Chord Length Distribution Research Articles

Monitoring Temperature Effect on the Polymorphic Transformation of Acitretin Using FBRM−Lasentec

Polymorphs have a tendency to undergo solution-mediated transformation from one form to another during crystallization. Various in situ techniques explored for understanding the crystallization process include, Raman spectroscopy, near-infrared spectroscopy (NIR), and focused beam reflectance measurement (FBRM). Both Raman and NIR techniques are used for polymorphic identification. FBRM has gained much popularity as an ideal technique for studying and improving particle size. The crystallization process can be improved using FBRM by studying the meta-stable zone, temperature of crystallization, and primary and secondary nucleation. This FBRM technique offers a quick and time-saving approach along with insight on the particle size of the product. The same technique can be used during scale up to understand and monitor crystallization processes. This report describes a different application of FBRM, which involves monitoring the changes in chord length distribution as a result of polymorphic transformation associated with temperature during crystallization. Needle-shaped Form III of acitretin undergoes solvent-mediated transformation to cube-shaped Form II. This polymorphic transformation is monitored by monitoring the chord length distribution.

Study of phosphoric acid crystallization using a focused beam reflectance measurement method

AbstractA way for restoring the crystal size distributions (CSD) from measured chord length distributions (CLD) was reported in this paper. The kinetics of phosphoric acid crystallization process was investigated in cooling mode using focused beam reflectance measurement (FBRM) and digital photo technique. In order to restore the CSD from measured CLD and verify the reliability of FBRM data, digital photo technique in real time and optical microscope were applied in large crystal size and small range, respectively. Results indicated a converting constant A existed between CLD and CSD when crystal growth follows size‐independent growth (Mcabe's ΔL law) law. It was verified by Malvern particles size analysis method. The converting constant A varied with crystal morphology. The crystal growth order increased with the stirring increasing speed during phosphoric acid crystallization process. The trend was especially notable at higher speed situations. It can illustrate that the state of phosphoric acid hemihydrate crystal growth was controlled by both diffusion and surface‐integration with the increasing stirring speed. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Small-angle X-ray scattering of two-phase systems: significance of polydispersity

Evaluation of the small-angle X-ray scattering of two-phase systems leads to the determination of the Porod lengthlpand the correlation lengthlc. In dilute systems, the parameter κl=lc/lp− 1 is a measure of the polydispersity of the chord lengthslwithin the dilute phase, which depends on the size distribution and the shape of the particles forming this phase. As an example, the change of κlwith the size distribution is calculated for spheres and spheroids. For dense two-phase systems, κldepends not only on the polydispersities of the chord lengthsl1andl2of the two phases but also on the spatial order in the system. This is demonstrated by examples related to microemulsions. The appendix contains a short discussion on the relationship between chord-length distributions and Bertrand's paradox.

Cellular Statistical Models of Broken Cloud Fields. Part II: Comparison with a Dynamical Model and Statistics of Diverse Ensembles

Abstract Cellular statistical models are designed to provide a simple two-parameter characterization of the structure of broken cloud fields described through distributions of cloud fraction and of chord lengths for clouds and clear gaps. In these analytical models cloud fields are assumed to occur on a semiregular grid of cells (which can be vaguely interpreted as atmospheric convective cells). In a simple, discrete cell model, cell size is fixed and each cell can either be completely filled with cloud with some probability or remain empty. Extending the discrete model to a continuous case provides more realism by allowing arbitrary cloud and gap sizes. Here the continuous cellular model is tested by comparing its statistics with those from large-eddy simulations (LES) of marine boundary layer clouds based on case studies from three trade-cumulus field projects. The statistics largely agree with some differences in small sizes approaching the LES model grid spacing. Exponential chord-length distributions follow from the assumption that the probability of any cell being cloudy is constant, appropriate for a given meteorological state (narrow sampling). Relaxing that assumption, and instead allowing this probability to have its own distribution, leads to a power-law distribution of chord lengths, appropriate to a broader sample of meteorological states (diverse sampling).

Confocal Laser Scanning Microscopy Method for Quantitative Characterization of Silica Monolith Morphology

We present a fast, nondestructive, and quantitative approach to characterize the morphology of capillary silica-based monolithic columns by reconstruction from confocal laser scanning microscopy images. The method comprises column pretreatment, image acquisition, image processing, and statistical analysis of the image data. The received morphological data are chord length distributions for the bulk macropore space and skeleton of the silica monolith. The morphological information is shown to be comparable to that derived from transmission electron microscopy, but far easier to access. The approach is generally applicable to silica-based capillary columns, monolithic or particulate. It allows the rapid acquisition of hundreds of longitudinal and cross-sectional images in a single session, resolving a multitude of morphological details in the column.

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.

