(a) Density profiles of H₂ (green), H₂O (blue), and Fe³⁺ (orange) and (b) the H₂O/H₂ density ratio normalized by its equilibrium value at each depth in the boundary layer at selected times during a boundary layer overturn time of 70 s. The full boundary layer thickness calculated from Equation (34) is 19 mm, but only the upper part of the boundary layer, where H₂ diffusion occurs, is shown for clarity. Color gradients indicate temporal evolution. The H₂ surface pressure is 300 bar, the surface temperature is 2400 K, and the initial Fe³⁺/Fe²⁺ ratio is 0.08. The overturn time of 70 s corresponds to a surface temperature of 2400 K, a magma ocean bottom pressure of 50 GPa, and an internal heat flux of 400 W m⁻², representative of the early stage of magma ocean evolution shown in Figures 6 and 7. (c) Corresponding temporal evolution of the H₂ diffusion rate normalized by the hydrogen molecular number in the present-day terrestrial seawater (N_TO). The dashed line represents the mean H₂ diffusion rate over the overturn time, as defined by Equation (41). (d) Corresponding temporal evolution of the amounts of H₂ (green) and H₂O (blue) in the boundary layer. The dashed line represents the cumulative H₂ inflow into the boundary layer.