Further developments of the Rayleigh fractionation equation for fractional crystallization

The equation developed by Neuman et al. [1] from the Rayleigh fractionation law is expressed as: C1 C0 = F(D - 1). Since the residual melt fraction F is not directly connected with the mass fraction of phase i in the solid xi, it is necessary to assign a series of arbitrary values to one of these variables. The modelling which results from using Rayleigh's equation is thus externally controlled and as such has little real significance. By introducing the variable yi to represent the mass of phase i in the solid in relation to the initial mass, we obtain F = 1 - Σyi and the previous equation can be rewritten: C1 C0 = (1 - Σyi)( ΣyiKi Σyi - 1). From this form of the equation it is possible to find the other system variables for known values of Ki, C1 and C0 where Ki represents the solid-liquid partition coefficient and C1 and C0 are the concentration of the differentiated and parent melts respectively. The system of simultaneous equations can be solved by least-squares methods and applied to the study of natural systems.