Mixing in a turbulent thermal and implications for metal-silicate equilibrium during Earth's formation
Abstract
During the differentiation of terrestrial planets, the metal phase from the impactor core segregates from the silicate phase of the magma ocean. This buoyant mass forms a turbulent thermal and settles toward the proto-core. During this descent, turbulent motions induce stirring of the metallic phase and entrainment of silicates. Thermal and chemical exchanges may occur at the boundary of the stirred phases. However, homogenization between the two phases only occurs when the metallic phase reaches the diffusive length scale, where mass or heat transfer became irreversible. Based on laboratory fluid dynamic experiments and on 3D direct numerical simulations mimicking the settling of the thermal turbulent, we used the “lamellar” description of the mixing by advecting a Lagrangian material line based on velocity fields. 3D simulations strengthen the results obtained from the experimental dataset, which is only 2D. We have tracked the evolution of the material elongated as lamellae by the turbulent stirring. We have characterized the elongation rate, the aggregation of lamellae, and the probability density function of the elongation and concentration, which are not accessible from direct measurements in the experiments. We have also investigated the effect of the Reynolds and Péclet number on these quantities. Based on these results, we have produced a stochastic model able to predict the temporal evolution of the concentration field, which can be used for understanding the equilibrium between metals and silicates during the accretion of terrestrial planets.