Crystal Shape Distribution Research Articles

Frost crystal growth behavior on a hydrophilic surface over a wide range of cold surface temperature

The initial frosting phenomenon is a discontinuous phase nucleation process, the cold surface temperature and properties have a decisive influence on this phenomenon, especially in the initial frosting stage. With the development of aerospace and energy transportation technology, frost formation at low temperatures (-100 °C∼-30 °C) and ultra-low temperatures (-273 °C∼-100 °C) has gradually attracted the attention of researchers. In this paper, the initial frosting phenomena on hydrophilic surfaces with a contact angle of 10° (CA= 10°) and ordinary (CA= 95°) surfaces are studied experimentally in a wide range of cold surface temperatures (-190 °C∼-30 °C). Four modes are confirmed: cold surface condensation frosting, cold surface sublimation frosting, air boundary layer condensation frosting and air boundary layer sublimation frosting. It is also found that the four frosting modes do not appear in turn with the decrease of the cold surface temperature, but two or more frosting modes appear at the same time. And the surface contact angle has an important influence on the frosting mode. The initial frost crystal morphology mainly depends on the cold surface temperature and the corresponding frosting mode. Four different forms of frost crystals are observed: hexagonal prism (feather), branch (pine needle), cluster (shrub) and floc (grape), in which the cluster frost crystal is more sensitive to the surface contact angle and can appear in different temperature ranges due to different contact angles. Based on the statistics of the size, quantity, and distribution of the initial frost crystals, it is found that -70 °C is a major turning point for frost formation from the cold surface sublimation frosting to the air boundary layer sublimation frosting, and an important change has taken place near this point. Furthermore, it affects the shape and size distribution of frost crystals. These findings are of great significance for the study and understanding of frost crystal growth mechanism in the initial stage of frost formation at low and ultra-low temperatures.

Complex decompression and fragmentation of mingled andesite magmas driving multi-phase Plinian eruptions at Mt. Taranaki, New Zealand

Estimating the kinetics of andesite magma vesiculation and crystallization inside volcanic plumbing systems is key for unraveling andesite Plinian eruption dynamics. The conduit kinetics provide the necessary input data for estimating the magma flow rates driving magma ascent and the fragmentation mechanisms controlling shifts in eruption explosivity and style. This information is crucial for increasing knowledge on expected hazards and for developing realistic eruption scenarios. In this work, we estimate conduit magma vesiculation and crystallization kinetics during the 3300 cal BP Upper Inglewood Plinian eruptive episode of Mount Taranaki, New Zealand. This episode comprised (i) low-intensity, conduit-opening phases of dome-collapse PDCs; (ii) pre-climactic, highly explosive phases of diverse PDCs, of up to violent 18-km-runout lateral blasts; (iii) climactic phases of steady 22-km-high Plinian eruption columns; and (iv) waning phases of column-collapse PDCs. By employing synchrotron microtomography, combined with mineral/glass chemistry and electron-microscopy, we quantified 3D vesicle and crystal size and shape distributions in juvenile pyroclasts over time, and corresponding number densities ranging from 1.1 × 105 to 2.5 × 106 mm−3 for vesicles, and from 8.0 × 104 to 5.1 × 106 mm−3 for crystals. Our results indicate that tapping of chemically alike yet rheologically contrasting magmas over a multi-phase andesite eruptive episode is linked to: (a) mafic magma recharge and differentiation in multiple storage reservoirs at distinct crustal levels, (b) stepwise to rapid magma decompression while mingling, producing variable pre- and syn-eruptive degassing and crystallization, and (c) syn-eruptive changes in melt viscosity, strain rate, localized shear deformation, and conduit geometry. The earliest and least explosive eruptive phases (≈ 2 × 106 kg s−1) were produced at the slowest rates of magma decompression (0.3–0.6 MPa s−1), ascent (0.01–0.02 m s−1) and strain (< 0.002 s−1), driven by volatile diffusion and exsolution. All subsequent pre-climactic and Plinian phases (4 × 107–1 × 108 kg s−1) were produced at either rapid or intermittent rates of magma decompression (2.0–6.0 MPa s−1), ascent (0.06–0.2 m s−1) and strain (> 0.003–0.010 s−1), powered by combined magma volatile supersaturation and delayed disequilibrium degassing, decompression-induced microlite crystallization and rapid heterogeneous vesiculation kinetics, shear deformation and magma mingling. These processes enabled complex fragmentation mechanisms of the rheologically most homogeneous magmas.

