A Semianalytical, Three Dimensional Model of Microstructure in Multiparticle, Multiphase Flow

This dissertation presents a three dimensional microgeodynamic model of grain-melt geometry in partially molten rocks. The isotropic unit cell of the partially molten rock is characterized by a face-centered-cubic symmetry, consisting of rhombic dodecahedral grains. The variation of surface tension between grain-grain and grain-melt contacts excites a coupled viscous flow within grains and the interstitial melt leading to a steady-state grain-melt geometry. The fractional area of intergranular contact, contiguity, is obtained from these models as a function of melt volume fraction, for melt fractions between 0.05 and 0.25. Comparison with previous results indicates that the contiguity in three dimensional models is lower than two dimensional models. We apply our model to the UltraLow Velocity Zones (ULVZ) in the Earth's core-mantle boundary. The observed seismic signature of the ULVZ can be explained by a melt volume fraction between 0.08 and 0.12