Crystal solute distribution

As an idealization of the classified-fines removal operation, assume that two streams are withdrawn from the crystallizer, one corresponding to the product stream and the other a fines removal stream. Such an arrangement is shown schematically in Figure 14. The flow rate of the clear solution in the product stream is designated and the flow rate of the clear solution in the fines removal stream is set as (R — 1) - Furthermore, assume that the device used to separate fines from larger crystals functions so that only crystals below an arbitrary size are in the fines removal stream and that all crystals below size have an equal probabiHty of being removed in the fines removal stream. Under these conditions, the crystal size distribution is characterized by two mean residence times, one for the fines and the other for crystals larger than These quantities are related by the equations... 

Eeactive crystalli tion addresses those operations ia which a reaction occurs to produce a crystallizing solute. The concentration of the solute formed generally is greater than that corresponding to solubiHty. In a subset of systems, the solubiHty is nearly zero and, concomitantly, the supersaturation produced by reaction is large. These are often referred to as precipitation operations, and crystal size distributions from them contain a large fraction of fine crystals. 

General solution of the population balance is complex and normally requires numerical methods. Using the moment transformation of the population balance, however, it is possible to reduce the dimensionality of the population balance to that of the transport equations. It should also be noted, however, that although the mathematical effort to solve the population balance may therefore decrease considerably by use of a moment transformation, it always leads to a loss of information about the distribution of the variables with the particle size or any other internal co-ordinate. Full crystal size distribution (CSD) information can be recovered by numerical inversion of the leading moments (Pope, 1979 Randolph and Larson, 1988), but often just mean values suffice. 

It was shown in Chapter 7 that the performance of continuous crystallizers is determined by the characteristics of a feedback loop relating the output performance expressed as crystal size distribution and to the feed concentration and residence time. Thus, an increase in crystallizer residence time, or decrease in feed concentration, reduces the working level of supersaturation. This decrease in supersaturation results in a decrease in both nucleation and crystal growth. This in turn leads to a decrease in crystal surface area. By mass balance, this then causes an increase in the working solute concentration and hence an increase in the working level of supersaturation and so on. There is thus a complex feedback loop within a continuous crystallizer, as considered in Chapter 7 and illustrated in Figure 8.11. 

Faiz et al. (1996) have applied micro-PIXE analysis to study solute distributions in a single crystal sample of YiBa2Cu307 5 high temperature superconductor (YBCO) of dimensions 1.3 mm x 1.5 mm x 75 pm. It contained a small secondary crystal overgrowth of dimensions 340 x 340 x 100 pm3. The interface region between the smaller crystal and the base crystal was covered with a material which appeared to be residual flux. The instrument employed a 2.5 MeV focused proton beam of about 4 pm resolution, which could scan an area of 500 x 500 pm2 on the sample surface. The microbeam current was kept low (typically about 30 pA) to avoid any damage to the sample. 

Ciystallization from solution is an important separation and purification process in a wide variety of industries. These range from basic materials such as sucrose, sodium chloride and fertilizer chemicals to pharmaceuticals, catalysts and specialty chemicals. The major purpose of crystallization processes is the production of a pure product. In practice however, a number of additional product specifications are often made. They may include such properties as the ciystd size distribution (or average size), bulk density, filterability, slurry viscosity, and dry solids flow properties. These properties depend on the crystal size distribution and crystal shape. The goal of crystallization research therefore, is to develop theories and techniques to allow control of purity, size distribution and shape of crystals. 

Crystallization from solution is a widely utilized separation and purification technique in chemical industry. It is characterized by the formation of a spectrum of differently sized crystals. This spectrum, called the Crystal Size Distribution or CSD, is highly important for the performance of the crystallizer, the crystal handling equipment like centrifuges and dryers, and the marketability of the produced crystals. However, in many industrial crystallizers, the observed CSD s show large transients due to disturbances or are unstable because of the internal feedback mechanisms of the crystallization process ). The main limitation for effective CSD control was the lack of a good on-line CSD measurement device, but recent developments show that this hurdle is taken (2). 

On-line particle sizing by ultrasonic (acoustic attenuation) spectroscopy was developed for use during batch crystallization processes.14 Crystallization of the alpha polymorph of (l) -glutamic acid from aqueous solution was monitored by continuously pumping the crystallizing solution through an on-line ultrasonic spectrometer. The method enabled measurement of the crystal size distribution and solid concentration throughout the... 

