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This work contributes to the research devoted to the recognition of a convex body by probabilistic characteristics of its lower-dimensional sections. In this paper, for any convex quadrilateral, five orientation-dependent characteristics are introduced and explicitly evaluated per direction. In terms of these characteristics, simple explicit representations of the orientation-dependent chord length distribution function and the covariogram are obtained not only for an arbitrary convex quadrilateral but also for any right prism based on it. [ABSTRACT FROM AUTHOR]

In various stereological problems a n-dimensional convex body is intersected with an (n−1)-dimensional Isotropic Uniformly Random (IUR) hyperplane. In this paper the cumulative distribution function associated with the (n−1)-dimensional volume of such a random section is studied. This distribution is also known as chord length distribution and cross section area distribution in the planar and spatial case respectively. For various classes of convex bodies it is shown that these distribution functions are absolutely continuous with respect to Lebesgue measure. A Monte Carlo simulation scheme is proposed for approximating the corresponding probability density functions.

In various stereological problems an n-dimensional convex body is intersected with an (n−1)-dimensional Isotropic Uniformly Random (IUR) hyperplane. In this paper the cumulative distribution function associated with the (n−1)-dimensional volume of such a random section is studied. This distribution is also known as chord length distribution and cross section area distribution in the planar and spatial case respectively. For various classes of convex bodies it is shown that these distribution functions are absolutely continuous with respect to Lebesgue measure. A Monte Carlo simulation scheme is proposed for approximating the corresponding probability density functions. [ABSTRACT FROM AUTHOR]

This study aimed to investigate the effect of polymer type on solidification rate of PLGA polymeric microparticles and particle size/distribution of the emulsion droplets/hardened PLGA polymeric microparticles during solvent evaporation process using FBRM (Focussed Beam Reflectance Measurement). PLGA polymeric microparticles were prepared by an O/W solvent evaporation method using various PLGA polymers, including PLGA Resomer® RG503H, RG502H and RG752H. The particle size mean, chord length distribution (CLD), and chord count of the emulsion droplets/hardened microparticles were monitored by FBRM. The morphology of polymeric microparticles were characterised by optical microscopy and scanning electron microscopy (SEM). The transformation of the emulsion droplets into solid microparticles occurred within the first 30 (± 1.04), 34 (± 1.15) and 37 (± 0.82) min and square weighted mean chord lengths are 64.08 (± 3.18), 52.36 (± 5.27) and 42.18 (± 4.61) µm when PLGA Resomer® RG503H, RG502H and RG752H were used respectively. Larger square weighted mean chord length of PLGA polymeric microparticles gave lower chord counts. PLGA RG752H microparticles gave smallest square weighted mean chord length and the chord counts was the highest. The CLDs measured by FBRM showed that a larger particle size mean gave longer CLD and a lower peak of particle number. SEM data revealed that the morphology of microparticles was influenced by type and physical properties of polymer. FBRM can be employed for online monitoring of the shift in the microparticle CLD and detect transformation of the emulsion droplets into solid microparticles during the solvent evaporation process. The microparticle CLD and transformation process were strongly influenced by polymer type. [ABSTRACT FROM AUTHOR]

In this paper, we express the Chord Length Distribution (CLD) measure associated to a given Particle Size Distribution (PSD) when particles are modeled as suspended spheroids in a reactor. Using this approach, we propose two methods to reconstruct the unknown PSD from its CLD. In the single-shape case where all spheroids have the same shape, a Tikhonov regularization procedure is implemented. In the multi-shape case, the measured CLD mixes the contribution of the PSD associated to each shape. Then, an evolution model for a batch crystallization process allows to introduce a Back and Forth Nudging (BFN) algorithm, based on dynamical observers. We prove the convergence of this method when crystals are split into two clusters: spheres and elongated spheroids. These methods are illustrated with numerical simulations. [ABSTRACT FROM AUTHOR]