Full-scale two-phase flow measurements on Athena research vessel

Measurements of gas volume fraction, bubble velocity, chord length and bubble size distributions were performed on the research vessel Athena II operating in Saint Andrew Bay in the gulf coast near Panama City, FL. Double tipped sapphire optical local phase-detection probes were used to acquire indicator functions downstream of the breaking bow wave, behind the masker and at the stern. These indicator functions were also taken at different depths, operating speeds and headings respect to the waves. The data processing includes the computation of velocity of individual bubbles and chord lengths, resulting in chord length distributions. These chord length distributions are used to obtain bubble size distributions using a novel procedure described in detail herein. Uncertainty analysis is performed for gas volume fraction, average bubble velocity and chord length. The results indicate that air entrainment increases with ship speed and sailing against the waves at all positions. The bow wave exhibits unsteady breaking that creates bubble clouds, which were characterized and identified by signal processing. At the stern a very strong dependence of bubble size with depth was found, with evidence that small bubbles (smaller than 500 μm) are transported through the bottom of the hull and reach the transom. The roller present at the transom, the associated strong unsteadiness and bubble entrainment are well captured, as indicated by the stern results, showing the frothy nature of the upper layer.

On the use of area-averaged void fraction and local bubble chord length entropies as two-phase flow regime indicators

In this work, the use of the area-averaged void fraction and bubble chord length entropies is introduced as flow regime indicators in two-phase flow systems. The entropy provides quantitative information about the disorder in the area-averaged void fraction or bubble chord length distributions. The CPDF (cumulative probability distribution function) of void fractions and bubble chord lengths obtained by means of impedance meters and conductivity probes are used to calculate both entropies. Entropy values for 242 flow conditions in upward two-phase flows in 25.4 and 50.8-mm pipes have been calculated. The measured conditions cover ranges from 0.13 to 5 m/s in the superficial liquid velocity j f and ranges from 0.01 to 25 m/s in the superficial gas velocity j g. The physical meaning of both entropies has been interpreted using the visual flow regime map information. The area-averaged void fraction and bubble chord length entropies capability as flow regime indicators have been checked with other statistical parameters and also with different input signals durations. The area-averaged void fraction and the bubble chord length entropies provide better or at least similar results than those obtained with other indicators that include more than one parameter. The entropy is capable to reduce the relevant information of the flow regimes in only one significant and useful parameter. In addition, the entropy computation time is shorter than the majority of the other indicators. The use of one parameter as input also represents faster predictions.

Densification behaviour of pure molybdenum powder by spark plasma sintering

Abstract Pure molybdenum was sintered with SPS under various temperatures, external pressures and heating rates. The microstructure of the specimens representing the different sintering conditions was investigated by classical metallographic methods. The relative density, the microhardness and the chord length distribution were measured. Linear shrinkage, depending on time or temperature, was calculated from piston travel, which was recorded during sintering process. These results show that the main part of consolidation takes place during fast heating up. The densification behaviour is controlled mainly by sintering temperatures and applied pressure. The molybdenum powder was successfully consolidated by SPS in very short times. A relative density of 95% was reached by sintering temperatures of 1600 °C and external pressure of 67 MPa.

Application of a recent FBRM-probe model to quantify preferential crystallization of dl-threonine

The process of preferential crystallization is controlled by crystallization kinetics. Thus a key to run the process satisfactorily is using a process monitoring system eventually combined with a process model. In this context information of the liquid phase composition as well as the time resolved particle size distributions are usually desired. In contrast to measuring the liquid phase composition the inline measurement of particle size distributions is often difficult. The Focused Beam Reflectance Measurement probe (Lasentec, Mettler-Toledo GmbH) is an inline monitoring tool that is capable of measuring so-called chord-length distributions (CLDs). However these CLDs are different to the desired particle size distributions (PSDs). In the presented study this problem is overcome using a recent rigorous mathematical model of the measurement technology to transform PSDs into CLDs. The study shows how the probe model can be adopted to the investigated system using a series of initial validation experiments. Chord-splitting seems to occur when using the Focused Beam Reflectance Measurement probe. A simple modification of the particle geometry is incorporated into the probe model in order to simulate the chord-splitting. The simulated CLDs are then compared to the measured CLDs of different preferential crystallization runs performed for the system d,l-threonine/water. More specifically, measured moments of the chord length distributions along with optical rotation trajectories are compared to calculated moments of a population balance model in order to estimate the kinetic model parameters. This way the presented case study gives a systematic approach on how to apply the used probe model to monitor a preferential crystallization process and parameterize a process model.

