Effect of the rate of stirring on crystal size in precipitating or salting-out systems

1986 ◽  
Vol 51 (8) ◽  
pp. 1609-1617 ◽  
Author(s):  
Jaroslav Nývlt ◽  
Stanislav Žáček
Keyword(s):  
Simple Model ◽  
Nucleation Rate ◽  
Crystal Size ◽  
Interfacial Area ◽  
Dissipated Energy ◽  
Potassium Sulphate ◽  
Salting Out ◽  
Derived Relations ◽  
Series Of Experiments ◽  
The Mean

A simple model is proposed to express the dependence of the mean crystal size on the rate of stirring in precipitating or salting-out systems. The nucleation rate is taken to be proportional to the interfacial area of segregated regions. This area is a function of the dissipated energy. The derived relations are applied to results of a series of experiments in which aluminium-potassium sulphate was salted out by the addition of aqueous solutions of methyl alcohol.

Scale-up of stirred crystallisers. Batch precipitation of aluminium potassium sulphate

1982 ◽  
Vol 47 (11) ◽  
pp. 3027-3031 ◽  
Author(s):  
Piotr Karpiński ◽  
Stanislav Žáček ◽  
Jaroslav Nývlt ◽  
Jerzy Budz
Keyword(s):  
Size Distribution ◽  
Kinetic Constant ◽  
Scale Up ◽  
Potassium Sulphate ◽  
Aluminium Sulphate ◽  
Mixing Intensity ◽  
Mean Size ◽  
Relative Kinetic ◽  
Series Of Experiments ◽  
The Mean

Aluminium potassium sulphate has been precipitated batchwise by mixing equal volumes of 0.6 mol/l solutions of potassium sulphate and aluminium sulphate with eventual addition of water in advance. The experiments were performed at 20 and 25 °C in the volume 100 to 200 cm3 and in the volume 0.021 m3. From the size distribution of product crystals, the mean size of crystals has been evaluated and calculated the system kinetic constant of crystallization BN. The system constant is different in both series of experiments and can be correlated with the size of the crystallizer or with mixing intensity. Its value and the value of relative kinetic exponent g/n is comparable with the values obtained in experiments with cooling of solutions.

System constant and its significance in industrial crystallisation

1979 ◽  
Vol 44 (12) ◽  
pp. 3549-3554 ◽  
Author(s):  
Jaroslav Nývlt ◽  
Miroslav Broul
Keyword(s):  
Steady State ◽  
Nucleation Rate ◽  
Derived Relations ◽  
Specific Output ◽  
Simple Arrangement ◽  
Mean Size ◽  
General Derivation ◽  
The Mean ◽  
Fundamental Equations ◽  
Selection Of

Fundamental equations describing behaviour of the continuous stirred crystalliser in steady state include a system constant B, whose value strongly depends on selection of the size of initial crystals LN. To avoid this dependence and to see that the equations be applicable for crystalliser design also in the case when the value LN approaches zero, a general derivation of the dependence between the mean size of crystals L and specific output of the crystalliser mc has been derived on basis of the numerical nucleation rate. The derived relations do not include the quantity LN and they can be transformed by a simple arrangement to the published relations.

Growth of crystals not obeying the McCabe ΔL-law

1979 ◽  
Vol 44 (7) ◽  
pp. 2173-2183 ◽  
Author(s):  
Jaroslav Nývlt
Keyword(s):  
Growth Rate ◽  
Crystal Growth ◽  
Population Density ◽  
Residence Time ◽  
Nucleation Rate ◽  
Crystal Size ◽  
Linear Growth ◽  
Linear Growth Rate ◽  
Derived Relations ◽  
Film Model

On basis of the film model of crystal growth the relation L = L0 (1 + az) has been derived which describes the dependence of the linear growth rate on crystal size as a function of the dimensionless residence time of crystals z. For the perfectly stirred (MSMPR) crystallizer were then derived relations for the reduced population density of crystals nucleation rate, mean crystal size and distribution of crystal sizes. For very small values of the parameter a all derived relations give numerical values close to those satisfying the McCabe ΔL-law.

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.

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.

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.

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.

Experiments on the flow of heat in liquid helium below 0.7 °K

1958 ◽  
Vol 246 (1246) ◽  
pp. 390-405 ◽  
Keyword(s):  
Thermal Conductivity ◽  
Liquid Helium ◽  
Free Path ◽  
Empirical Relation ◽  
Mean Free Path ◽  
Series Of Experiments ◽  
The Mean ◽  
Set Up ◽  
Low Pressures ◽  
Measured Thermal Conductivity

A series of experiments has been performed to study the steady flow of heat in liquid helium in tubes of diameter 0.05 to 1.0 cm at temperatures between 0.25 and 0.7 °K. The results are interpreted in terms of the flow of a gas of phonons, in which the mean free path λ varies with temperature, and may be either greater or less than the diameter of the tube d . When λ ≫ d the flow is limited by the scattering of the phonons at the walls, and the effect of the surface has been studied, but when λ ≪ d viscous flow is set up in which the measured thermal conductivity is increased above that for wall scattering. This behaviour is very similar to that observed in the flow of gases at low pressures, and by applying kinetic theory to the problem it can be shown that the mean free path of the phonons characterizing viscosity can be expressed by the empirical relation λ = 3.8 x 10 -3 T -4.3 cm. This result is inconsistent with the temperature dependence of λ as T -9 predicted theoretically by Landau & Khalatnikov (1949).

The Estimation of the Efficiency of Sampling, with Special Reference to Sampling for Yield in Cereal Experiments

1935 ◽  
Vol 25 (4) ◽  
pp. 545-577 ◽  
Author(s):  
F. Yates ◽  
I. Zacopanay
Keyword(s):  
Standard Deviation ◽  
Special Reference ◽  
Analysis Of Variance ◽  
Sampling Methods ◽  
Cereal Crops ◽  
Loss Of Information ◽  
Preliminary Discussion ◽  
Experimental Errors ◽  
Series Of Experiments ◽  
The Mean

The estimation of the experimental yields of cereal crops by sampling methods is considered in the light of results of eighteen experiments which were harvested by these methods at Rothamsted and its associated centres. The harvesting results of the Crop-Weather series of experiments are also included.A preliminary discussion of the interpretation of the analysis of variance as applied to sampling results is given, and an expression is found for the loss of information arising out of sampling. The results of the discussion are applicable to all types of sampling carried out on replicated experiments.The sampling and experimental errors of all the experiments have been calculated. The variation between sampling units in the same subplot (usually between l/100th and l/200th acre) was found to be such as would arise if each metre length of row had a standard deviation (about the plot mean) of the order of 25–30 per cent. of the mean yield.

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