The choice of method for generation of supersaturation to crystallize a substance also depends on the product properties desired and economic aspects. In all cases, it is always possible to establish adequate mathematical expressions for the supersaturation in terms of known properties Hurle, In a supersaturated solution, part of the solute tends to reorganize itself into the solid form.
However, the formation of the solid phase energetically favorable implies the generation of an interface energetically unfavorable. Therefore, if nucleation is to occur, an energy barrier has to be overcome. When nucleation from a clear solution takes place, it is known as primary homogeneous nucleation and is characterized by an exponential dependence on supersaturation as well as by very large metastable zone widths. Starting with the basic Gibbs-Thomson relationship and with the definition of the Gibbs free energy, it is possible to obtain the equation for the homogenous primary nucleation rate which takes the following form Mullin, :.
In industrial practice, this type of nucleation seldom occurs because solutions usually contain foreign particles that act as substrates for nucleation, known as primary heterogeneous nucleation. The metastable zone width is large, and due to the exponential dependence on supersaturation, the process is explosive and difficult to reproduce and should thus be avoided wherever possible in industrial practice.
It always takes place in the early stages of unseeded batch processes. When a supersaturated solution is in contact with particles of the crystallizing compound, secondary nucleation occurs. Particles collide with the agitator blades, with the crystallizer walls and with each other, thereby promoting their abrasion. Tiny crystals under mm in size that behave as nuclei are thus generated.
Attrition takes place preferentially at specific locations on the crystal surface such as the edges and corners. For high supersaturations, more of these preferential locations appear, since the crystal surfaces become atomically rough, macro-steps or even dendritic growth may occur Denk and Botsaris, There are many empirical expressions that correlate the secondary nucleation with crystallization parameters.
The dependence on supersaturation, b, is usually in the range of 1 to 3. Secondary nucleation is particularly important for coarse products sizes of mm and above due to the enhanced collision energy of larger crystals. On the other hand, if crystals are smaller than the Kolmogorov length scale which defines the smallest eddies in a turbulent field, usually 50 to mm within agitated reactors , they are encapsulated within the viscous limits of the Kolmogorov eddies and do not generate secondary nuclei.
If crystal size is characterized by a characteristic dimension, L, we can define its linear growth rate, G, and the mass growth rate can be defined as. Crystal growth involves transport of the so-called growth units molecules or ions of solute from the bulk solution to the surface of the crystal and their incorporation into the crystal lattice. For growth controlled by diffusion e.
For growth controlled by surface integration, the three mechanisms shown below can be distinguished Mullin, For small supersaturations, growth units are incorporated only at kinks on the crystal surface: first a defect has to be generated on the surface and then growth proceeds layer by layer upon this defect so that a spiral dislocation forms; this spiral is self-propagating and never dies.
The surface is thus smooth at the atomic level Burton et al. For relatively larger supersaturations, two-dimensional nucleation appears on the crystal surface, thereby generating the necessary kinks for further growth.
If the rate of lateral growth of the 2D nuclei is high in comparison to the nucleation rate, the surface is smooth. For higher supersaturations the nucleation rate dominates the process and the surface becomes rough Nielsen, Rough Growth Figure 5.
For even higher supersaturations, growth units attach anywhere on the crystal surface terraces, steps or kinks so the crystal surface becomes rough. For organic compounds, the transition between smooth and rough growth can be achieved by increasing not only the supersaturation, but also the temperature.
Growth controlled by surface integration can be described by the general empirical equation Mullin, Experimental determination of the growth kinetics supported by microscopic examination of crystals often allows the determination of the prevailing growth mechanism.
The most frequently found mechanism is spiral growth. As mentioned in the nucleation section, the rough regime should be avoided wherever possible, as it results in excessive secondary nucleation. Whichever the prevailing growth mechanism, the constant, k g , is proportional to solute concentration, i.
As noted before, small crystals generated by secondary nucleation may have varying degrees of mechanical stress, so they have a higher solubility and thus lower growth rate than larger crystals.
They heal as they grow so their growth behavior becomes similar to that of the larger crystals. This behavior explains two phenomena commonly observed during mass growth of crystals: growth rate dispersion, whereby different individual crystals show varying growth rates and size-dependent growth, whereby smaller crystals grow slower than large ones.
Continuous operation is usually applied for large capacities. It offers good control of average product size. Continuous processes are easier to operate than batch ones, requiring less manpower and less physical space for the same production capacity. They are not recommended for products with a strong scaling tendency.
Continuous processes can be represented by a simple mathematical treatment that takes population density n , defined as the number of crystals of a specific size per unit volume of crystallizer as the basic variable. The mass balance in the crystallizer can be obtained using the equilibrium data solubility curve and definition of the moments of distribution as pointed by Randolph and Larson The third moment of the distribution correspond to the mass of crystals produced in the crystallizer.
A population balance for the crystallizer is coupled to mass balance as well as to crystallization kinetic parameters as shown in Figure 6 , where the population balance does not take into account breakage and agglomeration processes. A straight line on a mono log scale Figure 7 can represent this. From the intercept with the y-axis, n o , it is possible to estimate the nucleation rate B 0 from.
With this formulation, the average product size for any operational condition can be easily obtained. Batch operation is usually preferred for small-scale production, but there are exceptions. Batch operation normally involves simpler equipment and the same crystallizer can be used for more than one product.
Batch is the recommended mode of operation for crystallization of substances with low growth rates. Good practices for batch operation involve a sound selection of cooling profiles and seeding procedures since they influence product quality Giulietti et al. Curve 3 in Figure 8 shows a typical cooling curve found in industrial practice derived from a constant flow rate of the cooling fluid. Several families of particles are generated by sequential nucleation bursts due to higher supersaturation in the early stages of the process, resulting in a product with a wide crystal size distribution CSD and a large number of fines.
