Supersaturation rate processes

Condensation is generally a transient operation in which, as discussed by Ueda and Takashima(106), simultaneous heat and mass transfer are further complicated by the effects of spontaneous condensation in the bulk gaseous phase. After the creation of supersaturation in the vapour phase, nucleation normally occurs which may be homogeneous in special circumstances, but more usually heterogeneous. This process is followed by both crystal growth and agglomeration which lead to the formation of the final crystal product. As a rate process, the condensation of solids from vapours is less well understood than vaporisation(98). Strickland-Constable(107) has described a simple laboratory technique... 

As with alt kinetic phenomena, the first concept to understand is the driving force for the rate processes. While supersaturation was represented above as the driving force for nucleation and growth, no clear definition of this quantity was given. In fact, there are various ways in which the driving foree or super-saturation can be defined ... 

Ammonium tetraborate tetrahydrate is prepared by crystallization from an aqueous solution of boric acid and ammonia having a B202 (NH4)20 ratio of 1.8 2.1. Ammonium pentaborate is similarly produced from an aqueous solution of boric acid and ammonia having a B202 (NH4)20 ratio of 5. Supersaturated solutions are easily formed and the rate of crystallization is proportional to the extent of supersaturation (130). A process for the production... 

Models used to describe the growth of crystals by layers call for a two-step process (/) formation of a two-dimensional nucleus on the surface and (2) spreading of the solute from the two-dimensional nucleus across the surface. The relative rates at which these two steps occur give rise to the mononuclear two-dimensional nucleation theory and the polynuclear two-dimensional nucleation theory. In the mononuclear two-dimensional nucleation theory, the surface nucleation step occurs at a finite rate, whereas the spreading across the surface is assumed to occur at an infinite rate. The reverse is tme for the polynuclear two-dimensional nucleation theory. Erom the mononuclear two-dimensional nucleation theory, growth is related to supersaturation by the equation. 

Secondary nucleation is an important particle formation process in industrial crystallizers. Secondary nucleation occurs because of the presence of existing crystals. In industrial crystallizers, existing crystals in suspension induce the formation of attrition-like smaller particles and effectively enhance the nucleation rate. This process has some similarity with attrition but differs in one important respect it occurs in the presence of a supersaturated solution. 

In this case, the co-solvent dosage rate is programmed in order to control the transient level of supersaturation in an effort to improve on the product crystal size distribution from simply dumping in all the solvent at the start of the batch. An experimental crystallizer within which a programmed microcomputer determines the set point of a variable speed-dosing pump is shown in Figure 7.7. Controlled co-solvent dosing improves the product crystal size, with a consequent increase in the filterability of the product. These process concepts are developed further in Chapter 9. 

In the SFM the reactor is divided into three zones two feed zones fj and (2 and the bulk b (Figure 8.1). The feed zones exchange mass with each other and with the bulk as depicted with the flow rates mi 2, i,3 and 2,3 respectively, according to the time constants characteristic for micromixing and mesomix-ing. As imperfect mixing leads to gradients of the concentrations in the reactor, different supersaturation levels in different compartments govern the precipitation rates, especially the rapid nucleation process. 

Pressure controls the thickness of the boundary layer and consequently the degree of diffusion as was shown above. By operating at low pressure, the diffusion process can be minimized and surface kinetics becomes rate controlling. Under these conditions, deposited structures tend to be fine-grained, which is usually a desirable condition (Fig. 2.13c). Fine-grained structures can also be obtained at low temperature and high supersaturation as well as low pressure. 

The overall rainfall rate and amoimt depend on these microphysical processes and even more greatly on the initial amount of water vapor present, and on the vertical motions that transport water upward, cool the air, and cause supersaturation to occur in the first place. Thus the delivery of water to the Earth s surface as one step in the hydrologic cycle is controlled by both microphysical and meteorologic processes. The global average precipitation amounts to about 75 cm/yr or 750 L/(m yr). 

Although cooling crystallization is the most common method of inducing supersaturation in batch crystallization processes, other methods can be used, as discussed in Chapter 10. For example, evaporation can be used, in which case the profile of the rate of evaporation through the batch can also be optimized7. Indeed, the profiles of both temperature and rate of evaporation can be controlled simultaneously to obtain greater control over the level of supersaturation as the batch proceeds7. However, it should be noted that there is often reluctance to use evaporation in the production of fine, specialty and pharmaceutical products, as evaporation can concentrate any impurities and increase the level of contamination of the final product. 

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