Importance of grain size-dependent viscosity for the early and present-day Earth

Grain size is one of the primary influencing factors for mantle viscosity. Larger grains lead to increased diffusion creep viscosity and vice-versa. Grain size is a thermally activated process, so with higher temperature grains grow. Increasing temperature lowers the mantle viscosity but the associated grain size would potentially increase the viscosity.  The net result of this counterbalancing effect of grain size evolution and temperature in the lower mantle remains limited. In this study, we use the self-consistent two-dimensional finite volume StagYY to investigate the evolving grain size and its impact on average mantle viscosity. We compare a model with constant grain size to models with evolving grain size along with dynamic recrystallization and analyze the effect of grain size. Using grain size evolution parameters for olivine in the upper mantle and bridgmanite-ferropericlase in the lower mantle shows comparable results with previous literature. In this model, the upper mantle primarily undergoes deformation through dislocation creep, while the lower mantle is dominated by diffusion creep. Despite this, the average viscosity of the lower mantle calculated using the evolving grain size model does not significantly differ from that of a constant grain size model. This suggests that grain size variations exert a limited impact on the average viscosity of the lower mantle, which is predominantly influenced by temperature. This limitation arises because of the slow grain growth of the bridgmanite-ferropericlase assemblage due to Zenner pinning. Such slow grain growth is insufficient to counteract the temperature-dependent viscosity effects. In the early Earth, the Zenner pinning effect could be absent due to single phase crystallization from the magma ocean. Without a secondary phase, bridgmanite could grow significantly larger grains. To investigate the impact of faster grain growth, we applied olivine grain growth parameters to the lower mantle. This hypothetical scenario resulted in the formation of exceptionally large grains (~10,000 μm) and delayed the onset of lid-breaking events in our models. It is possible that in the early Earth, the lid-breaking event was delayed due to strong grain size dependent viscosity. However, once whole-mantle convection began, increased lower mantle stress promoted dislocation creep in the presence of these large grains. In such cases, the lower mantle becomes largely independent of grain size, particularly in the present-day Earth scenario.