Steady-state Mantle–Melt Interactions in One Dimension: II. Thermal Interactions and Irreversible Terms

Progress in development of thermodynamically based models of silicate equilibria with explicit entropy budgets has motivated a reexamination of the conclusion of McKenzie (Journal of Petrology 25, 713–765, 1984) that isentropic upwelling suffices as a model of mantle melting. An entropy budget equation for fractional melting with melt migration in an upwelling two-phase continuum is presented. The energetically self-consistent melt production model predicted by MELTS is used to evaluate numerically the magnitudes of differences between fractional melting (with melt migration) and equilibrium melting (without relative movement) that can be bounded in one dimension: chemical advection by out-of-equilibrium melt; thermal disequilibrium between migrating liquid and residue; frictional dissipation of gravitational potential; dissipation as a result of solid compaction. Like the familiar isobaric case in which fractional melting is significantly less productive than equilibrium melting, chemical isolation of the escaping melts from the residue reduces the oceanic crustal thickness by ~1 km. Allowing escaping melts to move on their own adiabats and ascend at higher temperature than the residue further suppresses melting but yields only ~100 m less crustal thickness. Extra crustal thickness as a result of gravitational dissipation is ~100 m, much smaller than the effect of chemical isolation. Viscous dissipation as a result of compaction is negligible