Relationship between number and sizes of crystals growing in batch crystallization: Nuclei number density, nucleation kinetics and crystal polydispersity

2020 ◽  
Vol 546 ◽  
pp. 125786
Author(s):  
Christo N. Nanev
Keyword(s):  
Number Density ◽  
Nucleation Kinetics ◽  
Batch Crystallization ◽  
Nuclei Number

scholarly journals Sensitivities of Lagrangian modelling of mid-latitude cirrus clouds to trajectory data quality

2015 ◽  
Vol 15 (13) ◽  
pp. 7429-7447 ◽  
Author(s):  
E. Kienast-Sjögren ◽  
A. K. Miltenberger ◽  
B. P. Luo ◽  
T. Peter
Keyword(s):  
Cooling Rate ◽  
Temporal Resolution ◽  
Vertical Velocity ◽  
Input Data ◽  
Temperature Fluctuations ◽  
Box Model ◽  
Specific Humidity ◽  
Number Density ◽  
Ice Nuclei ◽  
Nuclei Number

Abstract. Simulations of cirrus are subject to uncertainties in model physics and meteorological input data. Here we model cirrus clouds along air mass trajectories, whose extinction has been measured with an elastic backscatter lidar at Jungfraujoch research station in the Swiss Alps, with a microphysical stacked box model. The sensitivities of these simulations to input data uncertainties (trajectory resolution, unresolved vertical velocities, ice nuclei number density and upstream specific humidity) are investigated. Variations in the temporal resolution of the wind field data (COSMO-Model at 2.2 km resolution) between 20 s and 1 h have only a marginal impact on the trajectory path, while the representation of the vertical velocity variability and therefore the cooling rate distribution are significantly affected. A temporal resolution better than 5 min must be chosen in order to resolve cooling rates required to explain the measured extinction. A further increase in the temporal resolution improves the simulation results slightly. The close match between the modelled and observed extinction profile for high-resolution trajectories suggests that the cooling rate spectra calculated by the COSMO-2 model suffice on the selected day. The modelled cooling rate spectra are, however, characterized by significantly lower vertical velocity amplitudes than those found previously in some aircraft campaigns (SUCCESS, MACPEX). A climatological analysis of the vertical velocity amplitude in the Alpine region based on COSMO-2 analyses and balloon sounding data suggests large day-to-day variability in small-scale temperature fluctuations. This demonstrates the necessity to apply numerical weather prediction models with high spatial and temporal resolutions in cirrus modelling, whereas using climatological means for the amplitude of the unresolved air motions does generally not suffice. The box model simulations further suggest that uncertainties in the upstream specific humidity (± 10 % of the model prediction) and in the ice nuclei number density (0–100 L−1) are more important for the modelled cirrus cloud than the unresolved temperature fluctuations if temporally highly resolved trajectories are used. For the presented case the simulations are incompatible with ice nuclei number densities larger than 20 L−1 and insensitive to variations below this value.

scholarly journals Stellar Encounters in Dense Systems

1996 ◽  
Vol 174 ◽  
pp. 243-252
Author(s):  
Melvyn B. Davies
Keyword(s):  
Globular Clusters ◽  
Large Fraction ◽  
Close Encounter ◽  
Solar Neighbourhood ◽  
Number Density ◽  
Age Of The Universe ◽  
The Universe ◽  
Nuclei Number

The number density of stars in the solar neighbourhood is sufficiently low that encounters between two stars will be extremely rare. However, in the cores of globular clusters, and glactic nuclei, number densities are sufficiently high (∼ 105 stars/pc3 in some systems) that encounter timescales can be comparable, or even less than, the age of the universe. In other words, a large fraction of the stars in these systems will have suffered from at least one close encounter or collision in their lifetime.

scholarly journals Sensitivities of Lagrangian modeling of mid-latitude cirrus clouds to trajectory data quality

2015 ◽  
Vol 15 (5) ◽  
pp. 7535-7584 ◽  
Author(s):  
E. Kienast-Sjögren ◽  
A. K. Miltenberger ◽  
B. P. Luo ◽  
T. Peter
Keyword(s):  
Cooling Rate ◽  
Temporal Resolution ◽  
Vertical Velocity ◽  
Weather Prediction ◽  
Specific Humidity ◽  
Number Density ◽  
Wind Fields ◽  
Ice Nuclei ◽  
Velocity Variance ◽  
Nuclei Number

