Dynamics of metal-silicate separation in a terrestrial magma ocean

Hoink T, Schmalzl J, Hansen U

Abstract

In a terrestrial magma ocean, the metal- silicate separation involved small metal droplets. Our goal is to better understand the dynamics of the metal droplet scenario. The mechanism of sedimentation in a vigorously convecting and strongly rotating magma ocean may differ significantly from settling droplets in a still fluid. In order to systematically study the parameter dependence on the style of motion we utilize two- dimensional and three- dimensional numerical convection models combined with a tracer- based sedimentation method. We investigate the characteristic flow patterns resulting from the competing effects of convection and droplet settling and find three styles of motion: a temperature- dominated style where most droplets remain suspended, a droplet- dominated style where the droplets separate from the fluid, and a style of repetitive motion. We find that the droplet- dominated style is relevant to the magma ocean. In this scenario the droplets settle and form a dense bottom layer. One of the key findings of this work is that the formation of the dense bottom layer, and therefore the separation of metal droplets from the liquid silicate, occurs on a characteristic timescale, which is identical with the Stokes' settling time. Finally, we study the chemical interaction of settling metal droplets and liquid silicate and discuss how accurately a simple parameterized model can describe the chemical equilibration in the metal- rain scenario of a terrestrial magma ocean. We find agreement between the parameterized model and our two- dimensional model. Our simulations, which include thermal convection into the metal- rain model, confirm the fundamental observation that metal droplets are not permanently suspended in the convecting silicate melt, but that they sink and rapidly form a dense layer at the base of the magma ocean.