Precipitation kinetics, determination nucleation rates

The model is able to predict the influence of mixing on particle properties and kinetic rates on different scales for a continuously operated reactor and a semibatch reactor with different types of impellers and under a wide range of operational conditions. From laboratory-scale experiments, the precipitation kinetics for nucleation, growth, agglomeration and disruption have to be determined (Zauner and Jones, 2000a). The fluid dynamic parameters, i.e. the local specific energy dissipation around the feed point, can be obtained either from CFD or from FDA measurements. In the compartmental SFM, the population balance is solved and the particle properties of the final product are predicted. As the model contains only physical and no phenomenological parameters, it can be used for scale-up. 

The influence of plastic deformation on the reaction kinetics is twofold. 1) Plastic deformation occurs mainly through the formation and motion of dislocations. Since dislocations provide one dimensional paths (pipes) of enhanced mobility, they may alter the transport coefficients of the structure elements, with respect to both magnitude and direction. 2) They may thereby decisively affect the nucleation rate of supersaturated components and thus determine the sites of precipitation. However, there is a further influence which plastic deformations have on the kinetics of reactions. If moving dislocations intersect each other, they release point defects into the bulk crystal. The resulting increase in point defect concentration changes the atomic mobility of the components. Let us remember that supersaturated point defects may be annihilated by the climb of edge dislocations (see Section 3.4). By and large, one expects that plasticity will noticeably affect the reactivity of solids. 

The inverse problems discussed in Sections 6.1 and 6.2 were addressed in the absence of nucleation and growth processes. In this section we investigate inverse problems for the recovery of the kinetics of nucleation and growth from experimental measurements of the number density. It is assumed, however, that particle break-up and aggregation processes do not occur. Determination of nucleation and growth rates is of considerable practical significance since the control of particle size in crystallization and precipitation processes depends critically on such information. We will dispense with the assumption of self-similar behavior, as it is often not observed in such systems. Also, we provide here only a preliminary analysis of this problem, as it is still in the process of active investigation by Mahoney (2000). 

In order to determine the mesomixing time, a least square fit of the 300 ml continuous calcium oxalate (CaOx) precipitation results for the number mean size and nucleation rate was performed. From these calculations, the factor A in equation 8.15 was obtained as 17.7. Using the kinetic parameters determined from the laboratory-scale continuous experiments (Zauner, 1999), the large-scale experiments were simulated with the SFM and compared with the experimental findings. 

---