Hydrodynamic Instabilities in Condensed Matter at High Pressures

Abstract

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 has not been well constrained. The goal of this dissertation is to study hydrodynamic instabilities in condensed matter at high pressures and leverage this understanding to provide a means to measure viscosity at high pressures (100s GPa). Interfacial hydrodynamic instabilities have been widely studied in classical fluid dynamics. Such instabilities occur when perturbations along a material interface are subjected to various processes, including accelerations. The Richtmyer-Meshkov (RM) instability specifically arises when the acceleration is caused by a shock wave. This thesis primarily focuses on the RM instability in condensed matter, which includes solids and liquids subjected to high pressures (i.e., one million pascals or greater). Unlike in gases and plasmas, the behavior of the RM instability in condensed matter is highly dependent on viscosity, given the relatively low Reynolds number. As a result, the evolution of the perturbations in such a regime is quite different from that in gases. We are motivated by recent experiments that use hydrodynamic instabilities to infer material properties, such as viscosity, under conditions relevant to planetary interiors and high-pressure environments. There lacks extensive knowledge on the behavior of the Richtmyer-Meshkov instability in condensed matter. We focus on analytically and numerically studying a shocked epoxy-MgO interface, represented by a stiffened equation of state. This thesis presents a comprehensive study of the behavior of condensed matter at shocked interfaces, focusing on both analytical and computational approaches.

We first develop an analytical method to determine equation of state parameters in shocked condensed matter for a given interface pressure. Next, we explore the Richtmyer-Meshkov instability in condensed matter. The evolution of a single-mode epoxy-MgO interface is simulated for increasing interface pressures ranging from 50 to 400 GPa. The observed behavior includes dynamic growth rate oscillations and deviations from different growth rate magnitude predictions. The effect of viscosity on this behavior is also probed, and found to decrease the growth rate. The behavior observed in this study is intended to inform the design of experiments in this regime.

Finally, we present a numerical investigation of a laser-driven Richtmyer-Meshkov instability accompanying innovative experiments aimed at constraining MgO viscosity. This work establishes a robust platform that incorporates the dynamic OMEGA-EP laser, the experimentally relevant equations of state for each material, and the constitutive relations of shocked condensed matter. Simulations are performed for a variety of different MgO viscosities in order to constrain the experimental data. The early-time evolution of the simulations, when compared to the experimental data, suggest the viscosity of MgO at these conditions is within an order of magnitude of 5000 Pa°§s. These multi-physics simulations are necessary and critical to constrain the viscosity in this campaign. We further investigate the strain-rate-dependence of viscosity. By accounting for the expected decrease in viscosity at the shock front and rarefaction, better agreement between the simulations and the experimental data is achieved, thus providing a characterization of the rate dependence of viscosity.