Daughter density distribution

At the onset of phase coexistence, one of the coexisting phases is by definition the parent p (cr) the lever rule does not yet play any role because the daughters p (a) (a = 1. ..p) occupy an infinitesimal fraction of the total volume. It then follows from Eq. (48) that all daughters lie within the family (39) of density distributions. As shown in Eq. (49), the condition for equality of chemical potentials p(a) between any two of the coexisting phases (parent and daughters) then becomes... 

From what we said about the character of drop breakage, it follows that the function g(y) is bimodal with two distinct maxima, one of which is in the interval of satellite sizes, and the other - in the interval of daughter drop sizes. Then it can be presented as a sum of two weighed unimodal distribution densities gi(y) and giiy), defined on the interval (0,1) and having the average values gj = Vi/[Pg.344]

In the limiting case, when the drop splits into daughter drops of identical sizes and satellites whose sizes are also identical, but different from the size of daughter drops, the variances of distribution densities gi(y) and g2(y) are equal to zero... 

About a decade later Martfnez-Bazan et al. [86] criticized their predecessor daughter distribution model for not being volume conservative. A detailed analysis of the model shows that the final normalization step implies that the probability density function (9.113) does not conserve volume. They revealed that the model derivation, the probability function was erroneously expressed as a function of d rather than in terms of volume V(d ), thus the correct way to express this relation is ... 

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