Dynamics and stability of an iron drop falling in a magma ocean

Abstract

The latest stages of planetary accretion involved large impacts between differentiated bodies, hence large scale melting events. Consequently, the iron brought by the impactors sank within a deep magma ocean, before reaching the proto-core. Yet the fluid dynamics of this process remains poorly known. Here, we report numerical simulations of the sinking dynamics of an initially spherical liquid iron drop within a molten silicate phase, up to its possible fragmentation. We consider a 2D cylindrical axisymmetric geometry. We vary the viscosity of the molten silicates in the range of 0.05 Pa.s–100 Pa.s and the initial radius of the iron drop in the range of 1 mm–350 mm. Hence, we investigate Reynolds number in the range of [0.027–85600] and Weber number in the range of [0.073–7480]. Our numerical model constrains 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. In particular, we show that the maximal stable drop radius and the critical Weber number are monotonically increasing functions of the magma ocean viscosity. The momentum boundary layer thickness depends mainly on the drop radius and slightly on 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, we confirm that 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, and we describe a variety of fragmentation regimes. Consequences for Earth’s formation models are briefly assessed.