Small-Scale Metal/Silicate Equilibration During Core Formation: The Influence of Stretching Enhanced Diffusion on Mixing

Abstract : Geochemical data provide key information on the timing of accretion and on the prevailing physical conditions during core/mantle differentiation. However, their interpretation depends critically on the efficiency of metal/silicate chemical equilibration, which is poorly constrained. Fluid dynamics experiments suggest that, before its fragmentation, a volume of liquid metal falling into a magma ocean undergoes a change of topology from a compact volume of metal toward a collection of sheets and ligaments. We investigate here to what extent the vigorous stretching of the metal phase by the turbulent flow can increase the equilibration efficiency through what is known as stretching enhanced diffusion. We obtain scaling laws giving the equilibration times of sheets and ligaments as functions of a Peclet number based on the stretching rate. At large Peclet, stretching drastically decreases the equilibration time, which in this limit depends only weakly on the diffusivity. We also perform 2-D numerical simulations of the evolution of a volume of metal falling into a magma ocean, from which we identify several equilibration regimes depending on the values of the Peclet (Pe), Reynolds (Re), and Bond (Bo) numbers. At large Pe, Re, and Bo, the metal phase is vigorously stretched and convoluted in what we call a stirring regime. The equilibration time is found to be independent of viscosity and surface tension and depends weakly on diffusivity. Equilibration is controlled by an efficient thermochemical stretching enhanced diffusion mechanism developing from the mean flow and entraining the surrounding silicate phase. Plain Language Summary During the formation of the solar system 4.5 billion years ago, collisions between primitive planetary bodies lead to the progressive growth of the Earth through a mechanism called accretion. Concomitantly, the metal contained in the impactors migrates toward the center of the accreting Earth, as a result of being denser than the surrounding rocks, through a process known as differentiation. During its descent, the metal exchanges heat and chemical elements with the Earth's rocks, modifying in this way its own temperature and chemical composition, as well as the one of the surrounding materials. The degree of thermal and compositional homogenization between metal and rocks is a key parameter for the thermal and magnetic evolution of the Earth, and the interpretation of geochemical data. Part of the mixing occurs in fully molten rocks (viz., a magma ocean), in which the sinking metal undergoes vigorous deformation and stretching. In this paper, we use analytical calculations and numerical simulations to examine the influence of deformation on mixing. We show that stretching of the metal can drastically accelerate thermal and compositional homogenization between metal and rocks.
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V. Lherm, Renaud Deguen. Small-Scale Metal/Silicate Equilibration During Core Formation: The Influence of Stretching Enhanced Diffusion on Mixing. Journal of Geophysical Research : Solid Earth, American Geophysical Union, 2018, 123 (12), pp.10496--10516. ⟨10.1029/2018JB016537⟩. ⟨hal-02327172⟩

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