Directionally solidified (DS) and single crystal (SC) Ni-based superalloys inevitably underwent microstructural degradation induced by the harsh operating environment. For the safety service and economic overhaul, constructing a quantitative mapping chain from service process to microstructural degradation and to property deterioration is critically essential. The present work started with stress-free and stress-assisted pre-service treatments of a DS Ni-based superalloy to obtain microstructures with different degraded states. An imaging process based on two-phase rotary chord length distributions was established to extract the high dimensional statistical information for identifying the morphology and size features of microstructures. To reduce the dimension of the statistical information and quantitatively characterize the microstructural states in fewer parameters, principal component analysis was employed to capture the core microstructural indicators, which was utilized to establish the response surface between the deterioration of fatigue resistance and the microstructural degradation. Finally, a multi-output support vector regression (SVR) model was constructed to map between service process and microstructural degradation. The results showed acceptable accuracy to estimate the microstructural degradation of pre-serviced alloys. Meanwhile, the framework provides a technical chain for the waste determination and microstructural degradation estimation of the hot section components made by DS and SC Ni-based superalloys.

Online monitoring of the solid phase in industrial processes of sugar crystallization is still a challenge. Laser backscattering is one of the most promising techniques; however, the measured chord length distribution (CLD) does not have a physical meaning of crystal size. This work converted sucrose CLD measured by an online sensor into particle size distribution (PSD) using an artificial neural network (ANN). CLD and suspension concentration of 116 experiments were the input to the ANN and PSD was its output. The trained ANN exhibited a coefficient of variation between experimental and calculated PSD of 0.998. Data of experimental sucrose crystallization was used to validate the model, resulting in a maximum deviation of 0.090 mm in mean size and 6.16% in the coefficient of variation of distribution. This model may be used to improve both industrial processes (process optimization and control) and laboratory studies (kinetics determination). [Display omitted] • Real-time monitoring of particle size distribution in sugar suspension. • Laser-backscattering use is limited to a particle size of 0.85 mm. • For sucrose particles, the limit is 0.159 mm. • Absolute deviation in mean size of 0.013 mm and 0.02% in coefficient of variation. [ABSTRACT FROM AUTHOR]

In this article for n-dimensional convex body D the relation between the chord length distribution function and the distribution function of the distance between two random points in D was found. Also the relation between their moments was found. [ABSTRACT FROM AUTHOR]

In the present paper a formula for calculation of the density function of the distance between two independent points randomly and uniformly chosen in a bounded convex body is given. The formula permits to find an explicit form of density function for body with known chord length distributions. In particular, we obtain an explicit expression for in the case of a ball of diameter . A simulation model is suggested to calculate empirically the cumulative distribution function of the distance between two points in a body from , where explicit form of the function is hard to obtain. In particular, simulation is performed for balls and ellipsoids in . [ABSTRACT FROM AUTHOR]

In chemical process engineering, fast gas‐liquid reactions often suffer from an inefficient distribution of gas and therefore mixing and mass transfer performance. This study deals with the possibility of influencing the local gas holdup and bubble size distribution in a gas‐liquid process using additively manufactured lattice structures (AMLS). The used measuring technique to study bubble size, velocity, and the local gas holdup is a photo‐optical needle probe. By using AMLS, a significant radial homogenization of the local gas holdup and the mean bubble size is achieved. Furthermore, it can be demonstrated that the bubble size can be tailored by the geometry of the inserted structure. It is illustrated that the mean bubble velocities are lowered within the lattice resulting in a higher residence time of the dispersed phase with an impact on the mass transfer performance within the AMLS. [ABSTRACT FROM AUTHOR]

We study means of extracting quantitative information about particle attributes using state-of-art in-line and off-line particle measurements and analysis techniques. The approach comprises a combination of image analysis, laser diffraction, inversion of chord length distribution, and multivariate analysis. Polystyrene particle suspensions are used as the model system to provide a wide range of particle loadings (up to 10 wt%), sizes (<90 to 800 μm) and shapes. We identify key challenges and limitation of the in-line imaging and chord length measurements; particularly, an upper limit of particle number density of 10,000 g−1 is observed, as well as the impact of internal reflections from large and transparent particles. The latter phenomena deteriorate the accuracy of the chord length distribution and the subsequent particle size estimation using inversion algorithms. The study demonstrates the use of multivariate analysis for quantifying particle size and concentration, which yields relative errors of 6 and 11%, respectively. Unlabelled Image • Compare means to quantify particle information from in-line and off-line analysis. • The effect of chord length splitting becomes significant for particle >300 μm. • Chord length counts increase nonlinearly for particle density > 10,000 particles g−1. • Good estimation on particle information can be obtained by PLSR analysis on CLD. [ABSTRACT FROM AUTHOR]

