Batch Melting Inversion of Melt Compositions

Problem. Demonstrate low-degree (F] )/high-degree (F ) concentration ratio (Q) of the same element decreases with increasing partition coefficients (Dq) during modal batch melting. 

During batch melting, the concentration in the melt ( Cq) is given by 

Do + F(l-Do) F + Do(l-F) where Cq is the source composition, F is the degree of partial melting, Do is the initial bulk partition coefficient. 

For batch melting, the low-degree/high degree concentration ratio is given by 

By differentiating Q with respect to, we find the first derivative 

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