Rayleigh fractionation with continuous removal of liquid

In its simple form the Rayleigh surface equilibrium fractionation equation is only valid for a closed system in which solid separates from liquid, and no liquid is lost. Many natural systems, particularly magma chambers, lose liquid continuously as they fractionate. Here it is shown that evolution in such a system can, if loss of liquid proceeds in a constant ratio to precipitation of solid, be modelled by a modified Rayleigh equation where the solid/liquid distribution coefficientD is replaced byD*=(q·D + 1)/(q + 1), whereq is the ratio of solid precipitated to liquid extracted. This can be visualised as treating the liquid removed as an additional phase extracted during fractionation for whichD = 1. The effect of this is particularly important for incompatible elements, where asD → 0,D* → 1/(q + 1), so that whenq = 1, the most incompatible element givesD* = 0.5.