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 Péclet number based on the stretching rate. At large Péclet, 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 Péclet (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.

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

“…Future models should also account for the thermal equilibration during metal/silicate separation (Wacheul & Le Bars, 2018) to characterize the effects of temperature on the partition coefficient values. Other phenomena, while important, are ignored due to being beyond the scope of the study, for instance the effect of the droplet size and shape (Qaddah et al, 2019), or stretch-enhancing diffusion (Lherm & Deguen, 2018), or the possibility of large core-merging events (Landeau et al, 2016). All these phenomena are beyond the scope of this study and should be taken into account in further work and models of accretion.…”

“…It is also worth noting that this parameterization is valid for a narrow range of Re and We values, and its precision is lower at high Re values (see section 2.4). For instance, different results can be found in turbulent cases (high Re, Deguen et al, 2014) and/or with deformed diapirs (high We, Lherm & Deguen, 2018). However, this form of equation (Eq.…”

“…This effect is weak in our study compared to the effect of Re and D met/sil (see Section 3.4), because the We range of our study does not allow major diapir deformation. For the deformation rate to have a strong impact on chemical equilibrium, the We values have to be much higher (We> 10, see Lherm & Deguen, 2018).…”

Activity coefficients of siderophile elements in Fe-Si liquids at high pressure

“…As this process unfolds, the energetics of accretion increase steadily providing sufficient energy to melteither partially or completelyplanetary mantles and metal-silicate mixtures (e.g., de Vries et al, 2016). The equilibration of metal and silicate melts is rapid and complete during this process (Kendall and Melosh, 2016;Lherm and Deguen, 2018) and thus the siderophile element content of the molten portion of the planet will change as the depth and associated pressure of metal-silicate equilibrium increases (e.g., Rubie et al, 2003). Modelling of siderophile element contents of molten upper mantle melts in equilibrium with Fe-Si-S-C metallic liquids during accretion now includes 26 elements (Fig.…”

Thermal evolution of a metal drop falling in a less dense, more viscous fluid

“…Note that in this work we do not calculate the chemical exchanges between the two phases. Instead, the main difference between the heat and mass transfer equations, if the thermal and chemical sources are neglected, is the partition coefficient between the two phases (30). When the partition coefficient is equal to 1, we can use the results of this study in geochemical models of planet building (31).…”