Modal Dynamic Melting with Constant

If ) is a constant, then by integrating both sides from 0 to X, we have 

Example. Calculate the concentration of an incompatible element normalized by the initial source concentration (C/Cq) with bulk partition coefficient D = 0.02 in the extracted dynamic melt and residual melt. Assuming 0 = 0.01. 

By substituting D = 0.02 and (Z = 0.01 into Eq. (3.6), we can obtain the source-normalized concentration in the extracted melt C/Cgas a function of X. The results are plotted in Fig. 3.1. Similarly, substituting Z) = 0.02 and (Z = 0.01 into Eq. (3.7), we can obtain the source normalized concentration in the residual melt C /Cg as a function of X. The results are also plotted in Fig. 3.1. Note that after melt extraction begins, residual melt is more depleted in incompatible elements than the extracted melt. At about 15% of melting, the residual melt does not contain much incompatible elements. 

The effects of varying critical porosity on the concentrations of incompatible elements in the extracted melt are displayed in Fig. 3.2. The incompatible element concentrations in the extracted melt increase with the decrease in the critical porosity, owing to more efficient removal of incompatible elements at lower critical porosity. 

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The previous four chapters deal with the fractionation of stable trace elements during partial melting. In this chapter, we study the behaviors of radioactive uranium decay series during partial melting. Since quantitative models for uranium-series disequilibria need to include additional parameters in decay constants and are thus more complicated, for simplicity, we assume that the partition coefficients remain constant during partial melting. Thus, we only present modal dynamic melting. 

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