Graphical abstract Highlights • Wet milling of particles in suspension is performed in a closed loop. • Data relating to particle size and shape is captured with inline sensors. • Analysis of the data shows quantitatively the effect of wet milling on the particles. • Performance of the inline sensors and the offline counterparts are assessed. Abstract Size and shape distributions are among critical quality attributes of particulate products and their inline measurement is crucial for monitoring and control of particle manufacturing processes. This requires advanced tools that can estimate particle size and shape distributions from multi-sensor data captured in situ across various processing steps. In this work, we study changes in size and shape distributions, as well as number of particles during high shear wet milling, which is increasingly being employed for size reduction in crystalline slurries in pharmaceutical processing. Saturated suspensions of benzoic acid, paracetamol and metformin hydrochloride were used in this study. We employ our recently developed tools for estimating particle aspect ratio and particle size distributions from chord length distribution (CLD) measurements and imaging. We also compare estimated particle size distributions from CLD and imaging with corresponding estimates from offline instruments. The results show that these tools are capable of quantitatively capturing changes in particle sizes and shape during wet milling inline. This is the first time that such a capability has been reported in the literature. The ability to quantitatively monitor particle size and shape distributions in real time will enable development of more realistic and accurate population balance models of wet milling and crystallisation, and aid more efficient control of crystallisation processes. [ABSTRACT FROM AUTHOR]

Research on hydrate dissociation mechanisms is critical to solving the issue of hydrate blockage and developing hydrate slurry transportation technology. Thus, in this paper, natural gas hydrate slurry decomposition experiments were investigated on a high-pressure hydrate experimental loop, which was equipped with two on-line particle analyzers: focused beam reflectance measurement (FBRM) and particle video microscope (PVM). First, it was observed from the PVM that different hydrate particles did not dissociate at the same time in the system, which indicated that the probability of hydrate particle dissociation depended on the particle's shape and size. Meanwhile, data from FBRM presented a periodic oscillating trend of the particle/droplet numbers and chord length during the hydrate slurry dissociation, which further demonstrated these micro hydrate particles/droplets were in a dynamic coupling process of breakage and agglomeration under the action of flow shear during the hydrate slurry dissociation. Then, the influences of flow rate, pressure, water-cut, and additive dosage on the particles chord length distribution during the hydrate decomposition were summarized. Moreover, two kinds of particle chord length treatment methods (the average un-weighted and squared-weighted) were utilized to analyze these data onto hydrate particles' chord length distribution. Finally, based on the above experimental data analysis, some important conclusions were obtained. The agglomeration of particles/droplets was easier under low flow rate during hydrate slurry dissociation, while high flow rate could restrain agglomeration effectively. The particle/droplet agglomerating trend and plug probability went up with the water-cut in the process of hydrate slurry decomposition. In addition, anti-agglomerates (AA) greatly prohibited those micro-particles/droplets from agglomeration during decomposition, resulting in relatively stable mean and square weighting chord length curves. [ABSTRACT FROM AUTHOR]

Carbonaceous nanomaterials have become important materials with widespread applications in battery systems and supercapacitors. The application of these materials requires precise knowledge of their nanostructure. In particular, the porosity of the materials together with the shape of the pores and the total internal surface must be known accurately. Small-angle X-ray scattering (SAXS) and small-angle neutron scattering (SANS) present the methods of choice for this purpose. Here we review our recent investigations using SAXS and SANS. We first describe the theoretical basis of the analysis of carbonaceous material by small-angle scattering. The evaluation of the small-angle data relies on the powerful concept of the chord length distribution (CLD) which we explain in detail. As an example of such an evaluation, we use recent analysis by SAXS of carbide-derived carbons. Moreover, we present our SAXS analysis on commercially produced activated carbons (ACN, RP-20) and provide a comparison with small-angle neutron scattering data. This comparison demonstrates the wealth of additional information that would not be obtained by the application of either method alone. SANS allows us to change the contrast, and we summarize the main results using different contrast matching agents. The pores of the carbon nanomaterials can be filled gradually by deuterated p-xylene, which leads to a precise analysis of the pore size distribution. The X-ray scattering length density of carbon can be matched by the scattering length density of sulfur, which allows us to see the gradual filling of the nanopores by sulfur in a melt-impregnation procedure. This process is important for the application of carbonaceous materials as cathodes in lithium/sulfur batteries. All studies summarized in this review underscore the great power and precision with which carbon nanomaterials can be analyzed by SAXS and SANS.

