A two-phase pure slurry model for planetary cores: one-dimensional solutions and implications for Earth's F-layer

We develop and analyse a continuum model of two-phase slurry dynamics for planetary cores. Mixed solid–liquid slurry regions may be ubiquitous in the upper cores of small terrestrial bodies and have also been invoked to explain anomalous seismic structure in the F-layer at the base of Earth's liquid iron core. These layers are expected to influence the dynamics and evolution of planetary cores, including their capacity to generate global magnetic fields; however, to date, models of two-phase regions in planetary cores have largely ignored the complex fluid dynamics that arises from interactions between phases. As an initial application of our model, and to focus on fundamental fluid dynamical processes, we consider a non-rotating and non-magnetic slurry comprised of a single chemical component with a temperature that is tied to the liquidus. We study one-dimensional solutions in a configuration set up to mimic Earth's F-layer, varying gravitational strength $R$ , the solid/liquid viscosity ratio $\lambda _{\mu }$ and the interaction parameter $K$ , which measures friction between the phases. We develop scalings describing behaviour in the limit $R \gg 1$ and $\lambda _{\mu } \gg 1$ , which are in excellent agreement with our numerical results. Application to Earth's core, where $R \sim 10^{28}$ and $\lambda _{\mu } \sim 10^{22}$ , suggests that a pure iron slurry F-layer would contain a mean solid fraction of at most 5 %.