Disequilibrium melting of a two phase multicomponent mantle

There are a number of geochemical and petrological arguments that suggest magma is not always in chemical equilibrium with the surrounding matrix as it rises to the Earth's surface. The most commonly used equations for modelling melt transport are the two phase flow equations of McKenzie (1984), and we have extended these equations to encompass multicomponent mantle melting with possible chemical disequilibrium between the two phases. The governing equations consist of conservation of mass, momentum, and energy; equations of state; and phenomenological laws relating fluxes of mass and heat to differences in temperature and chemical potential. The theory of non-equilibrium thermodynamics constrains the form of these phenomenological laws, through the necessity of positive entropy production (the second law) and the Onsager reciprocal relations. Our particular focus has been on the phenomenological laws for interphase mass transfer, which control melting and crystallisation. In different limits, fractional melting, fractional crystallisation and equilibrium melting can be recovered, but the laws also describe more general behaviour. We have performed some simple 1D melting column calculations to explore these phenomenological laws. The theory should prove useful in a wide range of two phase problems where kinetics plays a key role, and particularly in modelling melt-rock reactions on the continuum scale.