Abstract Quantification of mesoscale microstructures of polycrystalline materials is important for a range of practical tasks of materials design and development. The current protocols of quantifying grain size and morphology often rely on microstructure metrics (e.g., mean grain diameter) that overlook important details of the mesostructure. In this work, we present a quantification framework based on directionally resolved chord length distribution and principal component analysis as a means of extracting additional information from 2-D microstructural maps. Towards this end, we first present in detail a method for calculating chord length distribution based on boundary segments available in modern digital datasets (e.g., from microscopy post-processing) and their low-rank representations by principal component analysis. The utility of the proposed framework for capturing grain size, morphology, and their anisotropy for efficient visualization, representation, and specification of polycrystalline microstructures is then demonstrated in case studies on datasets from synthetic generation, experiments (on Ni-base superalloys), and simulations (on steel during recrystallization). Graphical Abstract Unlabelled Image Highlights • Microstructure quantification based on directional chord length distribution and principal component analysis is presented • A boundary-based algorithm of calculations of chord length distributions is introduced • Utility of the quantification framework is shown in three case studies on synthetic, experimental, and simulation datasets • Angularly resolved chord length distribution captures essential details of grain size and shape in diverse microstructures • Low-dimensional representations of directional chord length distributions are obtained using principal component analysis [ABSTRACT FROM AUTHOR]

Abstract: Chord length distribution (CLD) can be determined by an in‐line measuring system with focused‐beam reflectance measurement, but it can differ from crystal size distribution (CSD). However, expected values of CLD can be calculated from CSD by statistical methods and vice versa. In this study, a correlation equation between crystal size and aspect ratio during cooling crystallization was obtained and a mapping matrix was calculated based on the correlation equation. Then, the suspension obtained in cooling crystallization was sampled and CSDs were measured by microscopy at the same time that CLDs were measured with FBRM. As a result of error evaluation, transformation of CLD into CSD reduced the errors between CLDs and CSDs except in the early stage of crystallization. [ABSTRACT FROM AUTHOR]

Research on hydrate dissociation mechanisms is critical to solving the issue of hydrate blockage and developing hydrate slurry transportation technology. Thus, in this paper, natural gas hydrate slurry decomposition experiments were investigated on a high-pressure hydrate experimental loop, which was equipped with two on-line particle analyzers: focused beam reflectance measurement (FBRM) and particle video microscope (PVM). First, it was observed from the PVM that different hydrate particles did not dissociate at the same time in the system, which indicated that the probability of hydrate particle dissociation depended on the particle’s shape and size. Meanwhile, data from FBRM presented a periodic oscillating trend of the particle/droplet numbers and chord length during the hydrate slurry dissociation, which further demonstrated these micro hydrate particles/droplets were in a dynamic coupling process of breakage and agglomeration under the action of flow shear during the hydrate slurry dissociation. Then, the influences of flow rate, pressure, water-cut, and additive dosage on the particles chord length distribution during the hydrate decomposition were summarized. Moreover, two kinds of particle chord length treatment methods (the average un-weighted and squared-weighted) were utilized to analyze these data onto hydrate particles’ chord length distribution. Finally, based on the above experimental data analysis, some important conclusions were obtained. The agglomeration of particles/droplets was easier under low flow rate during hydrate slurry dissociation, while high flow rate could restrain agglomeration effectively. The particle/droplet agglomerating trend and plug probability went up with the water-cut in the process of hydrate slurry decomposition. In addition, anti-agglomerates (AA) greatly prohibited those micro-particles/droplets from agglomeration during decomposition, resulting in relatively stable mean and square weighting chord length curves.

