Crystal-growth rate coefficient, data

The values measured in the ISC for the overall crystal-growth rate coefficient of Na2HP04 are listed in Table 12.2. As can be seen, the reproducibility of the data is in a reasonable range and that of most data is very good. 

Except for a few questionable data, the values for the observed active energy measured in the two crystallizers of different types, EiS and EFB, show little difference and can be considered to be more or less identical. On the other hand, the values measured in the impinging stream crystallizer for the overall crystal-growth rate coefficient, KIS, are obviously and systematically larger than those in the fluidized bed crystallizer, A pe. Therefore it can be affirmed without the need for further analysis that, with the observed frequency factors, there must... 

The difficulty with each of the theoretical approaches to date, however, is that they cannot yet predict crystal growth rate coefficients and exponents for a particular substance a priori. Thus as with nucleation kinetics, crystal growth rate data from industrial crystallizers are usually correlated empirically with environmental conditions, such as concentration and temperature using a power law model of the form... 

One method is to solve the population balance equation (Equation 64.6) and to take into account the empirical expression for the nucleation rate (Equation 64.10), which is modified in such a way that the expression includes the impeller tip speed raised to an experimental power. In addition, the experimental value, pertinent to each ch ical, is required for the power of the crystal growth rate in the nncleation rate. Besides, the effect of snspension density on the nucleation rate needs to be known. Fnrthermore, an indnstrial suspension crystallizer does not operate in the fully mixed state, so a simplified model, such as Equation 64.6, reqnires still another experimental coefficient that modifies the CSD and depends on the mixing conditions and the eqnipment type. If the necessary experimental data are available, the method enables the prediction of CSD and the prodnction rate as dependent on the dimensions of the tank and on the operating conditions. One such method is that developed by Toyokura [23] and discussed and modified by Palosaari et al. [24]. However, this method deals with the CTystaUization tank in average and does not distinguish what happens at various locations in the tank. The more fundamental and potentially far more accurate simulation of the process can be obtained by the application of the computational fluid dynamics (CFD). It will be discussed in the following section. 

Geochemical kinetics is stiU in its infancy, and much research is necessary. One task is the accumulation of kinetic data, such as experimental determination of reaction rate laws and rate coefficients for homogeneous reactions, diffusion coefficients of various components in various phases under various conditions (temperature, pressure, fluid compositions, and phase compositions), interface reaction rates as a function of supersaturation, crystal growth and dissolution rates, and bubble growth and dissolution rates. These data are critical to geological applications of kinetics. Data collection requires increasingly more sophisticated experimental apparatus and analytical instruments, and often new progresses arise from new instrumentation or methods. 

Dissolution rate data, for example, are conveniently expressed in this way. The mass transfer coefficient, in the Sherwood number, depends on the solution velocity, u, raised to the power a. It is possible, therefore, that the effect of solution velocity on crystal growth may also be represented by an equation of this type in the region where diffusion influences the growth rate. 

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