Precipitation kinetics agglomeration

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. 

Hostomsky, J. and Jones, A.G., 1991. Calcium carbonate crystallization kinetics, agglomeration and fomi during continuous precipitation from solution. Journal of Physics D Applied Physics, 24, 165-170. 

Both modes can occur in precipitation processes, but in a stirred precipitator orthokinetic agglomeration clearly predominates. From the Smoluchowski kinetic expressions for perikinetic and orthokinetic agglomeration it can be deduced (Sohnel and Mullin, 1991) that the relationship between agglomerate size D and time t may be expressed by... 

Zauner, R. and Jones, A.G., 2000a. DeteiTnination of nucleation, growth, agglomeration and disruption kinetics from experimental precipitation data The calcium oxalate system. Chemical Engineering Science, 55, 4219-4232. 

The particle size distribution produced during precipitation is a result of the relative rates of reaction, nudeation, growth, and agglomeration, as well as the degree of backmixing in the precipitator. The kinetics of each of these steps will be discussed next. 

In kinetic studies of the formation of silver bromide, Meehan and Miller found that formation of colloidal material was complete within 6 msec or less. They further concluded that fast flocculation, in which every collision of particles results in an agglomeration, occurs during the mixing process and for a few seconds thereafter. Berry and Skillman and Berriman determined that the total number of silver halide crystals remained essentially unchanged after the first minute of doublejet precipitation. 

The effect of the urea concentration is somehow opposite to that of the yttrium ion concentration. As the urea concentration was increased from 0.04 to 4.0 M, the average particle size of the precipitates gradually decreased from 220 to 100 nm. However, too high urea concentration, e.g., 7.0 M, led to serious interparticle agglomeration. The rate of precipitation was increased with increasing urea concentration up to 3.0 M. Above 3.0 M, the effect of the urea concentration was weakened. Reaction temperature only affected the kinetics of precipitation. Figure 3.35 shows TEM images of representative precipitates derived from the solutions with different concentrations of urea [159]. 

Advances in pore structure control of the porous active aluminas have resulted in major improvements in commercial adsorbents. Zeolites have their pore structures determined simultaneously with the precipitation process and are constrained in size by the configuration of the sodalite cage. In contrast, active alumina porosity is relatively independent of the bulk phase formation process and is usually engineered following material synthesis. Microporosity is controlled via kinetics of the dehydroxylation process, whereas macroporosity is usually developed in the agglomeration process. 

When the chemical reaction leading to precipitation is a very rapid process, a continuous operation in a CSTR is perfectly feasible. The physical processes such as nucleation, surface growth and agglomeration are all very rapid processes. Meso-mixing is usually a critical factor for the nucleation (compare Example 11b), Generally, die reactor size will be not be determined by chemical or physical kinetics, but by the area needed for heat transfer (see section 8.3.2). 

It is even more difficult to estimate not only one but four parameters (nucleation rate, growth rate, agglomeration kernel and disruption kernel) simultaneously from a particle size distribution. The errors are likely to be unacceptably high and it might be impossible to distinguish between the mechanisms involved. Therefore, an alternative sequential technique has been developed to obtain the kinetic parameters nucleation rate, growth rate, and agglomeration and disruption kernels from experimental precipitation data. 

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