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.

Continuous Precipitation of Lead Iodide

1994 ◽  
Vol 59 (7) ◽  
pp. 1503-1510
Author(s):  
Stanislav Žáček ◽  
Jaroslav Nývlt
Keyword(s):  
Growth Rate ◽  
Particle Size ◽  
Crystal Size ◽  
Crystal Growth Rate ◽  
Laboratory Model ◽  
Lead Iodide ◽  
Secondary Nucleation ◽  
Equimolar Ratio ◽  
Continuous Precipitation ◽  
The Mean

Lead iodide was precipitated from aqueous solutions of 0.015 - 0.1 M Pb(NO3)2 and 0.03 - 0.2 M KI in the equimolar ratio using a laboratory model of a stirred continuous crystallizer at 22 °C. After reaching the steady state, the PbI2 crystal size distribution was measured sedimentometrically and the crystallization kinetics was evaluated based on the mean particle size. Both the linear crystal growth rate and the nucleation rate depend on the specific output of the crystallizer. The system crystallization constant either points to a significant effect of secondary nucleation by the mechanism of contact of the crystals with the stirrer blade, or depends on the concentrations of the components added due to the micromixing mechanism.

Microwave Assisted Direct Nucleation Control for Batch Crystallization: Crystal Size Control with Reduced Batch Time

2015 ◽  
Vol 16 (1) ◽  
pp. 440-446 ◽  
Author(s):  
Rohit Kacker ◽  
Pedro M. Salvador ◽  
Guido S. J. Sturm ◽  
Georgios D. Stefanidis ◽  
Richard Lakerveld ◽  
...  
Keyword(s):  
Crystal Size ◽  
Size Control ◽  
Batch Crystallization ◽  
Microwave Assisted ◽  
Batch Time

Investigation on some operating factors influencing batch cooling crystallization

1987 ◽  
Vol 52 (10) ◽  
pp. 2447-2450
Author(s):  
Jerzy Mydlarz
Keyword(s):  
Size Distribution ◽  
Crystal Size ◽  
Saturation Temperature ◽  
Crystal Size Distribution ◽  
Optimal Batch ◽  
Factors Influencing ◽  
Cooling Crystallization ◽  
Batch Time ◽  
The Mean ◽  
Batch Cooling

The influence of batch time as well as the saturation temperature of stock solution on crystal size distribution has been examined. The results show that there is an optimal batch time, tc, for which the mean crystal size of MgSO4.7 H2O has a maximum. For MgSO4.7 H2O and H2C2O4.2 H2O, the mean crystal size of the product increased with increasing saturation temperature of the solution.

Batch Precipitation of Lead Iodide

1994 ◽  
Vol 59 (6) ◽  
pp. 1301-1304
Author(s):  
Jaroslav Nývlt ◽  
Stanislav Žáček
Keyword(s):  
Aqueous Solution ◽  
Particle Size ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Crystal Size ◽  
Lead Nitrate ◽  
Lead Iodide ◽  
Constant Rate ◽  
Mean Size ◽  
The Mean

Lead iodide was precipitated by a procedure in which an aqueous solution of potassium iodide at a concentration of 0.03, 0.10 or 0.20 mol l-1 was stirred while an aqueous solution of lead nitrate at one-half concentration was added at a constant rate. The mean size of the PbI2 crystals was determined by evaluating the particle size distribution, which was measured sedimentometrically. The dependence of the mean crystal size on the duration of the experiment exhibited a minimum for any of the concentrations applied. The reason for this is discussed.

Non-isothermal crystallization behavior of spinel crystals in FeO-SiO2-TiO2-V2O3-Cr2O3 slag

2018 ◽  
Vol 116 (1) ◽  
pp. 110
Author(s):  
Lixiong Shao ◽  
Jiang Diao ◽  
Wang Zhou ◽  
Tao Zhang ◽  
Bing Xie
Keyword(s):  
Cooling Rate ◽  
Crystallization Behavior ◽  
Crystal Size ◽  
Growth Mechanisms ◽  
Vanadium Slag ◽  
Growth Behaviour ◽  
Temperature Range ◽  
Chromium Spinel ◽  
Mean Diameter ◽  
The Mean

The growth behaviour of spinel crystals in vanadium slag with high Cr2O3 content was investigated and clarified by statistical analyses based on the Crystal Size Distribution (CSD) theory. The results indicate that low cooling rate and Cr2O3 content benefit the growth of spinel crystals. The chromium spinel crystals firstly precipitated and then acted as the heterogeneous nuclei of vanadium and titanium spinel crystals. The growth mechanisms of the spinel crystals at the cooling rate of 5 K/min consist two regimes: firstly, nucleation control in the temperature range of 1873 to 1773 K, in which the shapes of CSD curves are asymptotic; secondly, surface and supply control within the temperature range of 1773 to 1473 K, in which the shapes of CSD curves are lognormal. The mean diameter of spinel crystals increases from 3.97 to 52.21 µm with the decrease of temperature from 1873 to 1473 K.

