Daughter distribution function

For the daughter distribution function, very different scenarios are possible depending on the nature of the disperse phase (i.e. solid versus fluid particles) as explained by Zac-cone et al. (2007) and Patruno et al. (2009). In general, the simplest functional form is a summation of delta functions ... 

If z is the daughter-to-parent mass ratio the corresponding daughter distribution function is... 

Most daughter distribution functions can be easily extended to bivariate problems. Let us consider two examples. In the first example particles with two components A and B are described. The particulate system is defined in terms of the size of these particles dp and the composition of the particles 0, expressed for example as the mass fraction of component A in the particle. When a particle breaks we can assume for example that the amount of component A is partitioned among the daughters proportionally to the mass of the fragments. Under these hypotheses, and the additional assumption of binary breakage following the beta distribution, the resulting bivariate distribution is... 

Table 7.1. Common daughter distribution functions and their moment transforms.

This procedure is very easy in the case of simple daughter distribution functions (e.g. symmetric binary breakage), whereas additional random numbers might have to be selected for more complex daughter distribution functions (e.g. beta, uniform, etc.)... 

For this specific example, consider the case of constant aggregation and breakage kernels, namelyPa,y,s,[Pg.326]

---