Influence of Crystal Properties on Powder Flow Behavior of an Aromatic Amine and L-Glutamic Acid

Polycrystalline particles with a roughly spherical shape (spherulites) have been identified in the industrial production of an aromatic amine derivative, where powder handling is one of the downstream processes following crystallization. This comparative study focuses on how uniaxial flow functions as measures of flowability of dry material of L-glutamic acid and an aromatic amine are affected by the crystal morphology and size, as analyzed by the chord length distribution measurements (FBRM) and scanning electron microscopy (SEM). L-glutamic acid was chosen as a model substance since it can be crystallized as spherulites as well as needle-shaped and polyhedral particles. Failure strength values were measured as a function of consolidation stress using the uniaxial tester. The failure strength values of L-glutamic acid were found to be lower for polyhedral particles than for needle-shaped particles with approximately the same mean chord length. Needle-shaped particles were found to have lower values for failure strength than L-glutamic acid spherulites with smaller chord lengths. It has been shown that spherulites are more unstable with respect to particle breakage than the other morphologies. Although the chord length distributions of the L-glutamic acid spherulites were shifted towards smaller values than those of the aromatic amine spherulites, the failure strength of the aromatic amine particles is more than four times as large. This can be explained by more extensive particle breakage during filtration, sample storage, and consolidation of the aromatic amine.

Contact and Chord Length Distribution Functions of the Poisson-Voronoi Tessellation in High Dimensions

In this paper we present formulae for contact distributions of a Voronoi tessellation generated by a homogeneous Poisson point process in the d-dimensional Euclidean space. Expressions are given for the probability density functions and moments of the linear and spherical contact distributions. They are double and simple integral formulae, which are tractable for numerical evaluation and for large d. The special cases d = 2 and d = 3 are investigated in detail, while, for d = 3, the moments of the spherical contact distribution function are expressed by standard functions. Also, the closely related chord length distribution functions are considered.

Contact and Chord Length Distribution Functions of the Poisson-Voronoi Tessellation in High Dimensions

In this paper we present formulae for contact distributions of a Voronoi tessellation generated by a homogeneous Poisson point process in the d-dimensional Euclidean space. Expressions are given for the probability density functions and moments of the linear and spherical contact distributions. They are double and simple integral formulae, which are tractable for numerical evaluation and for large d. The special cases d = 2 and d = 3 are investigated in detail, while, for d = 3, the moments of the spherical contact distribution function are expressed by standard functions. Also, the closely related chord length distribution functions are considered.

Influence of Water and Supercooling on Permeability and Compressibility of Acrylic Acid Crystal Beds

AbstractThe performance of a solid‐liquid separation process is often limited by size distribution and morphology of the crystals. To predict the filtration behavior, a robust and applicable model based only on crystallization process parameters is necessary. Therefore, a model has been successfully developed for the industrial system of aqueous acrylic acid melt to predict compressibility and permeability of a crystal bed. For this purpose, common equations are transferred successfully to nonspherical particles. Chord length distributions (CLDs) obtained from an inline focused beam reflectance measurement (FBRM) probe and crystal aspect ratios have been used in combination to determine the major input parameters for the model. Integration of a complex mathematical restoration of crystal size distribution (CSD) from CLD data by the use of existing models is avoided. Considering acceptable fault tolerances of the model, a simple approach used as a robust industrial application is employed. The adjustment of all required constants used in the permeability model was based on simple filtration tests.

Effects of ionic impurities on crystallization of cobalamin

In this paper, the influence of two typical ionic impurities (Na+ and Mg2+) is investigated with the focused beam reflectance measurement (FBRM) technique. In this system, the on-line FBRM is used as a tool for monitoring the crystallization process of cobalamin by measuring the chord length distribution of particles and the particle counts. It is noted that impurity Mg2+ has a more significant effect than Na2+ in crystal growth of the whole crystallization process. From the microscopic observation of crystals, Mg2+ has an obvious effect on the crystal habit, while Na2+ has little effect. In addition, the crystal habit changes can be monitored by particle vision measurement (PVM). Understanding these effects is helpful to aid optimization and improve process control.

Seeded Batch Cooling Crystallization with Temperature Cycling for the Control of Size Uniformity and Polymorphic Purity of Sulfathiazole Crystals

An experimental study has been conducted to evaluate the capability of a seeded batch cooling crystallization with a temperature cycling method to produce a narrow crystal size distribution and grow a desired polymorphic form of sulfathiazole crystals. The study used focused beam reflectance measurement (FBRM), and attenuated total reflectance ultraviolet/visible (ATR-UV/vis) spectroscopy for the in situ monitoring and control of the process. Based on the FBRM readings, the process was driven using a feedback control approach that employs alternating cycles of heating and cooling phases so that the number of counts, corresponding to the number of seed particles, is maintained, whilst the square-weighted chord length distribution, indicating the dynamic progress of the growth of the seeds in the system, is increased. Results of the experiments show that the temperature cycling method promoted Ostwald ripening, which helped in accelerating the growth and enhancing the size uniformity of the product. The method also has a good prospect to be implemented for the control of polymorphic purity. Seeds of Form I and Form II could be grown from n-propanol and water, respectively. Form I seeds in water were first transformed into Form II and/or swamped by nuclei of Form II, before the growth of the newly formed crystals took place. Seeds of Form II and Form III in n-propanol, however, were not able to grow at all. This study confirmed that the nucleation and growth of sulfathiazole crystals are solvent-mediated, and the insight into these phenomena was captured very well by the in situ monitoring tools.