Crystal Shape Control on the Repacking and Jamming of Crystal‐Rich Mushes

AbstractThe rheology of crustal mushes is a crucial parameter controlling melt segregation and magma flow. However, the relations between mush dynamics and crystal size and shape distribution remain poorly understood because of the complexity of melt‐crystal and crystal‐crystal interactions. We performed analog experiments to characterize the mechanisms that control pore space reduction associated with repacking. Three suspensions of monodisperse particles with different geometries and aspect ratios (1:1, 2:1, 4:1) in a viscous fluid were tested. Our results show that particle aspect ratios strongly control the melt extraction processes. We identify two competing mechanisms that enable melt extraction at grain scale. The first mechanism leads to continuous deformation and melt extraction and is associated with “diffuse” frictional dissipation between neighboring particles. The second is stochastic, localized, and nearly instantaneous and is associated with the development and destruction of force chains percolating through the granular assembly.

Geochemistry and crystal shape, size and spatial distribution in arc-related gabbro, Urmia, NW Iran

Geochemistry and crystal shape, size and spatial distribution in arc-related gabbro, Urmia, NW Iran

Three dimensional reconstruction of frost structure by replica method

To predict and control frosting phenomenon, three-dimensional structure of frost should be quantified in different environmental conditions. This paper experimentally studied frost structure using replica fabrication method. Supplying Formvar solution by a syringe pump under dry air, a plastic shell was successfully fabricated on the frost surface. The voids on the plastic shell were filled with a light-curing resin, from which a replica of frost was obtained. The three dimensional structures frost under different environmental conditions were reconstructed by μX-ray CT. The effects of environmental conditions on the local frost crystal shape, density and tortuosity factor distributions were quantitatively investigated. Frost shape was largely affected by the air relative humidity and temperature. A sheath-like crystal was observed at cooling plate temperature of -15 °C, while dendrite crystal formed at -25 °C. These results are consistent with the knowledge of snow crystal morphologies. The frost density and pore tortuosity factor increased with air velocity and relative humidity.

Crystal size and shape distributions plagioclase and determining of crystal residence time in the Chah-Musa intrusion (South Shahrood)

Crystal size and shape distributions plagioclase and determining of crystal residence time in the Chah-Musa intrusion (South Shahrood)

Application of PAT-Based Feedback Control Approaches in Pharmaceutical Crystallization

Crystallization is one of the important unit operations for the separation and purification of solid products in the chemical, pharmaceutical, and pesticide industries, especially for realizing high-end, high-value solid products. The precise control of the solution crystallization process determines the polymorph, crystal shape, size, and size distribution of the crystal product, which is of great significance to improve product quality and production efficiency. In order to develop the crystallization process in a scientific method that is based on process parameters and data, process analysis technology (PAT) has become an important enabling platform. In this paper, we review the development of PAT in the field of crystallization in recent years. Based on the current research status of drug crystallization process control, the monitoring methods and control strategies of feedback control in the crystallization process were systematically summarized. The focus is on the application of model-free feedback control strategies based on the solution and solid information collected by various online monitoring equipment in product engineering, including improving particle size distribution, achieving polymorphic control, and improving purity. In this paper, the challenges of feedback control strategy in the crystallization process are also discussed, and the development trend of the feedback control strategy has been prospected.

