A theoretical/computational framework to measure SiO2 and MgO viscosity at high pressure
The convection of the mantle of Earth and super-Earths is important for many terrestrial phenomena, from plate tectonics to outgassing. Rheological properties, such as viscosity, regulate the transport of thermal energy and mass. However, the viscosity of mantle-relevant materials, such as MgO, at relevant pressures (>120 GPa) are not well constrained. The objective of this work was to develop a computational platform to simulate novel experiments aiming to measure the viscosity of MgO at high pressures. Experiments performed by our collaborators at Johns Hopkins University and Lawrence Livermore National Laboratory use the OMEGA EP laser facility to shock a corrugated MgO interface to 170 GPa, with resulting velocity evolution governed by the viscous Richtmyer-Meshkov instability. We used an in-house hydrocode to simulate this process and thus provide a bound on viscosity by comparing our simulations results to these experiments, as well as to examine the physical processes at play. We simulated the experiments with different values of MgO viscosity (from inviscid to 10,000 Pa∙s) while taking into account the unsteady laser pulse, the material's equation of state, and the rate-dependent constitutive relation for MgO, and the materials' equations of state. Our results suggest that MgO at these conditions has a viscosity within an order of magnitude of 5000 Pa∙s.