Research progress with Thermal Lattice Boltzmann Method to study early Earth

The Thermal Lattice Boltzmann Method (TLBM) models finite Prandtl number thermal convection and multiphase flow at high Rayleigh numbers in the turbulent regime. As such, it offers a powerful means to study early earth which was shaped by magma oceans (MOs) where turbulent convection governed the transport of heat, silicates and volatiles. Ab-initio molecular dynamics shows that pressure and temperature dependent viscosity of silicates can vary by many orders of magnitude resulting in stratified Prandtl numbers ranging from much lower to much higher than unity spanning up to 3 – 5 orders of magnitude. We incorporated such P-T dependent viscosity into the Thermal LBM to explore the impact of stratified Pr on the convective dynamics of turbulent magma oceans. We find that the Pr stratification has a dramatic influence on turbulent flow, with strong vorticity only occurring at shallower depths above 1000 km for colder adiabats which implies greater chemical equilibration. We also combined the TLBM and multiphase LBM to model iron-silicate segregation due to large iron-rich impactors in a 3000 km thick magma ocean with a Prandtl number of unity. These studies indicate that thermal convection exerts only a modest influence on the spatial distribution of iron in MOs. Our results reveal that the time for iron droplets to fully settle lies in the range 15 – 30 days, and that vigorous thermal convection tends to confine fragments of smaller impactors to deeper regions of the MO, whereas, fragments of larger impactors disperse throughout all depths of the MO.