Comparative analysis of dextran-induced sucrose crystal modifications

The analysis of sucrose crystal size and shape modifications induced by the presence of dextran was key to this study. Therefore, evaporative crystallisation experiments using synthetic thick sucrose juices containing various contents of high molecular mass dextran (T2000) were performed.HPLC analysis of the dissolved sucrose crystals revealed that T2000 dextran gets incorporated into the sucrose crystal, indicating that dextran-related crystal size and shape modifications occur.For analysing the sucrose crystal size and shape distribution, static image analysis was implemented and compared to common sieve analysis as well as dynamic image analysis (Camsizer). All methods consistently indicate an increase of crystals with lower minimum and especially lower maximum feret diameters due to the presence of T2000 dextran.For the sucrose crystal shape analysis, average values and relative frequency distributions were evaluated. For more detail, the shape data were further processed using a crystal size-dependent evaluation. Thereby, it was found that cube-shaped crystals, elongated needle-shaped crystals and agglomerates can be related to the presence of dextran. The data suggest that the occurrence of the three dextran-related shapes depend on the dextran content present and also relate to certain sucrose crystal sizes. This way, cube-shaped crystals could be related to small-sized crystals, predominantly occurring at lower dextran contents. Agglomeration and distinct elongation were found to be related to mid- and especially large-sized crystals. The latter two, especially distinct elongation, seem to increasingly occur when higher dextran contents were present.

Real-Time Characterization of Crystal Shape and Size Distribution Based on Moving Window and 3D Imaging in a Stirred Tank

Crystal shape distribution, i.e. the multidimensional size distribution of crystals, is of great importance to their down-stream processing such as in filtration as well as to the end-use properties including the dissolution rate and bioavailability for crystalline pharmaceuticals. Engineering crystal shape and shape distribution requires knowledge about the growth behavior of different crystal facets under varied operational conditions e.g. supersaturations. Measurement of the facet growth rates and growth kinetics of static crystals in a crystallizer without stirring has been reported previously. Here attention is given to study on real-time characterization of the 3D facet growth behavior of crystals in a stirred tank where crystals are constantly moving and rotating. The measurement technique is stereo imaging and the crystal shape reconstruction is based on a stereo imaging camera model. By reference to a case study on potash alum crystallization, it is demonstrated that the crystal size and shape distributions (CSSD) of moving and rotating potash alum crystals in the solution can be reconstructed. The moving window approach was used to correlate 3D face growth kinetics with supersaturation (in the range 0.04 - 0.12) given by an ATR FTIR probe. It revealed that {100} is the fastest growing face, leading to a rapid reduction of its area, while the {111} face has the slowest growth rate, reflected in its area continuously getting larger.

Multi-sensor inline measurements of crystal size and shape distributions during high shear wet milling of crystal slurries

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.

A framework for model reliability and estimability analysis of crystallization processes with multi-impurity multi-dimensional population balance models

The development of reliable mathematical models for crystallization processes may be very challenging due the complexity of the underlying phenomena, the inherent Population Balance Models (PBMs) and the large number of parameters that need to be identified from experimental data. Due to the poor information content of the experiments, the structure of the model itself and correlation between model parameters, the mathematical model may contain more parameters than can be accurately and reliably identified from the available experimental data. A novel framework for parameter estimability for guaranteed optimal model reliability is proposed then validated by a complex crystallization process. The latter is described by a differential algebraic system which involves a multi-dimensional population balance model that accounts for the combined effects of different crystal growth modifiers/impurities on the crystal size and shape distribution of needle-like crystals. Two estimability methods were combined: the first is based on a sequential orthogonalization of the local sensitivity matrix and the second is Sobol, a variance-based global sensitivities technic. The framework provides a systematic way to assess the quality of two nominal sets of parameters: one obtained from prior knowledge and the second obtained by simultaneous identification using global optimization. A cut-off value was identified from an incremental least square optimization procedure for both estimability methods, providing the required optimal subset of model parameters. The implemented methodology showed that, although noisy aspect ratio data were used, the 8 most influential and least correlated parameters could be reliably identified out of twenty-three, leading to a crystallization model with enhanced prediction capability.