Chord length distributions measurements during crystallization and agglomeration of gas hydrate in a water-in-oil emulsion: Simulation and experimentation

The formation of gas hydrates from water-in-oil emulsion was investigated on two different flow loops: a laboratory scale flow loop (Archimede flow loop: 30 m long, and 1 cm diameter, St-Etienne School of Mines) and a pilot scale flow loop (Lyre flow loop: 150 m long, 5 cm diameter, IFP Solaize). Both flow loops are equipped with a focused beam reflectance measurement (FBRM) probe for in situ particle size analysis. These FBRM probes were used to monitor chord length distribution (CLD) during the crystallization process of water-in-oil emulsions into gas hydrate slurries. When water droplets crystallize into hydrate particles, an agglomeration phenomenon is evidenced by pressure drop measurements. This agglomeration phenomenon is also detected by the FBRM probe and is highlighted by a sharp change in the mean chord length and a spread of the CLD to larger chord length. In order to better interpret the chord length distribution measurements, a modelling work has been made. This paper gives a description of the algorithm used for building 3D fractal aggregates and simulating CLD measurements on them. Aggregates are constructed from a monodisperse spherical particle. The influence of different parameters (fractal dimension, number of particles in the aggregate, diameter of primary particles) on the simulated CLD is also discussed. Some comparisons between experimental and simulated CLD are finally used to describe the physical properties of aggregates during an experiment.

On‐line monitoring of lithium carbonate dissolution

AbstractDissolution of lithium carbonate (Li2CO3) in aqueous solution was investigated using three on‐line apparatuses: the concentration of Li2CO3 was measured by electrical conductivity equipment; CLD (Chord Length Distribution) was monitored by FBRM (Focused Beam Reflectance Measurement); crystal image was observed by PVM (Particle Video Microscope). Results show dissolution rate goes up with a decrease of particle size, and with an increase in temperature; stirring speed causes little impact on dissolution; ultrasound facilitates dissolution obviously. The CLD evolution and crystal images of Li2CO3 powders in stirred fluid were observed detailedly by FBRM and PVM during dissolution. Experimental data were fitted to Avrami model, through which the activation energy was found to be 34.35 kJ/mol. PBE (Population Balance Equation) and moment transform were introduced to calculate dissolution kinetics, obtaining correlation equations of particle size decreasing rate as a function of temperature and undersaturation. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A novel and effective multistage classification system for microscopic starch grain images

This article presents a novel and effective multistage system for classifying Chinese Materia Medica microscopic starch grain images. The proposed classification system is constructed based on the Gaussian mixture model-based clustering, the feature assignment algorithm, and the similarity measurement. Several features for each starch grain image are extracted and every class of drug is represented by a set of characteristic features. For each stage of the system, only one feature is chosen and assigned to that stage via the feature assignment algorithm, and the corresponding characteristic features are subdivided into smaller subsets based on clustering techniques. At the final stage, each subset contains a certain class of drugs (with corresponding characteristic features) and similarity measurement is carried out for starch grain classification. Three sets of the current state-of-the-art starch grain features including the granulometric size distribution, the chord length distribution, and the wavelet signature are used to construct the system. Experimental results on a database of 240 images of 24 classes of drugs reveal the superior performance of the multistage system. Comparison with the traditional starch grain classification approaches indicates that our proposed multistage method produces a marked improvement in classification performance.

Multivariable real‐time optimal control of a cooling and antisolvent semibatch crystallization process

AbstractThis article presents an experimental study of simultaneous optimization with respect to two variables (cooling rate and flow‐rate of antisolvent) in an offline and online (real‐time) manner on a semibatch crystallizer. The nucleation and growth kinetic parameters of paracetamol in an isopropanol‐water cooling, antisolvent batch crystallizer were estimated by nonlinear regression in terms of the moments of the crystal population density. Moments of crystal population were estimated from the measured chord length distribution, generated by the FBRM®, and the supersaturation was calculated from the measured concentration by attenuated total reflectance‐fourier transform infrared spectroscopy. The results of real‐time optimization showed a substantial improvement of the end of batch properties (the volume‐weighted mean size and yield). For the same objective function, the real‐time optimization method resulted in an increase in the volume‐weighted mean size by ∼100 μm and 15% of theoretical yield compared with the best result obtained in an offline optimization manner. © 2009 American Institute of Chemical Engineers AIChE J, 2009