Bubble properties, such as local gas holdup, bubble frequency, bubble velocity, bubble size, and interfacial area concentration, are of great significance for the design and scale-up of bubble columns. In the present study, bubble properties in a 0.15 m in diameter bubble column were measured by a dual-tip conductivity probe. A new method was proposed to establish the relationship between chord length distribution (CLD) and bubble size distribution (BSD) without the assumption of fixed bubble aspect ratio. The bubble velocity and BSD measured by the probe were validated by a high speed camera in a square column. The results indicate that considering the decreasing of bubble aspect ratio with bubble diameter is required to obtain accurate BSD from measured CLD. Furthermore, the measured bubble properties at different axial positions show that the flow development is much more rapid in the churn-turbulent regime than that in the homogeneous regime. It is also found that the bubble breakage is dominant over the bubble coalescence in the homogeneous regime due to the large bubbles generated at the perforated distributor. The measured results provide a benchmark data for validation of CFD simulation. [ABSTRACT FROM AUTHOR]

Measurement of dispersed modality at different spatial locations is performed in a 1000 ml borosilicate beaker at various dispersed volume fractions in both W/O and O/W system. It is found that mean chord length at different spatial locations shows a similar distribution in both W/O and O/W dispersion that the closer to impeller the smaller the mean chord length. Further, in dilute W/O dispersion (3%), results show that both number counts and mean chord length of droplets at impeller region are smaller than other locations; however, it gradually turns to be larger at higher dispersed fraction (20%). For O/W dispersion, it is found that number counts of small droplets in region around impeller become smaller than other locations with the addition of dispersed oil phase (10%). Flow characteristic measured by 2D angle-resolved particle image velocimetry in pure oil/water phase is employed to further explain the deviation. Besides, the critical dispersed fraction affecting the dispersed modality at different spatial location is discussed. [ABSTRACT FROM AUTHOR]

One step aqueous melt-crystallization and in situ granulation was utilized to produce ibuprofen-cationic dextran [diethylaminoethyl dextran (Ddex)] conjugate crystanules without the use of surfactants or organic solvents. This study investigates the mechanism of in situ granulation-induced crystanule formation using ibuprofen (Ibu) and Ddex. Laboratory scale batch aqueous crystallization system containing in situ monitoring probes for particle vision measurement (PVM), UV–vis measurement and focused beam reflectance measurements (FBRM) was adapted using pre-defined formulation and process parameters. Pure ibuprofen showed nucleation domain between 25 and 64 °C, producing minicrystals with onset of melting at 76 °C and enthalpy of fusion (ΔH) of 26.22 kJ/mol. On the other hand Ibu-Ddex crystanules showed heterogeneous nucleation which produced spherical core-shell structure. PVM images suggest that internalization of ibuprofen in Ddex corona occurred during the melting phase (before nucleation) which inhibited crystal growth inside the Ddex corona. The remarkable decrease in ΔH of the crystanules from 26.22 to 11.96 kJ/mol and the presence of broad overlapping DSC thermogram suggests formation of ibuprofen-Ddex complex and crystalline-amorphous transformation. However Raman and FTIR spectra did not show any significant chemical interaction between ibuprofen and Ddex. A significant increase in dissolution efficiency from 45 to 81% within 24 h and reduced burst release provide evidence for potential application of crystanules in controlled drug delivery systems. It was evident that in situ granulation of ibuprofen inhibited the aqueous crystallization process. It was concluded that in situ granulation-aqueous crystallization technique is a novel unit operation with potential application in continuous pharmaceutical processing. [ABSTRACT FROM AUTHOR]

Lactose accounts for about 75 and 85% of the solids in whey and deproteinized whey, respectively. Production of lactose is usually carried out by a process called crystallization. Several factors including rate of cooling, presence of impurities, and mixing speed influence the crystal size characteristics. To optimize the lactose crystallization process parameters to maximize the lactose yield, it is important to monitor the crystallization process. However, efficient in situ tools to implement at concentrations relevant to the dairy industry are lacking. The objective of the present work was to use a focused beam reflectance measurement (FBRM) system for in situ monitoring of lactose crystallization at supersaturated concentrations (wt/ wt) 50, 55, and 60% at 20 and 30°C. The FBRM data were compared with Brix readings collected using a refractometer during isothermal crystallization. Chord length distributions obtained from FBRM in the ranges of <50 μm (fine crystals) and 50 to 300 μm (coarse crystals) were recorded and evaluated in relation to the extent of crystallization and rate constants deduced from the refractometer measurements. Extent of crystallization and rate constants increased with increasing supersaturation concentration and temperature. The measured fine crystal counts from FBRM increased at higher supersaturated concentration and temperature during isothermal crystallization. On the other hand, coarse counts were observed to increase with decreasing supersaturated concentration and temperature. Square weighted chord length distribution obtained from FBRM showed that as concentration increased, a decrease in chord lengths occurred at 20°C and similar observations were made from microscopic images. The robustness of FBRM in understanding isothermal lactose crystallization at various concentrations and temperatures was successfully assessed in the study. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We present and discuss some open problems related to the determination of a set K from its covariogram, i.e. the function which provides the volumes of the intersections of K with all its possible translates.

