Periodic Reporting for period 4 - SEIC (Setting Earth's Initial Conditions: A fluid dynamics study of core-mantle differentiation)
Reporting period: 2021-10-01 to 2023-03-31
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.
The main results of the project are the following. (i) We have characterised and modelled the dispersion of impactor material produced by an impact on a magma ocean, obtaining simple scaling laws which can be used to evaluate the amount of silicates which interacted with the metal during its descent to the core. (ii) We have modelled heat and mass transfer between metal and silicates by using a formalism inspired by recent work on the theory of mixing, and obtained a parameterised model to quantify the distribution of the concentration of an element in the interacting metal-silicate mixture. Results (i) and (ii) can be used together to parameterise metal-silicates equilibration in geochemical models of core formation. (iii) In parallel, we have developed a coupled thermal/geochemical model of core formation which has allowed us to link the core heat content to the geochemical signature of core formation.
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.
The main results of the project are the following. (i) We have characterised and modelled the dispersion of impactor material produced by an impact on a magma ocean, obtaining simple scaling laws which can be used to evaluate the amount of silicates which interacted with the metal during its descent to the core. (ii) We have modelled heat and mass transfer between metal and silicates by using a formalism inspired by recent work on the theory of mixing, and obtained a parameterised model to quantify the distribution of the concentration of an element in the interacting metal-silicate mixture. Results (i) and (ii) can be used together to parameterise metal-silicates equilibration in geochemical models of core formation. (iii) In parallel, we have developed a coupled thermal/geochemical model of core formation which has allowed us to link the core heat content to the geochemical signature of core formation.
Based on fluid dynamics experiments and numerical simulations, we have developed a model of metal fragmentation in a magma ocean which is based on the idea that the interaction between turbulent fluctuations and the mean flow results 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. Heat and mass transfer between metal and silicates can be understood as a mixing problem for a scalar field (temperature or chemical composition) which is carried by both phases. We have developed what we think is a solid theoretical framework for modelling chemical and thermal equilibration during planetary core formation using a formalism inspired by recent advances made in the field of mixing theory, and developed laboratory experiments that have allowed us to characterise and model the time and spatial variability of the concentration field in the metal-silicate mixture.
In parallel, we have developed an experimental set-up allowing to study vertical and oblique 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. Together with the mixing model discussed in the first paragraph, this can be used to parameterise metal-silicates chemical interaction in geochemical models of core formation.
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 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 link the core heat content to the geochemical signature of core formation. 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 primordial heat content of the core. According to this model, the core heat content correlates with the core composition. Interestingly, many geochemically consistent accretion histories yield core temperatures which are inconsistent with the constraints we have on the present-day core temperature. This provides a previously unexplored way of constraining the evolution of magma ocean depth and thermal state of the mantle during accretion.
In parallel, we have developed an experimental set-up allowing to study vertical and oblique 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. Together with the mixing model discussed in the first paragraph, this can be used to parameterise metal-silicates chemical interaction in geochemical models of core formation.
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 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 link the core heat content to the geochemical signature of core formation. 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 primordial heat content of the core. According to this model, the core heat content correlates with the core composition. Interestingly, many geochemically consistent accretion histories yield core temperatures which are inconsistent with the constraints we have on the present-day core temperature. This provides a previously unexplored way of constraining the evolution of magma ocean depth and thermal state of the mantle during accretion.
Progress made during the project include the following: (i) We have characterised in details the dispersion of impactor material produced by an impact on a magma ocean, using a set of analogue fluid dynamics experiments. From the analysis of the experiments and associated modelling, we have obtained simple scaling laws which can be used to evaluate the amount of silicates which interacted with the metal during its descent to the core. (ii) We have modelled heat and mass transfer between metal and silicates by treating this problem as a mixing problem for a scalar carried by the two phases, the ‘mixed’ state being a state of thermodynamical equilibrium. We have obtained a parameterised model to quantify the distribution of the concentration of an element in the interacting metal-silicate mixture (mean, variance, and probability distribution shape). Results (i) and (ii) can be used together to parameterise metal-silicates equilibration in geochemical models of core formation. (iii) In parallel, we have developed a coupled thermal/geochemical model of core formation which has allowed us to link the core heat content to the geochemical signature of core formation. This opens the prospect of using the core heat content, which is inherited from the process of core formation, as a new constraint on the conditions prevailing during Earth’s differentiation.