The requirements for chemical disequilibrium during magma migration

Recent geochemical studies of MORB genesis suggest that at least some degree of chemical disequilibrium occurs during the transport of magma to the surface. If disequilibrium transport does occur in the mantle, it would seem to preclude melt being distributed in a porous network on grain boundaries that could rapidly re-equilibrate with the solid. The questions remain however, as to how big a melt "channel" is required to produce disequilibrium and whether flow in such channels would violate assumptions inherent in the equations of magma migration. Using a series of simple physical scaling arguments, we quantify the requirements for chemical disequilibrium and lay out the conditions for which the melt migration equations are valid. These arguments show that a vein network with veins ~ 10 cm apart is sufficient to cause significant disequilibrium. More precisely, these arguments show that to maintain equilibrium, the solid-state diffusion coefficient would need to increase by 2-4 orders of magnitude for every order of magnitude increase in channel spacing. Nevertheless, because the equations of magma migration are a macroscopic description of melt flow, they can readily describe even large scale networks of melt channels. By demonstrating the fundamental scalings governing the chemistry and motion of partial melts, these simple arguments show that, while the chemistry may be extremely sensitive to the microscopic distribution of melt, our physical understanding of magma migration is robust.