#	Pagina
attuale pagina	/open-h2020/projects/206325/results.html

Report

Teaser, summary, work performed and final results

Periodic Reporting for period 1 - SEIC (Setting Earth\'s Initial Conditions: A fluid dynamics study of core-mantle differentiation)

Teaser

Summary

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.

Work performed

Based on fluid dynamics experiments and numerical simulations, we have developped a conceptual 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 may then fragment into drops through the Rayleigh-Plateau capillary instability. We have developed what we think is a solid theoretical framework for understanding chemical and thermal equilibration during planetary core-formation, by generalizing to two-phases flows the formalism of stretching enhanced diffusion, which has been classically used to quantify homogenization 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 parallell, we have developped an experimental set-up allowing to study vertical impacts in liquid systems, which has already yielded interesting results on the impact-induced mixing. In particular, we have found a so-far undescribed Rayleigh-Taylor type instability developing around the expanding crater, which results in significant mixing.

We have also started working on the 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.

Final results

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 dipersion 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 plan to 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 parameterized geochemical models of Earth accretion and differentiation. This will give useful tools for interpreting the geochemical data in terms of the timescale of Earthâ€™s accretion, and physico-chemical conditions during differentiation.