Abstract. Simulations of cirrus are subject to uncertainties in model physics and meteorological input data. Here we model cirrus clouds, whose extinction has been measured with an elastic backscatter Lidar at Jungfraujoch research station in the Swiss Alps, and investigate the sensitivities to input data uncertainties (trajectory resolution, unresolved vertical velocities, ice nuclei number density and upstream specific humidity). Simulations with a microphysical stacked box model have been performed along trajectories derived from the high-resolution numerical weather prediction model COSMO-2 (2.2 km grid spacing). For the calculation of the trajectories we experimented with model wind fields at temporal resolutions between 20 s and 1 h. While the temporal resolution affects the trajectory path only marginally, it has a strong impact on the vertical velocity variance resolved along the trajectories, and therefore on the cooling rate distribution. In the present example, the temporal resolution of the wind fields must be chosen to be better than 5 min in order to resolve vertical velocities and cooling rates required to explain the measured extinction. The simulation improves slightly if the temporal resolution is increased further to 20 s. This means that on the selected day the cooling rate spectra calculated by COSMO-2 suffice to achieve agreement with the cirrus measurements. On that day cooling rate spectra are characterized bysignificantly lower vertical velocity amplitudes than those found previously in some aircraft campaigns (SUCCESS, MACPEX). A climatological analysis of the vertical velocity variance in the Alpine region based on COSMO-2 analyses and balloon sounding data suggests large day-to-day variability in small-scale temperature fluctuations. This demonstrates the necessity to apply numerical weather prediction models with high spatial and temporal resolutions in cirrus modeling, whereas using climatological means for the amplitude of the unresolved air motions does generally not suffice. The box model simulations further suggest that uncertainties in the upstream specific humidity (±10% of the model prediction) and in the ice nuclei number density are more important for the modeled cirrus cloud than the unresolved temperature fluctuations, if temporally highly resolved trajectories are used. For the presented case the simulations are incompatible with ice nuclei number densities larger than 20 L−1 and insensitive to variations below this value.

Mass Determination by Direct Measurement of Electron Scattering

1975 ◽  
Vol 33 ◽  
pp. 240-241
Author(s):  
M. K. Lamvik ◽  
A. V. Crewe
Keyword(s):  
Cross Section ◽  
Electron Scattering ◽  
Mass Density ◽  
Variable Mass ◽  
Scattering Cross Section ◽  
Mass Determination ◽  
Number Density ◽  
Cross Sectional ◽  
Thin Slice ◽  
Scattering Cross

If a molecule or atom of material has molecular weight A, the number density of such units is given by n=Nρ/A, where N is Avogadro's number and ρ is the mass density of the material. The amount of scattering from each unit can be written by assigning an imaginary cross-sectional area σ to each unit. If the current I0 is incident on a thin slice of material of thickness z and the current I remains unscattered, then the scattering cross-section σ is defined by I=IOnσz. For a specimen that is not thin, the definition must be applied to each imaginary thin slice and the result I/I0 =exp(-nσz) is obtained by integrating over the whole thickness. It is useful to separate the variable mass-thickness w=ρz from the other factors to yield I/I0 =exp(-sw), where s=Nσ/A is the scattering cross-section per unit mass.

AEM analysis of solidification catalysts in atomized Fe-Ni

1986 ◽  
Vol 44 ◽  
pp. 584-585
Author(s):  
Matthew R. Libera
Keyword(s):  
Powder Particle ◽  
Alloy Composition ◽  
Particle Diameter ◽  
Metastable Phases ◽  
Liquid Droplets ◽  
Nucleation Kinetics ◽  
Ni Alloys ◽  
Nonequilibrium Solidification

The liquid droplets produced by atomization processes are believed to undergo substantial supercooling during solidification, because the catalytic heterogeneities, for statistical reasons, tend to be isolated in the larger droplets. This supercooling can lead to the nucleation of metastable phases. As part of a study on the effect of liquid supercooling on nonequilibrium solidification, three binary Fe-Ni alloys have been produced by conventional argon atomization (Fe-20Ni, Fe-30Ni, and Fe-40Ni). The primary variables in these experiments are: i) the alloy composition; and ii) the powder particle diameter (inversely proportional to supercooling). Of particular interest in this system is the competitive nucleation kinetics between the stable fee and metastable bec phases. Bcc is expected to nucleate preferentially with decreasing %Ni and decreasing particle diameter.