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 data. While the algorithm searches for a global best solution to the inverse problem without requiring further a priori information on the range of particle sizes present in the population or aspect ratio of particles, suitable regularisation techniques based on relevant additional information can be implemented as required to obtain physically reasonable size distributions. We used the algorithm to analyse CLD data for samples of needle-like crystalline particles of various lengths using two previously published CLD models for ellipsoids and for thin cylinders to estimate particle size distribution and shape. We found that the thin cylinder model yielded significantly better agreement with experimental data, while estimated particle size distributions and aspect ratios were in good agreement with those obtained from imaging. [ABSTRACT FROM AUTHOR]

In this paper we obtain the explicit forms of the covariogram and the orientation-dependent chord length distribution function for any parallelogram. The explicit form of the chord length distribution function for a parallelogram is also obtained. [ABSTRACT FROM AUTHOR]

The paper considers the problem of recognition of triangles by orientation-dependent chord length distribution. The following results are obtained: 1. The explicit form of the covariogram and orientation-dependent chord length distribution function for a triangle. 2. The explicit form for the chord length distribution function for a triangle. 3. The length of the maximal chord of a triangle is continuous function on direction u ∈ S ( S is the space of all directions in the plane). 4. If we have orientation-dependent chord length distribution function for an everywhere dense set of S, then we can uniquely recognize the triangle with respect to reflections and translations. 5. For any finite subset A ⊂ S, there are two non-congruent triangles with the same values of orientationdependent chord length distribution functions on A. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a focused beam reflectance method is used to investigate the evolution of dispersed droplets at various dispersed volume fractions for an Exxsol D80 mineral oil–water dispersion in a stirring tank. Two types of inversion experiments are compared, the direct and continuous mixing of the oil–water phases. The number density of the chord lengths and distributions are identified as the main parameters for comparison. The drop coalescence is dominant slightly before inversion, at which point the measured mean square weighted (Sqr-wt) chord length increases significantly. The way of mixing will also influence the effect of drop coalescence and result in different inversion processes. [Copyright &y& Elsevier]

Abstract: The empirical model developed in the present work allows estimation of crystal size distributions from focused beam reflectance measurements (FBRM) of chord length distributions. The model is constructed from purposely varied crystal size distributions and the corresponding measured chord length distributions, which allows construction of a transformation matrix relating the two distributions. Experimental results show advantages over more complex phenomenological models, presumably because the transformation matrix implicitly embodies such phenomena. The ability of the model to address varying crystal concentration and selectively added size fractions is demonstrated with experimental results. Finally, the simplicity of the approach allows rapid (of order 0.1s) estimation of crystal size distributions from FBRM, which is a promising outcome for potentially using the approach in an on-line control scheme. [Copyright &y& Elsevier]

Abstract: The heterogeneous morphology of current silica monoliths hinders this column type to reach its envisioned performance goals. We present a new generation of analytical silica monoliths that deliver a substantially improved separation efficiency achieved through several advances in monolith morphology. Analytical silica monoliths from the 1st and 2nd Chromolith generation are characterized and compared by chromatographic methods, mercury intrusion porosimetry, scanning electron microscopy, and confocal laser scanning microscopy. The latter method is instrumental to quantify morphological differences between the monolith generations and to probe the radial variation of morphological properties. Compared with the 1st generation, the new monoliths possess not only smaller macropores, a more homogeneous macropore space, and a thinner silica skeleton, but also radial homogeneity of these structural parameters as well as of the local external or macroporosity. The 66.5% reduction in minimum plate height observed between silica monoliths of the 1st and 2nd Chromolith generation can thus be attributed to two key improvements: a smaller domain size at simultaneously increased macropore homogeneity and the absence of radial morphology gradients, which are behind the considerable peak asymmetry of the 1st generation. [Copyright &y& Elsevier]

