Magma density

This quantity, which is often referred to as magma density or soHds concentration (mass of crystals per unit system volume), is often an important process variable. A cumulative mass fraction of crystals having a size less than U can also be defined as... 

The magma density Mj- (mass of crystals per unit volume of slurry or Hquor) may be obtained from the third moment of the population density function and is given by... 

Although magma density is a function of the kinetic parameters fP and G, it often can be measured iadependentiy. In such cases, it should be used as a constraint ia evaluating nucleation and growth rates from measured crystal size distributions (62), especially if the system of iaterest exhibits the characteristics of anomalous crystal growth. 

Clearly, the form of the population density function resulting from a clear-Hquor advance system is identical to that expected from perfectly mixed systems in which T., is identical to T,. Unless the increase in magma density associated with clear-Hquor advance results in significant increases in... 

A reduction in the magma density will generally increase nucleation and decrease the particle size. This technique has the disadvantage that crystal formation on the equipment surfaces increases because lower shiny densities create higher levels of supersaturation within the equipment, particularly at the critical boiling surface in a vaporization-type ciystaUizer. 

Slurry density or magma density , Mt = 10.13g/lOOml slurry = 103.1 kg/m. A plot of In n versus L from the table is given below. 

Similarly, the dependenee j of nueleation rate B on magma density Mt and stirrer speed N in MSMPR erystallizers given by... 

Where most values of i a 1, within the range 0.14-1.07. Additionally, a dependenee on stirrer speed k is observed being in the range 0 < /c < 7.8 (Garside and Shah, 1980). Thus the observed nueleation rates in MSMPR erystallizers depend on both magma density and stirrer speed. They are thus likely to have been due to seeondary rather than primary nueleation. Further evidenee suggests these effeets result from erystal/solution interaetions (see Chapter 5). 

The CSD from an MSMPR crystallizer with a working volume of 10 m operated with a magma density of 250 kg crystals/m slurry and a production rate of 62 500 kg crystals/h has a mass mean size of 480 pm. Calculate ... 

Figure 8.23 Predicted time courses of supersaturation and magma density (Wachi and Jones, 1992)...

Mt suspension, or magma, density, kgm n L, t) population density distribution function, /m" nuclei population density (m m )... 

The constant fc uc depends on process variables other than supersaturation, magma density, and intensity of mixing these include temperature and presence of impurities. If sufficient data are available, these variables may be separated from the constant by adding more terms in a power-law correlation. knuc is specific to the operating equipment and not transferable from one equipment scale to another. The system-specific constants i and j are obtainable from experimental data and may be used in scale-up, although j may vary considerably with mixing conditions. 

System conditions often allow for the measurement of magma density, and in such cases is should be used as a constraint in evaluating nucleation and growth kinetics from measured population densities. This approach is especially useful in instances of uncertainty in the determination of population densities from sieving or other particle sizing techniques. 

In a circulating-magma crystallizer the supersaturation created in the vapor head does not rise to point b, for it is being deposited on the crystals as it is formed by evaporation. Higher recirculation rates and/or magma densities permit operation at lower actual supersaturations, thereby decreasing spontaneous nucleation, but increasing the number of nuclei formed by attrition. 

As shown above, growth rate G can be obtained from the slope of a pica of the log of population density data against crystal size nucleation rale B can he obtained from the same data by using the relationship B ° = n° G, where In n° Is iha intercept of the plot with the axis at L = 0. Nucleation rates obtained by these procedures should be checked by comparison with values obtained from a mass belance. It can be shown that the magma density of a sluny in a perfectly mixed ciystallizer is given by... 

F. P. O Dell and R. W. Rousseau. Magma Density nad Dominant Size for Size-Dependent... 

By removing a large fraction of the mother liquor from the jacket in this fashion, the magma density is sharply increased. Magma densities of 30 to 50... 

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