Effect of bridgmanite-ferropericlase grain size evolution on Earth’s average mantle viscosity: implications for mantle convection in early and present-day Earth

Recent experimental investigations of grain size evolution in bridgmanite-ferropericlase assemblages have suggested very slow growth for these bimodal phases. Despite numerous speculations on grain size-dependent viscosity, a comprehensive test with realistic grain size evolution parameters compatible with the lower mantle has been lacking. In this study, we develop self-consistent 2-D spherical half-annulus geodynamic models of Earth's evolution using the finite volume code StagYY to assess the role of grain size on lower mantle viscosity. We explore several models with and without grain size evolution to compare their effects on mantle viscosity. In models with grain size evolution, we consider three scenarios: (1) uniform grain growth throughout the entire mantle with a composite rheology, (2) different grain growth in the upper and lower mantle with a composite rheology, and (3) different grain growth in the upper and lower mantle with purely diffusion creep rheology. In the case of different grain size evolution, the upper mantle's grain size evolution law is controlled by forsterite-enstatite grain growth, while the lower mantle's grain size evolution law is controlled by bridgmanite-ferropericlase grain growth. Our results suggest that mantle viscosity is primarily controlled by temperature, whereas grain size has a minor effect compared to the effect of temperature. We attribute two primary reasons for this: First, the bridgmanite-ferropericlase growth is very slow in the lower mantle and the grain size variation is too small to significantly alter the mantle viscosity. Secondly, if grains grow too fast, thus the mantle deforms in the dislocation creep regime, making viscosity grain size-independent. To establish the robustness of this finding we vary several other model parameters, such as surface yield strength, phase transition grain size reset, different transitional stresses for creep mechanisms, pressure dependence on grain growth, and different grain damage parameters. For all our models, we consistently find that grain size has a very limited effect on controlling lower mantle viscosity in the present-day Earth. However, large grain size may have affected the lower mantle viscosity in the early Earth as larger grains of single phase bridgmanite could increase the viscosity of the early mantle delaying the onset of global convection.