task 1: The fluid dynamics of core formation

State-of-the-art and objectives: The seminal study for the fluid dynamics of core formation dates back to Stevenson (1990), who proposed the following sequence of events, now widely accepted. Telluric planets formed progressively by accretion, initially of grains, then of planetesimals with growing sizes, made mostly of silicate and iron. At some stage of planet accretion, heat generated by large impacts resulted in melting in the proto-planet surface, allowing the denser metallic compound already present, as well as the metal brought by further impacting planetesimals, to separate and settle in the form of drops down to the bottom of the magma ocean (the so-called “iron rain”). After forming an iron pond, the metal finally descended toward the proto-core under the form of iron-rich diapirs. The gravitational energy released in this process was enough to raise the core temperature by several thousand degrees; thus, also considering radiogenic and impact heating, the early core was entirely liquid. Most of chemical exchanges between iron and silicate took place during the iron-rain part of the scenario, where the surface of exchange between the two compounds was large (Rubie et al. 2003). Those early times thus fixed the initial thermochemical state of planets. Based on a schematic view of the fluid dynamics of iron rain, where all drops have the same radius given by the typical capillary length and settle at the corresponding Stokes velocity, and where chemical equilibration is modelled by Fick’s law of diffusion through an advective chemical boundary layer, Rubie et al. (2003) developed a reference model for determining the metal-silicate equilibration of our planet. Other models of Earth’s composition (e.g. Boujibar et al. 2014) have also been proposed, assuming that the whole iron coming from accreting planetesimals instantaneously equilibrates with the whole amount of melted mantle, taken as a fixed proportion of the mantle depth. But the real dynamics of the iron rain is far more complex: the effective distribution of drop size, shape and settling velocity, the internal circulation within drops, the non-linear interactions between drops within the cloud, ... all influence the exchanges of heat and chemical elements (i.e. siderophile vs. lithophile) at the interface between the main iron and silicate compounds.

The fluid dynamics of iron sedimentation and fragmentation has thus been the subject of a renewed interest. For instance, the maximum size of stable iron drops has been debated (Dahl & Stevenson 2010, Samuel 2012), the general consensus being now that any blob of radius “significantly” larger than the capillary length breaks up in smaller pieces after settling over a distance equal to “a few times” its diameter; more quantitative results are however still missing. Advanced models of thermal and chemical equilibration have been proposed, for instance accounting for the flows inside idealised spherical drops (Ulvrova et al. 2011). Finally, Deguen et al. (2011, 2014) showed that an incoming iron blob initially behaves as a turbulent thermal: metal-silicate equilibration is thus initially sustained by turbulent mixing, rather than by break up into droplets. This new fluid concept was included in the latest model of planet formation by Rubie et al. (2015), illustrating the scientific dynamism and responsiveness of this interdisciplinary research subject.

Our team participated in opening new horizons in this domain, using pioneering laboratory experiments (Wacheul et al. 2014, see also https://www.youtube.com/watch?v=g-AmGmWWK1o and figure 1b). In this study, we use liquid Gallium and mixtures of Glycerol and water to model the iron-silicate dynamics, and especially to reproduce the existing viscosity ratio between the two fluid compounds. Surprisingly, this ingredient was mostly ignored in the planetary context, while it is known from various studies of rising gas bubbles to play a significant role in the bubble dynamics (e.g. Bonometti and Magnaudet 2006). In our study, we successfully demonstrated the effects of the viscosity ratio on the drop’s shape variety, on the stabilization of large drops by intense internal circulation, and on the distribution of drop sizes and velocities. All those results were unexpected in a planetary context. We also paved the way for advanced models of thermal and chemical equilibration including those new dynamical effects. But our conclusions were inherently limited by the smallness of the working tank as well as the available diagnostic tools.

Ongoing research projects:

• Laboratory experiments on the fragmentation and turbulent exchanges of a metal blob falling in a viscous ambient: JB. Wacheul and M. Le Bars.
• Numerical simulations of the thermochemical exchanges at the drop scale: B. Qaddah, J. Monteux and M. Le Bars
• Regimes of solidification and convection in planetary cores: L. Huguet and M. Le Bars

Open positions for this project: check out projects listed here