OBM with one-time instantaneous addition of melt

The one-time addition of fluids can be regarded as a one-time fluid metasomatism of the solid rocks just as it starts melting. This is a potential important model for mantle metasomatism. 

The amount of one-time fluid metasomatism is related to the mass of the melting zone source rocks by 

Note that is independent of F in this one-time addition model. 

Problem. What if it is complete disequilibrium between melt and solid For complete disequilibrium, we have 

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