Balancing of Crystallizers

For solution evaporation, circulation evaporators are often used in the form of a tube bundle apparatus with vertical, horizontal or slanting tubes, operated with natural or forced solution circulation. TVibes may be mounted inside or, with respect to better cleaning, outside (Fig. 7-20) of the evaporator. The solution evaporates inside the tubes and is lifted by the vapor bubbles generated according to the principle of an air lift pump. Natural circulation of the solution is mainly intensified by adding circulation pumps (forced circulation). 

Circulation evaporators are characterized by large liquid holdups, large liquid loads and good heat exchange, but also by larger mean residence times. A high pressure drop appears, especially with forced circulation in narrow tubes. 

Thermally gentle treatment of a solution is enabled by continuous (one pass) evaporators (Fig. 7-21). The solution flows as a film through the evaporation zone, driven by gravitational force, and may be additionally whipped, or dragged up by the vapor. A small pressure drop, low liquid holdup and hence a small mean solution residence 

---

Figure 7 A series of theoretieal rod-coil phase diagrams, where the degree of polymerization is kept constant and the balance of crystallization and order-disorder driving forces ((w/x) is increased from (a) to (e). Bcc = body-centered cubic (spheres). Hex = hexagonally packed cylinders, Lam = lamellae and the angles associated with the smectic C phase describe the tilted angle of the rod blocks, 6, and the dashed lines are contour lines for 6, separating intervals of 5°. (Adapted from Ref. 16. American Chemical Society, 2002.)...

This fundamental relationship points out that the temperature at which crystal and liquid are in equilibrium is determined by the balancing of entropy and enthalpy effects. Remember, it is the difference between the crystal and... 

Rutile pigments, prepared by dissolving chromophoric oxides in an oxidation state different from +4 in the mtile crystal lattice, have been described (25,26). To maintain the proper charge balance of the lattice, additional charge-compensating cations of different metal oxides also have to be dissolved in the mtile stmcture. Examples of such combinations are Ni " + Sb " in 1 2 ratio as NiO + Sb202, + Sb " in 1 1 ratio as Cr202 + Sb O, and Cr " +... 

Small concentrations of vinylcarboxyhc acids, eg, acryhc acid, methacrylic acid, or itaconic acid, are sometimes included to enhance adhesion of the polymer to the substrate. The abihty to crystalline and the extent of crystallization are reduced with increa sing concentration of the comonomers some commercial polymers do not crystalline. The most common lacquer resins are terpolymers of VDC—methyl methacrylate—acrylonitrile (162,163). The VDC level and the methyl methacrylate—acrylonitrile ratio are adjusted for the best balance of solubihty and permeabihty. These polymers exhibit a unique combination of high solubihty, low permeabihty, and rapid crystallization (164). 

Although evidence exists for both mechanisms of growth rate dispersion, separate mathematical models were developed for incorporating the two mechanisms into descriptions of crystal populations random growth rate fluctuations (36) and growth rate distributions (33,40). Both mechanisms can be included in a population balance to show the relative effects of the two mechanisms on crystal size distributions from batch and continuous crystallizers (41). 

Population balances and crystallization kinetics may be used to relate process variables to the crystal size distribution produced by the crystallizer. Such balances are coupled to the more familiar balances on mass and energy. It is assumed that the population distribution is a continuous function and that crystal size, surface area, and volume can be described by a characteristic dimension T. Area and volume shape factors are assumed to be constant, which is to say that the morphology of the crystal does not change with size. 

In a 2-1. round-bottomed flask are placed 120 g. (1.83 moles) of 92% ethylenediamine (Note 1), 300 ml. of 95% ethanol, and 300 ml. of water. The flask is attached to an efficient reflux condenser, and 121 ml. of carbon disulfide is placed in a separatory funnel attached to the top of the condenser by means of a notched cork. About 15 to 20 ml. of the carbon disulfide is added, and the flask is shaken to mix the contents. A vigorous reaction takes place (Note 2), and it may be necessary to cool the flask. After the reaction has started, a water bath at 60° is placed under the flask and the balance of the carbon disulfide is added at such a rate that the vapors reflux about one-third the way up the condenser. About 2 hours are required for the addition of the carbon disulfide. At this time the bath temperature is raised to about 100°, and the mixture is allowed to reflux for 1 hour. Then 15 ml. of concentrated hydrochloric acid is added, and the mixture is refluxed under a good hood (bath at 100°) for 9 to 10 hours. The mixture is cooled in an ice bath, and the product is filtered by suction on a Buchner funnel and washed with 200-300 ml. of cold acetone (Note 3). A yield of 156-167 g. (83-89%) of white crystals is obtained melting at 197-198° (Note 4). 