PEMBUATAN SURFAKTAN DARI ASAM OLEAT

2019 ◽  
Vol 1 (3) ◽  
pp. 68
Author(s):  
Puguh Setyopratomo ◽  
Edy Purwanto ◽  
H. Yefrico ◽  
H. Yefrico
Keyword(s):  
Oleic Acid ◽  
Optimum Condition ◽  
Reaction Temperature ◽  
Catalyst Concentration ◽  
Acid Number ◽  
Esterification Reaction ◽  
Number Density ◽  
Sample Analysis ◽  
Reaction Conversion ◽  
Glycerol Mono

The synthesis of glycerol mono oleic from oleic acid and glycerol is classified as an esterification reaction. This research is aimed to study the influent of reaction temperature and catalyst concentration on reaction conversion. During the experiment the temperature of reaction mixture was varied as 110 oC, 130 oC, and 150 oC, while the catalyst concentration of 1%, 3 %, and 5% was used. The batch experiment was conducted in a glass reactor equipped with termometer, agitator, and reflux condensor. The oleic acid – glycerol mol ratio of 1 : 2 was used as a mixture feed. To maintain the reaction temperature at certain level, the oil bath was used. After the temperature of reaction mixture was reached the expected value, then H2SO4 catalyst was added to the reactor.  To measure the extent of the reaction, every 30 minutes the sample was drawn out from the reactor vessel. The sample analysis include acid number, density, and viscosity measurement. From this research the optimum condition which is the temperature of reaction of 150 oC and 1% catalyst concentration was obtained. At this optimum condition the convertion reach 86% and the analysis of other physical properties of the product show the acid number of 24.12, the density of 0.922 g/cc, and the viscosity of 118.4 cp.

Combining First-Principles and Data Modeling for the Accurate Prediction of the Refractive Index of Organic Polymers

2017 ◽  
Author(s):  
Mohammad Atif Faiz Afzal ◽  
Chong Cheng ◽  
Johannes Hachmann
Keyword(s):  
First Principles ◽  
Data Modeling ◽  
Accurate Prediction ◽  
Index Of Refraction ◽  
Structure Theory ◽  
Organic Polymers ◽  
Number Density ◽  
Lorenz Equation ◽  
In Silico Studies ◽  
Wide Range

Organic materials with a high index of refraction (RI) are attracting considerable interest due to their potential application in optic and optoelectronic devices. However, most of these applications require an RI value of 1.7 or larger, while typical carbon-based polymers only exhibit values in the range of 1.3–1.5. This paper introduces an efficient computational protocol for the accurate prediction of RI values in polymers to facilitate in silico studies that an guide the discovery and design of next-generation high-RI materials. Our protocol is based on the Lorentz-Lorenz equation and is parametrized by the polarizability and number density values of a given candidate compound. In the proposed scheme, we compute the former using first-principles electronic structure theory and the latter using an approximation based on van der Waals volumes. The critical parameter in the number density approximation is the packing fraction of the bulk polymer, for which we have devised a machine learning model. We demonstrate the performance of the proposed RI protocol by testing its predictions against the experimentally known RI values of 112 optical polymers. Our approach to combine first-principles and data modeling emerges as both a successful and highly economical path to determining the RI values for a wide range of organic polymers.

Batch Crystallization with Crystals Attrition

1993 ◽  
Vol 58 (8) ◽  
pp. 1855-1860 ◽  
Author(s):  
Jaroslav Nývlt ◽  
Stanislav Žáček
Keyword(s):  
Mathematical Model ◽  
Calcium Sulfate ◽  
Crystal Size ◽  
Theoretical Description ◽  
Secondary Nucleation ◽  
Batch Crystallization ◽  
Batch Time ◽  
The Mean

The dependence of the mean crystal size of the products from batch crystallizers on the batch time occasionally exhibits a maximum, which can be explained by secondary nucleation due to the attrition of crystals. A kinetic equatation of nucleation, comprising a term for crystal attrition, can be used for the theoretical description of such behaviour. A mathematical model of a batch crystallizer with crystal attrition has been verified on the calcium sulfate precipitation.

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