Cumulative CSD

Cumulative CSD Method. Misra and White (1971) used a cumulative CSD method to study the crystallization kinetics of aluminum trihydroxide from a seeded batch crystallizer. The population balance equation corresponding to Eq. (10.3) can be written as... 

The sizing methods for the cumulative CSDs are unfortunately limited to a minimum crystal size below which accurate counts... 

The analysis of batch crystallizers normally requires the consideration of the time-dependent, batch conservation equations (e.g., population, mass, and energy balances), together with appropriate nucleation and growth kinetic equations. The solution of these nonlinear partial differential equations is relatively difficult. Under certain conditions, these batch conservation equations can be solved numerically by a moment technique. Several simple and useful techniques to study crystallization kinetics and CSDs are discussed. These include the thermal response technique, the desupersaturation curve technique, the cumulative CSD method, and the characterization of CSD maximum. 

Both the number and weight basis probability density functions of final product crystals were found to be expressed by a %2-function, under the assumption that the CSD obtained by continuous crystallizer is controlled predominantly by RTD of crystals in crystallizer, and that the CSD thus expressed exhibits the linear relationships on Rosin-Rammler chart in the range of about 10-90 % of the cumulative residue distribution. 

Marsh (1988), Cashman and Marsh (1988), and Cashman and Ferry (1988) investigated the application of crystal size distribution (CSD) theory (Randolph and Larson, 1971) to extract crystal growth rate and nucleation density. The following summary is based on the work of Marsh (1988). In the CSD method, the crystal population density, n(L), is defined as the number of crystals of a given size L per unit volume of rock. The cumulative distribution function N(L) is defined as... 

Figure 16.4. Several ways of recording the same data of crystal size distribution (CSD) (MulUn, 1972). (a) The data, (b) Cumulative wt % retained or passed, against sieve aperture, (c) Log-log plot according to the RRS equation P = exp[(—d/dm)"J off this plot, = 850, dm = 1000, n = 1.8. (d) Differential polygon, (e) Differential histogram.

Figure 10.17(b) Cumulative undersize CSD in a suspension containing SrMo04 after 1-h stirring time as a function of mixer revolutions, as reported by Mullin el al. (1990). Growth occurred via an agglomeration mechanism. 

By use of the relative size, X, the CSD can be analysed without knowing the dependence of growth rate on super saturation. Equation 9.30, which is identical in form with equation 9.4, represents the cumulative mass distribution. The differential mass distribution is represented by... 

Figure 5.1 Cumulative growth of the CSD 1972-2010 in terms of numbers of structures in the database at year end.

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