own weight (section \[sec:path\]). Our numerical simulations and laboratory experiments [@deguen_2014; @landeau_2014; @wacheul_2014; @wacheul_2018] show that a mass of metal falling into a magma ocean is most probably in a regime which we call *stirring regime*, in which the metal is stretched into convoluted sheets and ligaments, before fragmenting into drops. We then study in section \[sec:basic\] the equilibration of what we consider to be the “building blocks” of the fragmentation and equilibration sequence, *i.e.* sheets, ligaments and droplets. In section \[sec:stirring\], we finally come back to the *stirring regime* which we characterize in light of our results on the equilibration of stretched sheets.

Equations and Numerical Model {#sec:equations}
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Geometries {#sec:equations-geometries}
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In sections \[sec:path\], \[sec:basic\], and \[sec:stirring\], we will carry out analytical and numerical calculations (*cf.* table S1 for numerical parameters) on the temperature and concentration evolution of sheets, ligaments and drops. In each geometry (figure \[fig:geometries\]), we consider a two-phase flow involving a liquid silicate-like outer phase (phase 2) and a liquid metallic-like inner phase (phase 1). Sheets and ligaments are stretched by a constant pure shear flow at a strain rate $\dot\epsilon$. We don’t consider the effect of gravity. The two phases have different densities, viscosities, 