Also, the CSD changes from batch to batch due to excessive primary nucleation. All these problems can be avoided if only one nucleation step or seeding occurs at the beginning of the process. This situation can be achieved with the cooling profile shown by curve 1 in the same figure. A similar curve can be obtained for evaporation crystallization. This "ideal cooling", however, is expensive in practice due to the control hardware and the high cooling capacity required van Rosmalen, Curve 2 in Figure 8 shows a linear cooling profile, an intermediary situation, which is a reasonable compromise between the "ideal" and "industrial" situations.
Seeding is frequently applied to avoid the supersaturation peak at the beginning of the process. The chosen mass of seeds is around 0. Seeds are normally obtained by screening the product in a narrow range. A good seeding procedure involves pre-washing the crystal seeds with a nearly saturated solution to dissolve small particles adhering to their surfaces.
Seeds should be fed into the crystallizer during the cooling process just after the solution has become supersaturated. When seeding a large quantity of crystals, a large surface area is provided for solute incorporation, lowering the average supersaturation of the batch process and resulting in a product with a narrow CSD Jagadesh, In normal operation, product size can vary from batch to batch.
The best way to have a more stable size is to control the time from the beginning of supersaturation to the end of the cooling process, the real crystallization batch time. Figure 9 shows an overview of the effect of average supersaturation on nucleation and growth rates and on average product size. Therefore, for each system, the adequate minimum batch time has to be observed in order to produce a more or less stable average crystal size.
Due to the transient nature of batch processes, their mathematical description is not as simple as that of the continuous mode of operation. A typical batch population density distribution is shown in Figure It is composed of an initial family of crystals from the seeds combined with another generated during the process to give the final distribution.
Growth and nucleation kinetics can be measured either simultaneously or independently. In this method, it is necessary to confirm that steady state was achieved before sampling.
Generally this occurs within 8 to 16 residence times from the beginning of operation Garside et al. In batch mode, nucleation and growth kinetic parameters can be derived by monitoring at least supersaturation or CSD and ideally both Gutwald and Mersmann, ; Myerson, Supersaturation can be monitored in an indirect way, i. Monitoring CSD allows estimation of the growth rate and population density Myerson, In this case more than three experiments at varying batch time or average supersaturation are needed.
The conditions should be in the range of unstable operation shown in Figure 9 so that substantially different average crystal sizes are experimentally derived Derenzo, Independent measurement of the growth kinetics is achieved in a fluid bed crystallizer: a known number or mass of uniformly sized crystals is fluidized in a solution of known supersaturation for a fixed time.
At the end of the experiment, average product size or total mass is measured again to calculate the size increment Garside et al. Nucleation kinetics may be independently determined by induction period measurements, defined as the time required after saturation of the solution to observe the formation of the first crystals when cooling the system at a linear rate. The design of industrial crystallizers has been sometimes called an art rather than a science due to the high complexity of the system: simultaneous heat and mass transfer with a strong dependence on fluid and particle mechanisms; multiphase and multicomponent system; concentration, particle size and size distribution that could vary with time; scarcity of data; low reproducibility in the experiments to determine both nucleation and growth rates; secondary effects like agglomeration and the effect of impurities that can alter the morphology and the quality of the crystalline product.
The strategy of basic design of industrial cristallizers can be divided into three steps: choice of the solvent, basic design and detailed design. The solvent chosen should give the desired polymorph and the optimal shape of the crystals. In general this choice is made based on experimental tests, but also using molecular modeling techniques. The use of additives often helps to change the crystal shape or the crystallization kinetics. This design involves the following steps: definition of design specifications and information, crystallization method cooling, evaporation, flash, precipitation or second solvent addition , mode of operation batch or continuous, single or multistage , type of industrial crystallizer and estimation of the basic dimensions of the crystallizer.
This basic process design is the traditional way of designing an industrial crystallizer McCabe et al. Some design specifications are defined first: the yield, the mean crystal size for a good estimeted value, this specification must be defined by laboratory tests or taken from the literature and the final purity of the product. At this stage, other specifications such as polymorphs and crystal inclusions are not taken into account. In addition, some design information is needed: the feed composition, temperature, concentration and presence of crystals; physical and transport properties for solute and solvent, such as densities, viscosities, heat conductivities and heat capacities and their dependence on temperature; thermodynamic properties such as solubility curve and other phase diagrams; and for systems with more than one solvent, the mutual solubility.
After these definitions and a survey of the data, a number of design decisions have to be made. The crystallization method is in general chosen on the basis of the physical and thermodynamic properties of the solute and solvent and the required purity of the final crystalline product van Rosmalen, An adequate choice of reactant and solvent can result in a good yield and purity of the final product Giulietti and Danese, The second criterion for the choice of the crystallization mode is based on the solubility curve.
The choice of mode of operation follows. Multiple effect crystallizers are used to save energy and to provide products with a narrower CSD. Investment costs can play an important role in this decision. The type of industrial crystallizer can be selected from the mean crystal size specified.
At this stage, design calculations are performed in order to obtain the general dimensions of the crystallizer, making use of mass overall and component and energy balance equations. The solution of these equations provides the feed and product flow rates, the heat duties for the heat exchangers and the evaporation or cooling rates for the crystallization process.
If product purity needs to be considered, impurity balances must be done. Using an adequate distribution factor, the purge stream is derived to ensure the required impurity level of the magma. The mean residence time of the magma in continuous crystallizers can be estimated by using the equation.
For rough calculations, L m can be assumed to vary from to mm for highly soluble materials and G m in the range of 4. Read more about how to correctly acknowledge RSC content. Fetching data from CrossRef. This may take some time to load. Loading related content. Jump to main content. Jump to site search. You do not have JavaScript enabled.
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