Disequilibrium melting of a two phase multicomponent mantle

Melt generation and segregation in Earth's mantle is typically modelled using the mixture theory of two phase flows, which combine a set of conservation laws for mass, momentum and energy with phenomenological laws for fluxes of mass and heat. Most current two phase flow models assume local thermodynamic equilibrium between melt and matrix, but geochemical observations suggest disequilibrium transport may play an important role. Here we generalise the existing two phase flow theories to encompass multiple thermodynamic components and disequilibrium. Our main focus is on the phenomenological laws describing phase change and we present general disequilibrium melting laws, which reduce to the familiar fractional and equilibrium melting laws in appropriate limits. To demonstrate the behaviour of our melting laws, we address two simple model problems for a binary system: melting at constant pressure and melting in a 1-D upwelling column at steady state. The framework presented here will prove useful in future for modelling reaction infiltration instabilities in a thermodynamically consistent manner. This framework will be useful not only for magma dynamics but for a wide range of reactive two phase flow problems