Nucleation population density parameter

This removal function gives rise to a discontinuity in the population density at the cutsize of the fines. The nucleation parameters are given in equation 19 In Figure 3 the responses are shown of the population density at 120 pm and of the growth rate after a step in the heat input to the crystallizer from 120 to I70 kW for three simulation edgorithms. The cut-size of the fines was 100 pm, a size dependent growth rate was used as described by Equation 4 with a= -250 and the number of grid points was kOO. When the simulation was performed with the method of lines, severe oscillations are present in the response of the population density at 120 pm, which dampen out rather slowly. Also the response of the Lax-Wendroff method shows these oscillations to a lesser extend. 

The magma density Mr (mass of ciystais per unit volume of slurry or liquor) may be obtained from the third moment of the population density function. As shown above, this quantity is related to nucleation and growth rates by Eq. (II. 2-38). Although magma density is a function of the Idnetic parameters n° and C, it can be measured independently of crystal size distribution and, where possible, it should be used, as indicated above, as a constraint in evaluating nucleation and growth rates from measured crystal size distributions. 

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