On the stability of the first solid skin at the surface of a magma ocean: stable on early Venus, breaking on early Earth ?

The physical processes involved in the transition of a planet  from a liquid magma ocean (‘MO’) to a convective solid mantle are still debated. Highly turbulent penetrative convection prevails when the MO is still liquid on the surface. But as the MO cools down in interaction with its atmosphere, its upper surface thermal boundary layer (‘TBL’) will eventually first becomes partially molten, then solid. As soon as the rheological front, with a melt content less than 40%, reaches the surface, the upper part of the TBL could behave like a solid skin. This has led to suggest that MO cooling would always end up in a stagnant lid regime of convection, whereby mantle convection proceeds under a surface plate that remains stagnant, limiting the heat and volatile transfers to the atmosphere. This would help retaining water within the mantle, but would render the onset of subduction and plate tectonics more difficult (how to break a thick lid?). On the other hand, another family of cooling MO models suggests that the numerous impacts during the early stages of a planet would break repeatedly any floating skin on the MO, so that it would be difficult to establish a stagnant lid regime. 

Laboratory experiments of penetrative convection-evaporation using visco-elasto-plastic colloidal dispersions (Di Giuseppe et al, 2012) suggest that two other phenomena could also be at play to destabilize the first solid skin: (1) melt flowing through a porous skin would generate in-plane compression that could generate buckling, exceed the yield strength of the material and initiate subduction; (2) rapid thermal contraction due to large temperature gradients across the skin could generate stresses large enough to exceed the yield strength and initiate subduction. 

We use these insights to explore the growth and stability of the TBL at the surface of a cooling magma ocean which interacts with a H₂O-CO₂ atmosphere. Our results indicate that, while on Earth, thermal stresses due to cooling could easily exceed the early lithosphere yield strength, this might not have been the case on Venus. On Venus, this process is strongly influenced by atmospheric conditions. For a high albedo of 0.5, the upper TBL could yield as early as 1.5 million years after cooling begins, similar to Earth, and therefore the MO stage would end up directly into a convective regime with repeated breaking and foundering of the lithosphere (e.g. subduction). But for an albedo of 0.2, thermal stresses never overcome the TBL’s yield strength. In such a scenario, the MO stage would end in a stagnant lid regime, which could act as a barrier to heat transfer and potentially filter degassing.