Application of an Empirical FBRM Model to Estimate Crystal Size Distributions in Batch Crystallization

2014 ◽  
Vol 14 (2) ◽  
pp. 607-616 ◽  
Author(s):  
Huayu Li ◽  
Yoshiaki Kawajiri ◽  
Martha A. Grover ◽  
Ronald W. Rousseau
Keyword(s):  
Crystal Size ◽  
Size Distributions ◽  
Batch Crystallization ◽  
Crystal Size Distributions

Validation of New Mathematical Model of Flank Wear by Different Methods

2012 ◽  
Vol 729 ◽  
pp. 169-174 ◽  
Author(s):  
Zoltán Pálmai ◽  
Márton Takács ◽  
Balázs Zsolt Farkas
Keyword(s):  
Activation Energy ◽  
Mathematical Model ◽  
Flank Wear ◽  
Technological Parameters ◽  
Wear Process ◽  
Oxidation Processes ◽  
Industrial Manufacturing ◽  
Thermally Activated ◽  
Optical Electron ◽  
The Mean

Having reviewed the literature on cutting and based on the optical, electron-optical and morphological examinations of wear processes we have reached the conclusion that it is possible to describe the abrasive, adhesive and thermally activated diffusion, oxidation processes in a single mathematical model. The model is a non-linear autonomous differential equation, which can be solved by simple numerical methods. The complex wear equation was validated by the results of the cutting tests performed with P20 carbide on C45 carbon steel. If we have this data, we can calculate the activation energy of the process determining the nature of the wear process. The apparent activation energy of wear is Q=151,7kJ/mol. The model can even be used with changing technological parameters, and the data necessary for the constants of the wear equation may as well be determined even by measurements performed on the tool during industrial manufacturing. By the mean of this data, we can calculate the activation energy determining the nature of the wear process.

Non-invasive determination of the systolic peak-to-peak gradient in children with aortic stenosis: validation of a mathematical model

2000 ◽  
Vol 10 (2) ◽  
pp. 115-119 ◽  
Author(s):  
Valter C. Lima ◽  
Evan Zahn ◽  
Christine Houde ◽  
Jeffrey Smallhorn ◽  
Robert M. Freedom ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Pulse Pressure ◽  
Linear Regression Analysis ◽  
Systolic Pressure ◽  
Pressure Gradients ◽  
Non Invasive ◽  
The Mean ◽  
Congenital Aortic Valvar Stenosis ◽  
Peak Gradient

AbstractDoppler derived systolic pressure gradients have become widely applied as noninvasively obtained estimates of the severity of aortic valvar stenosis. There is little correlation, however, between the Doppler derived peak instantaneous gradient and the peak-to-peak gradient obtained at catheterisation, the latter being the most applied variable to determine severity in children. The purpose of this study was to validate a mathematical model based on data from catheterisation which estimates the peak-to-peak gradient from variables which can be obtained by noninvasive means (Doppler derived mean gradient and pulse pressure), according to the formula: peak-to-peak systolic gradient=6.02+1.49*(mean gradient)−0.44*(pulse pressure). Simultaneous cardiac catheterization and Doppler studies were performed on 10 patients with congenital aortic valvar stenosis. Correlations between the gradients measured at catheter measured, and those derived by Doppler, were performed using linear regression analysis. The mean gradients correlated well (y=0.67 × + 11.11, r=0.87, SEE=6 mm Hg, p=0.001). The gradients predicted by the formula also correlated well with the peak-to-peak gradients measured at catheter (y=0.66 × + 14.44, r=0.84, SEE=9 mm Hg, p=O.002). The data support the application of the model, allowing noninvasive prediction of the peak-to-peak gradient across the aortic valvar stenosis.

Mathematical Model of the Dissolution Stage in Cooling Batch Crystallization

2005 ◽  
Vol 40 (11) ◽  
pp. 2231-2243
Author(s):  
L. I. Salcedo ◽  
M. Serna ◽  
A. J. Castro ◽  
E. Bolaños ◽  
P. A. Quintana
Keyword(s):  
Mathematical Model ◽  
Batch Crystallization
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