Transport properties of Mg2SiO4 liquid at high pressure: Physical state of a magma ocean

We use a flexible potential model to perform large-scale molecular dynamics simulations on self-diffusivity and viscosity of Mg2SiO4 melt up to pressures of 32 GPa and over a temperature range of 2600 to 3200 K. We find that self-diffusivity decreases and viscosity increases uniformly with pressure, the latter from values of 10− 2 Pa s at 0 GPa to 10− 1 Pa s at 32 GPa (2600 K). Both transport properties can be readily fit with a closed Arrhenius expression over the whole pressure and temperature range considered. Independent estimates of self-diffusivities and viscosity allow us to examine their relation through the Stokes–Einstein and the Eyring equations. While at low pressures the SiO4 tetrahedron seems to be the viscous flow unit, bare ion diffusion becomes more dominant at high pressure. Combining previous simulation results on thermodynamic properties with the current viscosity simulations we compute a magma ocean adiabat and the associated viscosity profile. We find that viscosity in the magma ocean is ∼ 2 · 10− 2 Pa s near the surface, and that it increases by less than 0.5 log-unit up to 35 GPa. Combining scenarios for magma ocean dimensions in the young Earth with thermodynamic properties and viscosity of Mg2SiO4 melt we compute a magma ocean Rayleigh number Ra in the range of 1028 and 1029, putting the magma ocean in the dynamic regime of hard turbulence. Using scaling relations for the Nusselt number Nu at very high Ra we estimate the heat flux of the magma ocean to be in the range of 1018 to 1019 W.