Direct numerical simulation of an iron rain in the magma ocean

[1] Core formation in terrestrial planets is a complex process, possibly involving several mechanisms. This paper presents a direct numerical simulation of one of these, the separation of an emulsion of metal in a magma ocean. The model, using a fully Lagrangian approach called the moving particle semi-implicit method, solves the equations of fluid dynamics, including a proper treatment of surface tension. It allows investigation of the balances controlling the distribution of drop size and velocity, in both twoand three-dimensional situations. A scaling analysis where buoyancy is balanced by both surface tension and inertia correctly predicts the average values in these quantities. The full calculation gives an average drop radius of 1.5 cm falling at a velocity of about 30 cm s . Analysis of the full distribution remains interesting and shows that a significant part of the smallest droplets is entrained upward by the return flow in molten silicate and might be entrained by succeeding thermal convection. In addition, we investigate the conversion of gravitational energy into viscous heating and the thermal equilibration between both phases. We find that viscous heating is essentially produced at the surface of iron drops and that thermal equilibration is dominated by advection. Scaling thermal diffusion to chemical diffusion leads to the estimation that the latter would happen in less than 100 m in the magma ocean.