Abstract: The Boolean model is a successful short-range order model for ensembles of overlapping grains possessing many applications. Convex grains, randomly distributed in space with a certain density, are characterized by their SAS correlation function γ 0(r). Characteristics, such as volume fraction c (porosity 1− c) and sample correlation function γ(r) result. The function γ 0(r) of unknown grains can be re-constructed from γ(r). Information on size and shape of the grains results. The chord length distributions of grain phase and matrix phase are analyzed. The latter distribution is an exponential distribution. The distribution law of the grain phase is determined explicitly, incorporating formulas for the moments. [Copyright &y& Elsevier]

Abstract: We report an experimental study on the structural (especially radial) heterogeneity of eleven 100μm i.d. capillary tetramethoxysilane–methyltrimethoxysilane hybrid silica monoliths with different pore and skeleton sizes, which were imaged by an optimized confocal laser scanning microscopy method. This method allows the optical sectioning of the monoliths, which is a prerequisite for quantitative morphological image analysis. Both radial porosity profiles and chord length distributions were calculated in the macropore domain for each column from at least 100 complete cross-sectional views along the column axis. The statistical approach visualized radial heterogeneities on different length scales in the monolithic structures. Chord length distributions followed a simplified k-gamma function, and a structural parameter obtained from this function is introduced to provide a scalar measure of column heterogeneity. It enables the comparison of monoliths with different pore sizes and helps to establish correlations between the microscopic properties of a column, eddy dispersion, and its separation efficiency. [Copyright &y& Elsevier]

Abstract: 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. [Copyright &y& Elsevier]

Abstract: Flow and transport in porous media is determined by its structure. Beside spatial correlation, especially the connectivity of heterogeneous conductivities is acknowledged to be a key factor. This has been demonstrated for well defined random fields having different topological properties. Yet, it remains an open question which morphological measures carry sufficient information to actually predict flow and transport in porous media. We analyze flow and transport in classical, two-dimensional random fields showing different topology and we determine a selection of structural characteristics including classical two-point statistics, chord-length distribution and Minkowski functions (four-point statistics) including the Euler number as a topological measure. Using the approach of simulated annealing for global optimization we generate analog random fields that are forced to reproduce one or several of theses structural characteristics. Finally we evaluate in how far the generated analogons reproduce the original flow and transport behavior as well as some more elaborate structural characteristics including percolation probabilities and the pair connectivity function. The results confirm that two-point statistics is insufficient to capture functional properties since it is not sensitive to connectivity. In contrast, the combination of Minkowski functions and chord length distributions carries sufficient information to reproduce the breakthrough curve of a conservative solute. Hence, global topology provided by the Euler number together with local clustering provided by the chord length distribution seems to be a powerful condensation of structural complexity with respect to functional properties. [ABSTRACT FROM AUTHOR]

Abstract: Particle image velocimetry techniques coupled with advanced image processing tools are receiving an increasing interest for measuring flow quantities and local bubble-size distributions in gas–liquid mechanically agitated vessels. When trying to analyze image information the problem arises that bubble sizes are generally underestimated, due to the fact that the laser sheet used for lighting the system randomly cuts bubbles over non-diametrical planes, leading to an apparent bubble size distribution even in the ideal case of single sized bubbles. Clearly in the case of bubbles with a size distribution the experimental information obtained is affected by the superposition of effects. Aim of this work is that of providing a numerical procedure able to reconstruct actual bubble size distributions from relevant apparent size distributions obtained by laser sheet illumination and image analysis. The procedure proposed is robust and viable and can account for laser sheet thickness. The procedure is shown to provide fully satisfactory results even with quite extreme distributions. BSD resolution dependence on the numerousness of raw data processed is discussed. Use of the proposed procedure for extracting BSD from bubble chord raw data obtained by other devices, such as point probes, is straightforward. [Copyright &y& Elsevier]

Abstract: A popular in situ particle characterization technique, which can be applied without dilution, is the focused beam reflectance measurement . 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 -lactose-monohydrate particles. The applicability of the FBRM for PSD measurements is discussed on the basis of these results. [Copyright &y& Elsevier]