

Bubble properties and pressure fluctuations in bubble columns

The effects of gas (0.02-0.1 m/s) and liquid velocities (0.0-0.10 m/s) on the bubble properties and pressure fluctuations have been determined in a 0.376 m-IDx 2.1 m-high bubble column. The pressure fluctuations have been analyzed by resorting to the Fractal analysis; the time series of pressure fluctuation signals have been analyzed by means of the Rescaled range analysis and the Hurst exponent has been obtained. The bubble chord length and its rising velocity increase but the Hurst exponent decreases with increasing gas velocity. Whereas, the bubble chord length decreases, but the Hurst exponent increases with an increase in liquid velocity in the continuous bubble column (U_L>0.02 m/s). The Hurst exponent has been found to have a definite relationship with the bubble chord length and its standard deviation.     

Online Particle Size Measurement in Microgel Particle Suspensions: Principles and Data Analysis

If a gelled system is subjected to shearing or the concentration of reactive components is low, microgel particles are formed. Since labile microgel particles with high water capacities can often be found in food systems, and as they are important for the textural properties, particle size measurement is relevant for fundamental research and control of industrial processes. A chord length measurement system was tested for online particle sizing.     

Analysis of FBRM measurements by means of a 3D optical model

Continuous process monitoring is desirable for many particulate processes such as the crystallization of active pharmaceutical ingredients. Only an in-line measurement technique can achieve such a continuous monitoring.A popular in-line measurement technique, which can be applied without dilution, is the focussed beam reflectance measurement (FBRM). However, FBRM is at this point mainly used for qualitative measurements. The measured chord length distribution is different from a particle size distribution. For a quantitative measurement a sound understanding of the measurement principle is necessary. In this paper, an optical model of the FBRM probe and a three-dimensional simulation of the measurement are presented.A three-dimensional particle field is generated with a Monte-Carlo approach. The back scattered light intensity is calculated as a function of the position of the laser beam with respect to this particle field. A vector of scattering intensities is obtained for a given laser path. This vector is processed with the simulated electronics of the Lasentec FBRM system. The output of this processing step is a chord length distribution which can be compared to the output of the Lasentec FBRM system.Simulation studies with mono-disperse polystyrene particles of different sizes and concentrations are conducted and compared to measurements of a Lasentec D600L FBRM probe. With the presented model yet unexplained massive over-estimation of small particles and concentration-dependent changes in the chord length distribution can be described.     

Influence of the heating rate on grain size of alumina ceramics prepared via spark plasma sintering (SPS)

The dependence of grain size on the heating rate has been investigated for alumina ceramics prepared via spark plasma sintering (SPS). For this purpose, the local grain size has been determined via position-dependent microscopic image analysis, using two independent grain size measures (mean chord length and Jeffries grain size). For alumina ceramics prepared with heating rates between 5 and 100 °C/min (pressure 80 MPa, maximum temperature 1300 °C) it is found that for higher heating rates the grain size is smaller. However, the microstructural non-uniformity is so large that any grain size determination that does not take this non-uniformity into account becomes meaningless, because grain size gradients from the specimen periphery to the center are larger than the differences in grain size due to different heating rates. Temperature and pressure gradients are discussed as the most plausible reasons for the microstructural non-uniformity.     

Measurement of particle size and shape by FBRM and in situ microscopy

In this work a model is defined allowing for a rapid calculation of chord length distributions as well as the prediction of in situ microscopy data. Both calculations are done using the same underlying algorithm. The model assumes convex polyhedral particles that are defined by their vertices only, connected by straight lines, but imposes no further restrictions on particle geometry. Due to its speed, the model can easily be used for the prediction of experimental data from in situ monitoring tools based on whole particle populations, also with non-constant shape. The model has been verified using in situ microscopy to characterize a population of disc shaped particles.The applications of the model are focused on crystallization processes, but are not limited to these. Several relations between data measured by in situ instruments and the underlying multidimensional particle size distribution have been derived. The model is used extensively in a method that is presented allowing for the calculation of bidimensional growth rates from Focused Beam Reflectance Measurement or in situ microscopy measurements.     

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.     

Local hydrodynamic properties of gas phase in an internal-loop airlift reactor

The local hydrodynamic properties of the gas phase in an internal-loop airlift reactor were investigated in this study. The hydrodynamic properties including gas holdup, bubble velocity and bubble chord length were measured by dual electrical resistivity probes. The chord length distribution was then transformed to the bubble size distribution by modeling the bubbles as ellipsoids. It was found that the gas holdup increased with decreasing bubble velocity. In addition, most bubbles tended to rise along the riser central axis. Thus, the gas holdup in the axis was higher. The bubble size, bubble velocity and gas holdup were relatively constant in the axial direction of the riser except in the zones near the gas sparger and the gas–liquid separator. The bubble velocity became slower when the bubbles approached the gas–liquid separator. Moreover, the bubble size and bubble velocity for the three-phase system were relatively insensitive to the radial direction compared to those for the two-phase system. It was also found in this study that the bubble rise velocity and bubble size for the three-phase system were lower than that for the two-phase system. However, the gas holdup for the three-phase system were higher than that for the two-phase system due to bubble breakage caused by the solid particles.     

Small-angle X-ray study of particulate reinforced composites

Small-angle X-ray scattering technique can be used to quantify the microvoids structure within a particulate reinforced composite. An expression for the correlation function of three-phase systems has been derived in terms of the correlation function of the individual phases. By using this expression and the scattered intensities from the damaged and the undamaged composites; it has been show that the volume fraction and the chord length of the microvoids can be obtained, provided no damage occurs to the reinforcement particles. In cases where the microvoids are preferentially oriented within the composites, an approximation scheme based on a linear transformation method has also been developed to measure the aspect ratio of the microvoids provided the volume fraction of these microvoids is much smaller than the other two phases.