# Small-Scale Metal/Silicate Equilibration During Core Formation: The Influence of Stretching Enhanced Diffusion on Mixing

## TL;DR

This study explores how turbulent stretching of metal during core formation enhances chemical mixing efficiency, revealing that stretching significantly reduces equilibration times and depends weakly on diffusivity at high Péclet numbers.

## Contribution

It introduces scaling laws and numerical simulations demonstrating the impact of stretching enhanced diffusion on metal-silicate equilibration during core formation.

## Key findings

- Stretching reduces equilibration times at high Péclet numbers.
- Equilibration time depends weakly on diffusivity in vigorous stretching regimes.
- Vigorous stretching leads to a stirring regime with efficient mixing.

## Abstract

Geochemical data provide key information on the timing of accretion and on the prevailing physical conditions during core/mantle differentiation. However, their interpretation depends critically on the efficiency of metal/silicate chemical equilibration, which is poorly constrained. Fluid dynamics experiments suggest that, before its fragmentation, a volume of liquid metal falling into a magma ocean undergoes a change of topology from a compact volume of metal toward a collection of sheets and ligaments. We investigate here to what extent the vigorous stretching of the metal phase by the turbulent flow can increase the equilibration efficiency through what is known as stretching enhanced diffusion. We obtain scaling laws giving the equilibration times of sheets and ligaments as functions of a P\'eclet number based on the stretching rate. At large P\'eclet, stretching drastically decreases the equilibration time, which in this limit depends only weakly on the diffusivity. We also perform 2D numerical simulations of the evolution of a volume of metal falling into a magma ocean, from which we identify several equilibration regimes depending on the values of the P\'eclet (Pe), Reynolds (Re), and Bond (Bo) numbers. At large Pe, Re and Bo, the metal phase is vigorously stretched and convoluted in what we call a stirring regime. The equilibration time is found to be independent of viscosity and surface tension and depends weakly on diffusivity. Equilibration is controlled by an efficient thermochemical stretching enhanced diffusion mechanism developing from the mean flow and entraining the surrounding silicate phase.