Attrition controlled nucleation

The kinetics of crystallization of such systems is often controlled by secondary attrition-induced nucleation and growth rates which are valid in the transition range between diffusion-limited and surface integration-limited growth. Diffusion hm-ited means G Ac//7j.. ... 

The left-hand sideofEq. (40)isthe accumulationofparticlesofagivensize. The terms on the right-hand side are, in turn, the bulk flow into and out of the control volume, the convective flux along the size axis due to layering and attrition, the birth of new particles due to nucleation, and birth and death of granules due to coalescence. 

How can particle size be controlled The answer is clear controlling primary nucleation and avoiding secondary nucleation and attrition can potentially enable chemists to achieve the same crystal size distribution with each batch. A later discussion outlines some of the inherent difficulties in these strategies and how best to overcome them. 

Besides agglomeration and attrition, the rates of nucleation and growth are the main kinetic parameters that determine the size distribution. These parameters, which are reqnired in crystallizer design and simulation, can be determined on the basis of the population balance equations. Section 64.2 discusses the methods for controlling the particle size and particle size distribution. 

The equation = 3.67 G x is only valid when all MSMPR assumptions are fulfilled (besides other no attrition and no agglomeration). However, in the case a < 0.1 the mean crystal size L q and especially the maximum ciystal size with max 2 Z50 is controlled by attrition, see Fig. 8.5-1 below. On the other hand, agglomeration can be the dominant process parameter for a > 10. Nanocrystals can only be produced if the relative supersaturation is high with the result of high rates of activated nucleation and by the avoidance of agglomeration. Aggregates which are formed under low or zero supersaturation do not possess crystalline bridges and can be redispersed. 

Whereas the fines dissolving is a strong tool to correct the effects of secondary nucleation, attrition, and breakage toward larger particle diameters, it also has one negative effect on the steady-state operation of the DTB and Oslo crystallizers most of the time it is too strong. Unfortunately, its intensity is difficult to control. 

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