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Setting Earth's Initial Conditions: A fluid dynamics study of core-mantle differentiation

Periodic Reporting for period 3 - SEIC (Setting Earth's Initial Conditions: A fluid dynamics study of core-mantle differentiation)

Reporting period: 2020-04-01 to 2021-09-30

The initial conditions of the Earth and other terrestrial planets were set 4.5 Gy ago during their accretion from the solar nebula and their concomitant differentiation into an iron-rich core and a silicate mantle. Accretion in the solar system went through several different dynamical phases involving increasingly energetic and catastrophic impacts and collisions. The last phase of accretion, in which most of the Earth mass was accreted, involved extremely energetic collisions between already differentiated planetary embryos (1000 km size), which resulted in widespread melting and the formation of magma oceans in which metal and silicates segregated to form the core and mantle. Geochemical data provide critical information on the timing of accretion and the prevailing physical conditions, but it is far from a trivial task to interpret the geochemical data in terms of physical conditions and processes.

We propose here a fluid dynamics oriented study of metal-silicate interactions and differentiation following planetary impacts, based in part on fluid dynamics laboratory experiments. The aim is to answer critical questions pertaining to the dynamics of metal-silicate segregation and interactions during each core-formation events, before developing parameterized models of metal-silicate mass and heat exchange, which will then be incorporated in geochemical models of the terrestrial planets formation and differentiation. The expected outcomes are a better understanding of the physics of metal-silicate segregation and core-mantle differentiation, as well as improved geochemical constraints on the timing and physical conditions of the terrestrial planets formation.

In addition, we expect our results to impact other fields than geodynamics and geochemistry. The experiments and numerical simulations planned in this project are also of interest for fundamental and applied fluid mechanics. Fragmentation in turbulent conditions has also a number of industrial or environmental applications.
Based on fluid dynamics experiments and numerical simulations, we have developed a model of metal fragmentation in a magma ocean which states that the interaction between hydrodynamic instability, turbulent fluctuations, and the mean flow, will result in vigorous stirring and stretching of the metal phase. The metal phase topology is predicted to quickly evolve from a compact blob of metal (the impactor's core) toward metal sheets and ligaments, which can then fragment into drops due to a capillary instability. We have developed what we think is a solid theoretical framework for understanding chemical and thermal equilibration during planetary core formation, by generalising to two-phases flows the formalism of stretching enhanced diffusion, which has been classically used to quantify homogenisation of compositional heterogeneities in chaotic flows. Our theoretical analysis allows to predict the degree of equilibration and the timescale of chemical equilibration from the time evolution of the stretching rate of the metal.

In parallel, we have developed an experimental set-up allowing to study vertical impacts in liquid systems, which has allowed us to develop scaling laws for the amount of large scale silicate/metal mixing following a vertical impact. The model predicts significant dispersion of the metal phase by impact-related process.

Using geochemical modelling of core formation, we have obtained theoretical bounds for the evolution during accretion of the pressure and temperature of equilibration, which are key ingredients for estimating the composition of the core and its initial heat content. Our approach allows to get rid of the usually made assumption of equilibration at a pressure which is a constant fraction of the core-mantle boundary pressure. Our bounds show that the equilibration pressure must have remained relatively low (less than half of the core-mantle boundary pressure) during the first ~80% of accretion, while much larger equilibration pressures (up to CMB pressure or higher) are allowed in the last ~20% of accretion. This is consistent with the idea that the final stages of Earth’s accretion have involved giant impacts.

Finally, we have developed a coupled thermal/geochemical modelling approach which allows to predict the temperature of the core at the end of accretion from geochemical data. The idea is to feed geochemical constraints on the metal/silicates equilibration pressure and temperature into a model of the thermal evolution of the metal phase to predict the temperature of the core. Interestingly, many geochemically consistent accretion histories yield core temperatures which are markedly lower than the current core temperature. Accepting that the core temperature at the end of accretion must have been higher than what it is now, this means that these accretion histories are inconsistent with available constraints on Earth’s core thermal state. This provides a previously unexplored way of constraining the evolution of magma ocean depth and thermal state of the mantle during accretion.
Our theoretical analysis suggests that both chemical equilibration and fragmentation depend critically on the magnitude and time evolution of the stretching rate of the metal phase.
The next step is therefore to obtain predictive laws for the stretching of the metal phase following each impact. To do this, we have planned a suite of experiments in what we think is the correct dynamical regime, where we will quantify the dispersion and stretching of the dense falling phase, as well as heat and compositional transfer between the two liquid phases. The expected outcome is a better understanding of the physics of metal-silicate segregation and core-mantle differentiation. More specifically, we will develop models and scaling laws predicting the amount of metal dispersion following an impact, and the rate at which metal and silicates can exchange chemical elements during each core-formation events. One of our aims is to provide simple but realistic models of metal-silicate chemical interactions, which can then be incorporated in parameterised geochemical models of Earth accretion and differentiation. This will give useful tools for interpreting the geochemical data in terms of the timescale of Earth’s accretion, and physico-chemical conditions during differentiation.
Rayleigh-Taylor instability developing at the rim of an expanding crater.