Solution turbulence, crystallization

Since, as discussed above, it is impossible to achieve dynamic similarity between laboratory and full scale, the predictive capability of empirical modeling of crystallization is limited. Mathematical modeling also has its shortcomings. Suspension flows in crystallizers are turbulent, two and perhaps even three phase (for boiling crystallizers), the particle size is distributed, and the geometry is complicated with perhaps multiple moving parts (impellers). This is of course beyond the possibility of analytical solution of the equations of motion, so we must turn to computational fluid dynamics (CFD). However, even CFD is not capable of successfully dealing with all of these features. Successful computational models of crystallizers to date are limited to very specific limited problems. 

Computational fluid dynamics (CFD) is the numerical analysis of systems involving transport processes and solution by computer simulation. An early application of CFD (FLUENT) to predict flow within cooling crystallizers was made by Brown and Boysan (1987). Elementary equations that describe the conservation of mass, momentum and energy for fluid flow or heat transfer are solved for a number of sub regions of the flow field (Versteeg and Malalase-kera, 1995). Various commercial concerns provide ready-to-use CFD codes to perform this task and usually offer a choice of solution methods, model equations (for example turbulence models of turbulent flow) and visualization tools, as reviewed by Zauner (1999) below. 

Figure 3.3. Various features of diffusion and convection associated with crystal growth in solution (a) in a beaker and (b) around a crystal. The crystal is denoted by the shaded area. Shown are the diffusion boundary layer (db) the bulk diffusion (D) the convection due to thermal or gravity difference (T) Marangoni convection (M) buoyancy-driven convection (B) laminar flow, turbulent flow (F) Berg effect (be) smooth interface (S) rough interface (R) growth unit (g). The attachment and detachment of the solute (solid line) and the solvent (open line) are illustrated in (b).

Rock-crystal occurring in vein-type ore deposits grows in ascending hydrothermal solution through cracks in the strata. The flow of solution causes the solute component to be supplied to crystals growing inclined to or perpendicular to the wall of the crack. In laminar flow, the growth rate of the side facing the flow increases compared with the opposite side. In turbulent flow, the situation will be reversed. 

Convection in Melt Growth. Convection in the melt is pervasive in all terrestrial melt growth systems. Sources for flows include buoyancy-driven convection caused by the solute and temperature dependence of the density surface tension gradients along melt-fluid menisci forced convection introduced by the motion of solid surfaces, such as crucible and crystal rotation in the CZ and FZ systems and the motion of the melt induced by the solidification of material. These flows are important causes of the convection of heat and species and can have a dominant influence on the temperature field in the system and on solute incorporation into the crystal. Moreover, flow transitions from steady laminar, to time-periodic, chaotic, and turbulent motions cause temporal nonuniformities at the growth interface. These fluctuations in temperature and concentration can cause the melt-crystal interface to melt and resolidify and can lead to solute striations (25) and to the formation of microdefects, which will be described later. 

First, the role of system design on the details of convection and solute segregation in industrial-scale crystal growth systems has not been adequately studied. This deficiency is mostly because numerical simulations of the three-dimensional, weakly turbulent convection present in these systems are at the very limit of what is computationally feasible today. New developments in computational power may lift this limitation. Also, the extensive use of applied magnetic fields to control the intensity of the convection actually makes the calculations much more feasible. 

Density gradients are established at several stages in the crystallization process (Fig. 5). As molecules attach to the growing crystal surface, the solution near the crystal is depleted of solute and becomes less dense than the bulk solution. Under the influence of gravity, such density differences result in convection currents. However, in microgravity, solutions with different densities are not subject to convection, so that solutions mix with less turbulence (Littke and John, 1984) and equilibration between solutions is much slower (DeLucas et al., 1986). 

In general, the initiation of the precipitation process may result from the presence of particulate matter in the bulk water that seeds the crystallization. The process is usually termed heterogeneous nucleation. It is possible for homogeneous nucleation to occur when the nucleation is spontaneous. Once nucleation has occurred, crystals can grow, provided that the solution is supersaturated. Suitable nucleation points on the heat transfer surface facilitate deposit formation on the surface. In turbulent flow, it is possible that crystallites that are formed in the bulk fluid may be carried into regions, where they can redissolve. 

The temperature and flow conditions within the heat exchanger will determine the location at which these various stages occur. For instance the supersaturation and crystallite formation may occur in the bulk fluid with the growing crystals moving towards the wall to form the deposit. The movement of foulant will under these circumstances, follow the processes described in Chapter 7 for particulate deposition. It is possible that due to the level of turbulence within the system, that some (or possibly many) of the crystallites formed are swept into re ons where the solution is not supersaturated. Under these conditions the particles will redissolve. On the other hand crystallisation may occur near or at the heat transfer surface. The presence of nucleation sites on a solid surface may encourage the formation of scale on the surface. Under these circumstances the process is largely governed by the mechanics of the crystallisation process. 

It is important then to recognize that the flow in crystallizers is of a suspension and not a single-phase fluid. There are obvious differences. The effective viscosity of the suspension is larger than that of the solution by itself. The flow velocities everywhere must be large enough so that the particles do not settle appreciably. Then, there are more subtle differences. The presence of particles blunts velocity profiles and affects turbulence. The particles are not in general uniformly suspended, but are distributed in unexpected ways. The particle size distribution is also not uniform throughout the vessel. The net result is that transport projjerties and the variables that affect crystallization most, such as supersaturation, are affected. 

In a dynamic process, the mixture is mixed different methods of mixing can be used. Movement of food particles in a stationary solution, mixing of the whole suspension, and the flow of the osmoactive substance through the stationary layer of food pieces are the commonly used designs of the dynamic process. If crystals of the osmoactive substance are used, the fluidized bed is the solution for the dynamic process. It has been shown that the rate of motion has little effect on the rate of osmotic dehydration [71,133]. It is just sufficient to induce motion of particles or solution in the system to have increased mass transfer rates. Moreover, it was shown that the motion of osmotic solution in a turbulent region affected water flux but no difference in solids gain occurred in comparison with laminar flow [134]. 

High heat transfer coefficients, up to 1 kW m K, and hence high production rates, are obtainable with double-pipe, scraped-surface heat exchangers. Although mainly employed in the crystallization of fats, waxes and other organic melts (section 8.2.2) and in freeze concentration processes (section 8.4.7), scraped-surface chillers have occasionally been employed for crystallization from solution. Because of the high turbulence and surface scraping action, however, the size of crystal produced is extremely small. 

---