Clear-liquor advance from what is called a double draw-off crystallizer is simply the removal of mother liquor without simultaneous removal of crystals. The primary action in classified-fines removal is preferential withdrawal from the crystallizer of crystals of a size below some specified value this may be coupled with the dissolution of the crystals removed as fines and the return of the resulting solution to the crystallizer. Classified-product removal is carried out to remove preferentially those crystals of a size larger than some specified value. In the following discussion, the effects of each of these selective removal functions on crystal size distributions will be described in terms of the population density function n. Only the ideal solid-liquid classification devices will be examined. It is convenient in the analyses to define flow rates in terms of clear liquor. Necessarily, then, the population density function is defined on a clear-liquor basis. 

Crystallization from an overall viewpoint represents transfer of a material from solution (or even a gas) to a solid phase by cooling, evaporation, or a combination of both. But there is more to it. Of considerable importance are economics, crystal size distribution, purity, and the shape of the crystals. Impurities or mother solution are carried along only in the surface or occlusions in the crystals. The partical size distribution depends on the distribution of seed crystals, which are injected into the crystallizer prior to initiation of crystallization (batch) or continuously from recycled undersized particles, the mixing in the system, the crystal growth rate, and the degree of supersaturation of the mother liquor. As in shown in the figures, both batch and continuous crystallization are used in industry. 

For different values of n ing(i ) = i2", other kinetic expressions can be developed. Figure 8.10 [18] shows the type of powder produced on spray diydng a solution that consists of metal salts of barium and iron in the ratio 1 12 (i.e., barium ferrite). Here we see the remains of the spherical droplets with a surface that consists of the metal salt precipitates, which form a narrow size distribution of platelet crystals (see Figure 8.10(a) and (b)). This narrow crystal size distribution is predicted by the population balance model if nudeation takes place over a short period of time. When these particles are spray roasted (in a plasma gun), the particles are highly sintered into spherical particles (see Figure 8.10(c)). 

There are two major processes for the manufacture of titanium dioxide pigments, namely (1) sulfate route and (2) chloride route. In the sulfate process, the ore limonite, Fe0Ti02, is dissolved in sulfuric acid and the resultant solution is hydrolyzed by boiling to produce a hydrated oxide, while the iron remains in solution. The precipitated titanium hydrate is washed and leached free of soluble impurities. Controlled calcinations at about 1000°C produce pigmentary titanium dioxide of the correct crystal size distribution this material is then subjected to a finishing coating treatment and milling. The process flow sheet is shown in Fig. 7.1 [4],... 

Even distribution of crystallizing solute on the nuclei produces elongated crystals with small particle size distribution... 

Crystal growth is a layer-by-layer process, and the retention time required in most commercial equipment to produce crystals of the size normally desired is often on the order of 2 to 6 h. Growth rates are usually limited to less than 1 to 2 pm/min. On the other hand, nucle-ation in a supersaturated solution can be generated in a fraction of a second. The influence of any upsets in operating conditions, in terms of the excess nuclei produced, is very short-term in comparison with the total growth period of the product removed from the crystallizer. A worst-case scenario for batch or continuous operation occurs when the explosion of nuclei is so severe that it is impossible to grow an acceptable crystal size distribution, requiring redesolution or washout of the system. In a practical sense, this means that steadiness of operation is much more important in crystallization equipment than it is in many other types of process equipment. 

Aamir, E., Nagy, Z. K., Rielly, C. D., Kleinert, T. Judat, B. 2009 Combined quadrature method of moments and method of characteristics approach for efficient solution of population balance models for dynamic modeling and crystal size distribution control of crystallization processes. Industrial Engineering Chemistry Research 48, 8575-8584. 

FIGURE 7.6 Acoustic effect on crystal size distribution in frozen sucrose solution. (Adapted from Acton, E. and Morris, G.J., Method and apparatus for the control of solidification in liquids. WO/1992/020420, U.S. Patent Application (Granted 12/03/1997, Withdrawn 19/10/1999,1992.)... 

Crystallization kinetics. Expressions that describe crystal growth and nnclention rates from solution. CSD. Crystal size distribution. 

The kinetic phenomena that influence crystal size distributions are nudearkm and growth. The driving force for both these phenomena is supersaturtekm, and at some levels of supersatwratina, both nudestion and growth occur and compete for available solute. The purpose of the present discussion is to summarize key... 

Ostwald ripening is often important in proeesses in which crystallization is rapid and crystal sizes are small. This is especially true in a precipitation process and will be diseussed in detail in Chapter 6 of this volume. It is important to remember that the effect of Ostwald ripening is to alter the crystal size distribution with time in a suspension of erystals that is an apparent equilibrium with its saturated solution. Ostwald ripening is an important phenomena if you are concerned with obtaining fine particles or are concerned about changes in the crystal size distribution of your product prior to drying. 

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