Crystallizers perfectly-mixed

Determination of Crystallization Kinetics. Under steady-state conditions, the total number production rate of crystals in a perfectly mixed crystallizer is identical to the nucleation rate, B. Accordingly,... 

Preferential Removal of Crystals. Crystal size distributions produced ia a perfectiy mixed continuous crystallizer are highly constraiaed the form of the CSD ia such systems is determined entirely by the residence time distribution of a perfectly mixed crystallizer. Greater flexibiUty can be obtained through iatroduction of selective removal devices that alter the residence time distribution of materials flowing from the crystallizer. The... 

The growth of long chains ( > 10 ) in the perfectly mixed 1 1 crystals of ethylene with chlorine and bromine at 20-70 K was studied in detail by Wight et al. [1993]. Active radicals were generated by pulse photolysis of CI2 or Br2. The rate constant was found to be /Cc = 8-12s below Tc = 45 K. The chain grows according to the well known radical mechanism including the reactions... 

In batch operations, mixing takes place until a desired composition or concentration of chemical products or solids/crystals is achieved. For continuous operation, the feed, intermediate, and exit streams will not necessarily be of the same composition, but the objective is for the end/exit stream to be of constant composition as a result of the blending, mixing, chemical reaction, solids suspension, gas dispension, or other operations of the process. Perfect mixing is rarely totally achieved, but represents the instantaneous conversion of the feed to the final bulk and exit composition (see Figure 5-26). 

The first-principle method used in the present study will be outlined below. Population balance analysis on a perfectly mixed batch crystallizer with negligible crystal breakage and agglomeration yields the familiar nucleation rate equation used by Misra and White (5)... 

The special flow configuration of the perfect mixing-plug flow in series in the impinging stream crystallizer is more suitable to crystallization process and so it is much easier to prepare uniformly large-sized crystalline particles and... 

MSMPR crystallizer A vessel operating in a continuous manner in which crystallization occurs and whose contents are perfectly mixed. As a result of perfect mixing, all variables descriptive of the mother liquor and crystals are constant throughout the vessel and are identical to corresponding variables in the product stream leaving the vessel. 

FIGURE 16 Typical population density plot from perfectly mixed, continuous crystallizer. 

The perfectly mixed crystallizer of the type described in the preceding discussion is highly constrained. Alteration of the characteristics of crystal size distributions produced by such systems can be accomplished only by modifications of the nucleation and growth kinetics of the system being crystallized. Indeed, examination of Eq. (54) shows that once nucleation and growth kinetics... 

As indicated above, crystal size distributions produced in a perfectly mixed crystallizer are constrained by the nature of the system. This is because both liquor and solids... 

These two equations are plotted in Fig. 25, from which it is seen that in a perfectly mixed crystallizer the dominant-size fraction (mode) appears at l/L = 3. Saeman illustrated his analysis with data from large-scale vacuum crystallization of ammonium nitrate (M9, SI). 

Kinetics can also be studied at surface science conditions. Feed can be leaked at a constant rate into the chamber containing the crystal face, and the gas is removed at a constant rate by the pumps. The composition of the chamber gas can be continuously monitored by mass spectrometry. The pressure in the reaction chamber is low enough to ensure Knudsen flow The gaseous molecules collide almost exclusively with the exposed solid surfaces, and the system behaves as a perfectly mixed flow reactor (CSTR). Experiments in the transient regime with various forcing functions can be performed, and response times can be orders of magnitude smaller than those at atmospheric pressure. The catalytic oxidation of CO on Pt(llO) was one of the first studies of this type (33). 

Figure 5 Calculated fractional crystallization trends for group IIIAB iron meteorites using several different types of models. The simple fractional crystallization models assume a perfectly mixed liquid whereas the other four models assume different types of imperfect mixing (reproduced by permission of the Meteoritical Society from Meteorit.

Randolph and Larson showed that for a continuous crystallizer with a (perfectly) mixed suspension, (perfectly) mixed product removal (MSMPR) crystallizer. 

While this methodology has been shown to be very useful for many crystallization processes, it is subject to size dispersion and the other nonlinear effects of Fig. 4-24, and has the additional need to assure (perfect) mixing up to and including the product exit line. Use of large amounts of material is often impossible for pharmaceutical products in the early stages of development, so this technique has only limited use in our industry. 

Its chemical composition, for example, is still uncertain. The powerful H-atom abstracting ability of MP" was overlooked in the otherwise careful early work and has yet to be controlled convincingly. The so-called second phase of MP-TCNQ turned out to be HMP-TCNQ, which as summarized in Section 4.1 has typical mixed stacks of D and A ion radicals. Photochemical generation of HMP and the concomitant degradation of MP in solution are apparently general phenomena 119,120) gio crystallization to enhance crystal perfection then becomes counterproductive. Sandman has addressed such questions about the kinetic control... 

This misconception is particularly common in crystallization. The hypothesis of a perfectly mixed system is, for crystallization and precipitation processes, labeled as mixed-suspension, mixed-product removal (MSMPR). With diis model the crystalUzer is modeled with a spatially homogeneous NDF, generally called the crystal-size distribution (CSD). However, the fact that the CSD is constant through the vessel does not mean that the rates of crystal nucleation, molecular growth, aggregation, and breakage are constant. 

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... 

The perfectly mixed, contineous. stendy-state mixed-suspension mixed-product removal (MSMPR) ciys-laHirer is restrictive in the degree to which characteristics of a crystal size distribution can be varied. Indeed, examination of Eqs. (11.2-32) and (11.2-40) shows that once nucleation and growth lunatics are fixed in these systems the crystal size distribution is determined in its entirety. In addition, such distributions have the following characteristics ... 

An experimental setup for gaseous systems is shown in Fig. 7. The actual ZLC column consists of a thin layer of adsorbent material placed between two porous sinter discs. The individual particles (or crystals) are dispersed approximately as a monolayer across the area of the sinter. This minimizes the external resistances to heat and mass transfer, so that the adsorption cell can be considered as a perfectly mixed isothermal, continuous-flow cell. The validity of this assumption has been examined in detail [52]. The isothermal approximation is generally valid for studies of diffusion in zeoHte crystals, but it can break down for strongly adsorbed species in large composite particles under conditions of macropore diffusion control. 

The next important contribution was made by Bransom, Dunning and Millard (1949) who, like McCabe, considered a perfectly mixed crystallizer, now commonly referred to as a mixed-suspension mixed-product removal (MSMPR) crystallizer (section 9.1.1). In addition, however, they considered the more realistic case where spontaneous nucleation and subsequent growth occurs. They also assumed a first-order growth law... 

Another early paper was that of Robinson and Roberts (1957) who derived mathematical relationships for residence times, and hence the CSDs, in a cascade series of perfectly mixed crystallizers (section 9.1.2). 

It is appropriate, however, to make some comment here on a few common departures from MSMPR operation. Three basic types of continuously operated mixed-suspension crystallizer are shown in Figure 9.7. In the simple MSMPR unit Figure 9.7a), where the outflow is of identical composition to that in the perfectly mixed vessel, the crystal and liquor residence times are equal ... 

In multiciystal magma systems, growth kinetics become difficult to isolate from other phenomena, although a combined analysis, such as that described fai Section 11.2-4 for the perfectly mixed ciystallizer, gives a realistic view of the actual process that occurs in a crystallizer that is, nucieatirm and growth kinetics are measured simultaneously and therefore at the same process conditions. 

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