In-situ particle segmentation approach based on average background modeling and graph-cut for the monitoring of l-glutamic acid crystallization

The crystal morphology often represents a critically important property for the reason that different morphological characteristics such as crystal shape and size distribution will directly affect crystal growth and the quality of final products. However, minor changes in reaction conditions can have a significant impact on crystal morphology. As a consequence, crystallization processes demand an on-line technique for real-time monitoring of crystal morphology. Image-based monitoring methods show a great potential for real-time monitoring, and performing particle segmentation accurately becomes a key issue in the particle image analysis. To avoid the influences of droplets and to eliminate the particle shadow of particle images obtained by invasive imaging system, an effective approach is proposed for particle segmentation based on combing the background difference method and the graph-cut based local threshold method. Through building the background model and performing subtraction between particle image and background model, droplets could be eliminated effectively. Then the local threshold method is performed further to eliminate the influences of particle shadow. Several particle images are used to demonstrate the efficiency and accuracy of the proposed method. In order to further evaluate the real-time performance of the proposed method, comparison experiments between the proposed method and other advanced or classic algorithms are presented. Experimental results show that the proposed method is efficient and has an impressive real-time performance.

Crystal Engineering in Continuous Plug-Flow Crystallizers.

Size, shape, and polymorphic form are the critical attributes of crystalline particles and represent the major focus of today’s crystallization process design. This work demonstrates how crystal properties can be tuned efficiently in solution via a tubular crystallizer that facilitates rapid temperature cycling. Controlled crystal growth, dissolution, and secondary nucleation allow a precise control of the crystal size and shape distribution, as well as polymorphic composition. Tubular crystallizers utilizing segmented flow such as the one presented in our work can provide plug flow characteristics, fast heating and cooling, allowing for rapid changes of the supersaturation. This makes them superior for crystal engineering over common crystallizers. Characterization of particle transport, however, revealed that careful selection of process parameters, such as tubing diameter, flow rates, solvents, etc., is crucial to achieve the full benefits of such reactors.

A New Model for Nano-TiO2 Crystal Birth and Growth in Hydrothermal Treatment Using an Oriented Attachment Approach

The synthesis of TiO2 was studied in an original hydrothermal process that uses triethanolamine titanium complex Ti(TeoaH)2 as a Ti precursor and triethanolamine (TeoaH3) as a shape controller to obtain bipyramidal anatase nanoparticles. Backed-up by experimental evidence, i.e., time profiles for Ti(IV) species concentrations together with crystal shape and particle size distributions measured by dynamic light scattering and electron microscopy, a mathematical model was built. The model includes chemical reactions responsible for TiO2 generation in solution and the subsequent anatase nucleation and crystal growth. The oriented attachment mechanism was adopted to explain the build-up of crystals with equilibrium anatase structure (Wulff structure) and time-varying shape factor. This complex mathematical model was solved writing and validating an in-house software using the Matlab (Natick, MA, USA) environment. The process was simulated for a batch time of 50 h, and the results, in terms of main species con...

Real-time feasible multi-objective optimization based nonlinear model predictive control of particle size and shape in a batch crystallization process

This paper presents nonlinear model predictive control (NMPC) and nonlinear moving horizon estimation (MHE) formulations for controlling the crystal size and shape distribution in a batch crystallization process. MHE is used to estimate unknown states and parameters prior to solving the NMPC problem. Combining these two formulations for a batch process, we obtain an expanding horizon estimation problem and a shrinking horizon model predictive control problem. The batch process has been modeled as a system of differential algebraic equations (DAEs) derived using the population balance model (PBM) and the method of moments. Therefore, the MHE and NMPC formulations lead to DAE-constrained optimization problems that are solved by discretizing the system using Radau collocation on finite elements and optimizing the resulting algebraic nonlinear problem using Ipopt. The performance of the NMPC–MHE approach is analyzed in terms of setpoint change, system noise, and model/plant mismatch, and it is shown to provide better setpoint tracking than an open-loop optimal control strategy. Furthermore, the combined solution time for the MHE and the NMPC formulations is well within the sampling interval, allowing for real world application of the control strategy.

