Population Balances on a Discrete Mass Basis

In some cases population balances are performed on a cumulative basis. One reason for such a population balance is so that theory can be easily compared to experimental data obtained from sieve analysis. To predict the mass on a sieve with size L, which cstme from the sieve above of size L + AL, we must perform the integrsd 

The mass is related to the cumulative (percent less than) size distribution by volume (or mass), F iL), as follows  

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Macroscopic Population Balance on a Discrete Mass Basis... 

The death rate in grinding is also referred to as the breakage rate and, for the population balance on a discrete mass basis, is given by [11]... 

In batch comminution, the summation term in equation (4.11) is zero because there are no flows into or out of the mill. Therefore the population balance on a discrete mass basis is simplified to... 

Several classification functions, C(L), are given in Figure 4.20. Here, the fraction of particles by mass reporting to the recycle stream is given as a function of particle size, L, for a screen and a cyclone. Several authors have used empirical classification functions instead of dassifier performance curves with reasonable results for the overall comminution-classification circuit control. The steady state (i.e., dmidt = 0) macroscopic population balance on a discrete mass basis over the grind-... 

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