Numerical simulations of the thermochemical exchanges at the drop scale

B. Qaddah, J. Monteux and M. Le Bars

The aim of this numerical project is to determine the dynamics of the liquid iron fragmentation within the molten silicates of the Early Earth mantle and to characterize the fractionation of the siderophile / lithophile elements as well as the thermal exchanges during this fragmentation.

In the first part of this project, we are interested in determining the morphology, dynamics and stability of the iron drop as a function of the dimensionless Weber and Reynolds numbers as well as of the viscosity ratio between the molten silicates and the liquid iron drop. We are interested also in determining the potential exchange surface between the iron and the silicates flows, the characteristic falling time, the breakup distance and the iron fragmentation modes.

For this, we vary the viscosity of the silicates in the range of 0.05 Pa.s to 100 Pa.s and the initial radius of iron diapir in the range of 1mm to 350mm, in order to capture and explain all the dynamical changes between the iron and the silicate phases before adding the modelisation of thermochemical exchanges.

Numerically, we use a 2D cylindrical axisymmetric computational domain and the level-set model in the sofware Comsol multiphysics. Our computational domain is 200R*12R where R is the initial radius of the iron blob. We have submitted a paper (Qaddah et al. 2019, in revision) about this systematic numerical study and the main results are:

• the maximal stable drop radius and the critical Weber number are monotonically increasing functions of the magma ocean viscosity.
• increasing the viscosity of the silicate phase prevents oscillations of the iron phase and limits the exchange surface.
• oppositely, increasing the initial radius of the iron drop enhances its deformation and increases its relative exchange surface.
• above the critical Weber number, the fragmentation of the liquid iron occurs within a falling distance equal to 3.5-8 times the drop initial radius in the explored range of moderate Weber number
• a variety of fragmentation regimes are possible, as shown as in the following figure.

References

• Dynamics and stability of an iron drop falling in a magma ocean, Qaddah, B., Monteux, J., Clesi, V., Bouhifd, M. A., & Le Bars, M. Physics of the Earth and Planetary Interiors, 289, 75-89 (2019).
• Thermal evolution of a metal drop falling in a less dense, more viscous fluid. B Qaddah, J Monteux, M Le Bars. Physical Review Fluids 5 (5), 053801 (2020)
• Dynamics of core-mantle separation: Influence of viscosity contrast and metal/silicate partition coefficients on the chemical equilibrium, V Clesi, J Monteux, B Qaddah, M Le Bars, J-B Wacheul, A Bouhifd, Physics of the Earth and Planetary Interiors, in press (2020).