Crystal Population Growth in a Continuous Helically Coiled Flow Tube Crystallizer

AbstractA helically coiled flow tube crystallizer was investigated as a novel device for the shape‐selective generation of crystals with potassium alum as the model solid. The shape evolution of the crystal population was analyzed for growth‐dominated seeded cooling crystallization. The macro‐mixing behavior was characterized by residence time distribution measurements for the fluid phase and the crystals. At the crystallizer outlet, a flow‐through microscope was used to analyze the crystal size and shape distribution, where the 3D shape of individual crystals was estimated from 2D projections. The experiments showed a separation of the particle population according to the crystal size. This process allows the controlled shaping of crystals under continuous operating conditions.

Effect of Acetonitrile‐Based Crystallization Conditions on the Crystal Quality of Vitamin D3

AbstractTo design an integrated continuous crystallization setup that is directly coupled to a photochemical synthesis in flow, the crystallization of vitamin D3 was studied in detail. Because of the high solubility of the vitamin in the reaction solvent tert‐butylmethyl ether, a solvent swap to acetonitrile was necessary. While other methods use a multistep procedure, with the proposed approach, crystalline vitamin D3 can be obtained within one crystallization step. The influence of crystallization parameters, such as the initial concentration of vitamin D3, stirring as well as cooling temperature, rate, and time, on the obtained results in terms of yield, crystal shape, polymorphism, and particle size distribution are discussed in detail.

Continuous Crystallization in a Helically Coiled Flow Tube: Analysis of Flow Field, Residence Time Behavior, and Crystal Growth

A continuously operated helically coiled flow tube (HCT) crystallizer is investigated for crystal growth. Inline video-imaging is used for crystal shape analysis and residence time estimation of potash alum. The main finding is that there is a size-dependent particle residence time. Large particles move faster through the HCT than small particles. Consequently, small crystals have more time to grow in the HCT. Physical reasons for this behavior are proposed, for example, small-scale flow characteristics. In a direct numerical simulation of the instationary Navier–Stokes equations, velocity fluctuations and a secondary flow are identified. The presented flow field may have a different impact on the particles and cause the size-dependent particle residence time. A particle size dependent residence time may potentially narrow the crystal size and shape distribution in such a process, frequently a desired feature in solids’ production.

Optimal Control of Crystal Shapes in Batch Crystallization Experiments by Growth-Dissolution Cycles

The control of the evolution of the crystal size and shape distribution (CSSD) during crystallization processes is an important task in crystallization, as the final CSSD decisively influences the physical and solid state properties of crystalline material. This work utilizes sequential growth and dissolution cycles, which turn out to result in an essentially enlarged region of attainable crystal sizes and shapes. Using potassium dihydrogen phosphate as a model substance, such a cyclic crystallization process is realized in a batch scale and in a novel, fully automated, and controlled manner. To this end, a novel observer setup is presented, which is based on video microscopy, and facilitates the real-time monitoring of the evolution of the crystal size and shape distribution. Given this information, optimal strategies for the control of supersaturation profiles as well as CSSD are experimentally successfully implemented, proving a reliable and high-precision generic control scheme for crystal shape manip...

Stereo imaging of crystal growth

Significance A methodology that directly images the full three‐dimensional (3‐D) shape of crystals within a crystallizer is reported. It is based on the mathematical principle that if the two‐dimensional (2‐D) images of an object are obtained from two or more different angles, the full 3‐D crystal shape could be reconstructed. A prototype instrument is built and proof of concept study performed to demonstrate the potentials in using the system for 3‐D measurement of crystal shape and shape distribution. It is our belief that 3‐D measurement of crystal shape represents a significant step forward from existing work of 2‐D measurement of crystal morphology and is potentially of great significance to research toward closed‐loop control of crystal morphology. © 2015 American Institute of Chemical Engineers AIChE J, 62: 18–25, 2016