Dynamics of core-mantle separation: Influence of viscosity contrast and metal/silicate partition coefficients on the chemical equilibrium

Abstract

The composition of the Earth's core and mantle is set by the chemical equilibrium between metals and silicates during core/mantle segregation. The metallic core separated from the mantle by gravitational descent in the form of diapirs in a magma ocean, and therefore the dynamics of the diapir's downward movement has an influence on the chemical equilibrium. In this study, we characterize the descent of metallic droplets into a molten silicate using numerical models. By varying the silicate and metal viscosities (between 0.1 and 1000 Pa·s for each phase) as well as the partition coefficient between metal and silicate (Dmet/sil, varying between 1 and 1000), we obtained quantifying parametrizing equations for the degree of equilibrium between molten metal and molten silicate, in a regime characterized by low We (We < 10) and low Re (10−3 < Re<102). We showed that the main parameters controlling the equilibrium for a siderophile element are the viscosity of the silicate and the partition coefficient. We applied our parameterization for Ni and Co in the context of late accretion on Earth so as to quantify the variation of the Ni/Co ratio after a large impact as a function of the magma ocean viscosity, for an iron-rain scenario of metal/silicate segregation. Using previous models (Canup, 2004) of the Moon–forming impact, we showed that the Moon formation had an effect on the current Ni/Co ratio. Depending on the radius of Theia's core and the viscosity of the magma ocean produced after the impact between the proto-Earth and Theia, the Moon formation could account for 0.45% to 3% of the current Ni/Co ratio for magma ocean viscosities of 0.1 to 100 Pa·s, respectively.