ODM with continuous addition of melt and solid

The idea of continuous input of both melt and solid into the melting zone was first proposed by Shaw (2000) and Shaw (2006). Here we present a further full development of the model on the basis of the idea. 

Since the change of the mass of the trace element is due to the extraction of the residual melt, we have 

The rate of addition is taken to be constant and is equal to P per unit of melting F 

We also assume that the material added contributes to both melt and solid in mass proportions y and (1 - y) 

The total mass of residual melt and extracted melt is 

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