In a 3-I. three-necked flask, fitted with a mechanical stirrer, a reflux condenser, and a separatory funnel, are placed 24.3 g. (i gram atom) of magnesium turnings, 500 cc. of absolute ether, a crystal of iodine, and a 5- to lo-cc. portion of 126.5 g- cc., I mole) of freshly distilled benzyl chloride (b.p. 177-179°). In a few minutes the reaction starts (Note 1) and is controlled if necessary by cooling with a wet towel. The stirrer is started and the balance of the benzyl chloride is run in as fast as the refluxing will permit. The addition requires from one to two hours, and when completed the mixture is refluxed ofi the steam bath with stirring for three hours. With the stirrer stUl running, 182 g. (r mole) of benzophenone (Org. Syn. Coll. Vol. i, 89) dissolved in 500 cc. of absolute ether is added at such a rate that the mixture refluxes rapidly. This requires about twenty minutes and then the reaction mixture is allowed to stand for two hours (Note 2). 

The first, and simplest, step in predicting crystallizer performance is the calculation of crystal yield. This can easily be estimated from knowledge of solution concentration and equilibrium conditions permitting calculation of the overall mass balance... 

The CSD from the continuous MSMPR may thus be predicted by a combination of crystallization kinetics and crystallizer residence time (see Figure 3.5). This fact has been widely used in reverse as a means to determine crystallization kinetics - by analysis of the CSD from a well-mixed vessel of known mean residence time. Whether used for performance prediction or kinetics determination, these three quantities, (CSD, kinetics and residence time), are linked by the population balance. 

Theoretical representation of the behaviour of a hydrocyclone requires adequate analysis of three distinct physical phenomenon taking place in these devices, viz. the understanding of fluid flow, its interactions with the dispersed solid phase and the quantification of shear induced attrition of crystals. Simplified analytical solutions to conservation of mass and momentum equations derived from the Navier-Stokes equation can be used to quantify fluid flow in the hydrocyclone. For dilute slurries, once bulk flow has been quantified in terms of spatial components of velocity, crystal motion can then be traced by balancing forces on the crystals themselves to map out their trajectories. The trajectories for different sizes can then be used to develop a separation efficiency curve, which quantifies performance of the vessel (Bloor and Ingham, 1987). In principle, population balances can be included for crystal attrition in the above description for developing a thorough mathematical model. 

Several authors have presented methods for the simultaneous estimation of crystal growth and nucleation kinetics from batch crystallizations. In an early study, Bransom and Dunning (1949) derived a crystal population balance to analyse batch CSD for growth and nucleation kinetics. Misra and White (1971), Ness and White (1976) and McNeil etal. (1978) applied the population balance to obtain both nucleation and crystal growth rates from the measurement of crystal size distributions during a batch experiment. In a refinement, Tavare and... 

The significance of this novel attempt lies in the inclusion of both the additional particle co-ordinate and in a mechanism of particle disruption by primary particle attrition in the population balance. This formulation permits prediction of secondary particle characteristics, e.g. specific surface area expressed as surface area per unit volume or mass of crystal solid (i.e. m /m or m /kg). It can also account for the formation of bimodal particle size distributions, as are observed in many precipitation processes, for which special forms of size-dependent aggregation kernels have been proposed previously. 

Disruption of an agglomerated particle L, S), produces a single primary crystal (Ld, 1) and the residual particle (Ldd, —1). Conservation of crystal mass balance requires the following equations to be satisfied ... 

Vo) in the crystal. (Vo) can catch electrons to form F and centers. (Pb) is also able to attract electrons while (Vb)" can trap holes to give rise to color centers. They vdll make a contribution to the X-ray irradiation-induced absorption. Of course, the charge balance of the crystal is kept by charge compensation among these defects. Regretfully, the detailed characterization of these defects is too difficult to cover here and further experiments need to be performed. 

---