A regime diagram for the slurry F-layer at the base of Earth's outer core

Seismic observations of a slowdown in P wave velocity at the base of Earth's outer core suggest the presence of a stably-stratified region known as the F-layer. This raises an important question: how can light elements that drive the geodynamo pass through the stably-stratified layer without disturbing it? We consider the F-layer as a slurry containing solid particles dispersed within the liquid iron alloy that snow under gravity towards the inner core. We present a regime diagram showing how the dynamics of the slurry F-layer change upon varying the key parameters: P\'eclet number ($Pe$), the ratio between advection and chemical diffusion; Stefan number ($St$), the ratio between sensible and latent heat; and Lewis number ($Le$), the ratio between thermal and chemical diffusivity. We obtain four regimes corresponding to stable, partially stable, unstable and no slurries. No slurry is found when the heat flow at the base of the layer exceeds the heat flow at the top, while a stably-stratified slurry arises when advection overcomes thermal diffusion ($Pe \gtrsim Le$) that exists over a wide range of parameters relevant to the Earth's core. Our results estimate that a stably-stratified F-layer gives a maximum inner-core boundary (ICB) body wave density jump of $\Delta \rho_\textrm{bod} \leq 534 \ \mathrm{kg} \mathrm{m}^{-3}$ which is compatible with the lower end of the seismic observations where $280 \leq \Delta \rho_\textrm{bod} \leq 1,100 \ \mathrm{kg} \mathrm{m}^{-3}$ is reported in the literature. With high thermal conductivity the model predicts an inner core age between $0.6$ and $1.2 \ \mathrm{Ga}$, which is consistent with other core evolution models. Our results suggest that a slurry model with high core conductivity predicts geophysical properties of the F-layer and core that are consistent with independent seismic and geodynamic calculations.